Slađana Babić, Laetitia Gelbgras, M. Hallin, Christophe Ley
Although the assumption of elliptical symmetry is quite common in multivariate analysis and widespread in a number of applications, the problem of testing the null hypothesis of ellipticity so far has not been addressed in a fully satisfactory way. Most of the literature in the area indeed addresses the null hypothesis of elliptical symmetry with specified location and actually addresses location rather than non-elliptical alternatives. In thi spaper, we are proposing new classes of testing procedures,both for specified and unspecified location. The backbone of our construction is Le Cam’s asymptotic theory of statistical experiments, and optimality is to be understood locally and asymptotically within the family of generalized skew-elliptical distributions. The tests we are proposing are meeting all the desired properties of a “good” test of elliptical symmetry:they have a simple asymptotic distribution under the entire null hypothesis of elliptical symmetry with unspecified radial density and shape parameter; they are affine-invariant, computationally fast, intuitively understandable, and not too demanding in terms of moments. While achieving optimality against generalized skew-elliptical alternatives, they remain quite powerful under a much broader class of non-elliptical distributions and significantly outperform the available competitors
{"title":"Optimal tests for elliptical symmetry: specified and unspecified location","authors":"Slađana Babić, Laetitia Gelbgras, M. Hallin, Christophe Ley","doi":"10.3150/20-BEJ1305","DOIUrl":"https://doi.org/10.3150/20-BEJ1305","url":null,"abstract":"Although the assumption of elliptical symmetry is quite common in multivariate analysis and widespread in a number of applications, the problem of testing the null hypothesis of ellipticity so far has not been addressed in a fully satisfactory way. Most of the literature in the area indeed addresses the null hypothesis of elliptical symmetry with specified location and actually addresses location rather than non-elliptical alternatives. In thi spaper, we are proposing new classes of testing procedures,both for specified and unspecified location. The backbone of our construction is Le Cam’s asymptotic theory of statistical experiments, and optimality is to be understood locally and asymptotically within the family of generalized skew-elliptical distributions. The tests we are proposing are meeting all the desired properties of a “good” test of elliptical symmetry:they have a simple asymptotic distribution under the entire null hypothesis of elliptical symmetry with unspecified radial density and shape parameter; they are affine-invariant, computationally fast, intuitively understandable, and not too demanding in terms of moments. While achieving optimality against generalized skew-elliptical alternatives, they remain quite powerful under a much broader class of non-elliptical distributions and significantly outperform the available competitors","PeriodicalId":186390,"journal":{"name":"arXiv: Methodology","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115518222","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Data consisting of samples of probability density functions are increasingly prevalent, necessitating the development of methodologies for their analysis that respect the inherent nonlinearities associated with densities. In many applications, density curves appear as functional response objects in a regression model with vector predictors. For such models, inference is key to understand the importance of density-predictor relationships, and the uncertainty associated with the estimated conditional mean densities, defined as conditional Frechet means under a suitable metric. Using the Wasserstein geometry of optimal transport, we consider the Frechet regression of density curve responses and develop tests for global and partial effects, as well as simultaneous confidence bands for estimated conditional mean densities. The asymptotic behavior of these objects is based on underlying functional central limit theorems within Wasserstein space, and we demonstrate that they are asymptotically of the correct size and coverage, with uniformly strong consistency of the proposed tests under sequences of contiguous alternatives. The accuracy of these methods, including nominal size, power, and coverage, is assessed through simulations, and their utility is illustrated through a regression analysis of post-intracerebral hemorrhage hematoma densities and their associations with a set of clinical and radiological covariates.
{"title":"Wasserstein $F$-tests and confidence bands for the Fréchet regression of density response curves","authors":"Alexander Petersen, Xi Liu, A. Divani","doi":"10.1214/20-AOS1971","DOIUrl":"https://doi.org/10.1214/20-AOS1971","url":null,"abstract":"Data consisting of samples of probability density functions are increasingly prevalent, necessitating the development of methodologies for their analysis that respect the inherent nonlinearities associated with densities. In many applications, density curves appear as functional response objects in a regression model with vector predictors. For such models, inference is key to understand the importance of density-predictor relationships, and the uncertainty associated with the estimated conditional mean densities, defined as conditional Frechet means under a suitable metric. Using the Wasserstein geometry of optimal transport, we consider the Frechet regression of density curve responses and develop tests for global and partial effects, as well as simultaneous confidence bands for estimated conditional mean densities. The asymptotic behavior of these objects is based on underlying functional central limit theorems within Wasserstein space, and we demonstrate that they are asymptotically of the correct size and coverage, with uniformly strong consistency of the proposed tests under sequences of contiguous alternatives. The accuracy of these methods, including nominal size, power, and coverage, is assessed through simulations, and their utility is illustrated through a regression analysis of post-intracerebral hemorrhage hematoma densities and their associations with a set of clinical and radiological covariates.","PeriodicalId":186390,"journal":{"name":"arXiv: Methodology","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127802104","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-10-16DOI: 10.23668/PSYCHARCHIVES.2623
E. V. Kesteren, D. Oberski
Structural equation modeling (SEM) is a popular tool in the social and behavioural sciences, where it is being applied to ever more complex data types. The high-dimensional data produced by modern sensors, brain images, or (epi)genetic measurements require variable selection using parameter penalization; experimental models combining disparate data sources benefit from regularization to obtain a stable result; and genomic SEM or network models lead to alternative objective functions. With each proposed extension, researchers currently have to completely reformulate SEM and its optimization algorithm -- a challenging and time-consuming task. In this paper, we consider each SEM as a computation graph, a flexible method of specifying objective functions borrowed from the field of deep learning. When combined with state-of-the-art optimizers, our computation graph approach can extend SEM without the need for bespoke software development. We show that both existing and novel SEM improvements follow naturally from our approach. To demonstrate, we discuss least absolute deviation estimation and penalized regression models. We also introduce spike-and-slab SEM, which may perform better when shrinkage of large factor loadings is not desired. By applying computation graphs to SEM, we hope to greatly accelerate the process of developing SEM techniques, paving the way for new applications. We provide an accompanying R package tensorsem.
{"title":"Structural Equation Models as Computation Graphs","authors":"E. V. Kesteren, D. Oberski","doi":"10.23668/PSYCHARCHIVES.2623","DOIUrl":"https://doi.org/10.23668/PSYCHARCHIVES.2623","url":null,"abstract":"Structural equation modeling (SEM) is a popular tool in the social and behavioural sciences, where it is being applied to ever more complex data types. The high-dimensional data produced by modern sensors, brain images, or (epi)genetic measurements require variable selection using parameter penalization; experimental models combining disparate data sources benefit from regularization to obtain a stable result; and genomic SEM or network models lead to alternative objective functions. With each proposed extension, researchers currently have to completely reformulate SEM and its optimization algorithm -- a challenging and time-consuming task. In this paper, we consider each SEM as a computation graph, a flexible method of specifying objective functions borrowed from the field of deep learning. When combined with state-of-the-art optimizers, our computation graph approach can extend SEM without the need for bespoke software development. We show that both existing and novel SEM improvements follow naturally from our approach. To demonstrate, we discuss least absolute deviation estimation and penalized regression models. We also introduce spike-and-slab SEM, which may perform better when shrinkage of large factor loadings is not desired. By applying computation graphs to SEM, we hope to greatly accelerate the process of developing SEM techniques, paving the way for new applications. We provide an accompanying R package tensorsem.","PeriodicalId":186390,"journal":{"name":"arXiv: Methodology","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125262448","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Boyan Duan, Aaditya Ramdas, Sivaraman Balakrishnan, L. Wasserman
Global null testing is a classical problem going back about a century to Fisher's and Stouffer's combination tests. In this work, we present simple martingale analogs of these classical tests, which are applicable in two distinct settings: (a) the online setting in which there is a possibly infinite sequence of $p$-values, and (b) the batch setting, where one uses prior knowledge to preorder the hypotheses. Through theory and simulations, we demonstrate that our martingale variants have higher power than their classical counterparts even when the preordering is only weakly informative. Finally, using a recent idea of "masking" $p$-values, we develop a novel interactive test for the global null that can take advantage of covariates and repeated user guidance to create a data-adaptive ordering that achieves higher detection power against structured alternatives.
{"title":"Interactive martingale tests for the global null","authors":"Boyan Duan, Aaditya Ramdas, Sivaraman Balakrishnan, L. Wasserman","doi":"10.1214/20-ejs1790","DOIUrl":"https://doi.org/10.1214/20-ejs1790","url":null,"abstract":"Global null testing is a classical problem going back about a century to Fisher's and Stouffer's combination tests. In this work, we present simple martingale analogs of these classical tests, which are applicable in two distinct settings: (a) the online setting in which there is a possibly infinite sequence of $p$-values, and (b) the batch setting, where one uses prior knowledge to preorder the hypotheses. Through theory and simulations, we demonstrate that our martingale variants have higher power than their classical counterparts even when the preordering is only weakly informative. Finally, using a recent idea of \"masking\" $p$-values, we develop a novel interactive test for the global null that can take advantage of covariates and repeated user guidance to create a data-adaptive ordering that achieves higher detection power against structured alternatives.","PeriodicalId":186390,"journal":{"name":"arXiv: Methodology","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121558758","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The current standard Bayesian approach to model calibration, which assigns a Gaussian process prior to the discrepancy term, often suffers from issues of unidentifiability and computational complexity and instability. When the goal is to quantify uncertainty in physical parameters for extrapolative prediction, then there is no need to perform inference on the discrepancy term. With this in mind, we introduce Gibbs posteriors as an alternative Bayesian method for model calibration, which updates the prior with a loss function connecting the data to the parameter. The target of inference is the physical parameter value which minimizes the expected loss. We propose to tune the loss scale of the Gibbs posterior to maintain nominal frequentist coverage under assumptions of the form of model discrepancy, and present a bootstrap implementation for approximating coverage rates. Our approach is highly modular, allowing an analyst to easily encode a wide variety of such assumptions. Furthermore, we provide a principled method of combining posteriors calculated from data subsets. We apply our methods to data from an experiment measuring the material properties of tantalum.
{"title":"Bayesian Model Calibration for Extrapolative Prediction via Gibbs Posteriors.","authors":"S. Woody, N. Ghaffari, L. Hund","doi":"10.2172/1763261","DOIUrl":"https://doi.org/10.2172/1763261","url":null,"abstract":"The current standard Bayesian approach to model calibration, which assigns a Gaussian process prior to the discrepancy term, often suffers from issues of unidentifiability and computational complexity and instability. When the goal is to quantify uncertainty in physical parameters for extrapolative prediction, then there is no need to perform inference on the discrepancy term. With this in mind, we introduce Gibbs posteriors as an alternative Bayesian method for model calibration, which updates the prior with a loss function connecting the data to the parameter. The target of inference is the physical parameter value which minimizes the expected loss. We propose to tune the loss scale of the Gibbs posterior to maintain nominal frequentist coverage under assumptions of the form of model discrepancy, and present a bootstrap implementation for approximating coverage rates. Our approach is highly modular, allowing an analyst to easily encode a wide variety of such assumptions. Furthermore, we provide a principled method of combining posteriors calculated from data subsets. We apply our methods to data from an experiment measuring the material properties of tantalum.","PeriodicalId":186390,"journal":{"name":"arXiv: Methodology","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130064484","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Keefe Murphy, Brendan Murphy, R. Piccarreta, I. C. Gormley
Sequence analysis is an increasingly popular approach for analysing life courses represented by ordered collections of activities experienced by subjects over time. Here, we analyse a survey data set containing information on the career trajectories of a cohort of Northern Irish youths tracked between the ages of 16 and 22. We propose a novel, model-based clustering approach suited to the analysis of such data from a holistic perspective, with the aims of estimating the number of typical career trajectories, identifying the relevant features of these patterns, and assessing the extent to which such patterns are shaped by background characteristics.Several criteria exist for measuring pairwise dissimilarities among categorical sequences. Typically, dissimilarity matrices are employed as input to heuristic clustering algorithms. The family of methods we develop instead clusters sequences directly using mixtures of exponential-distance models. Basing the models on weighted variants of the Hamming distance metric permits closed-form expressions for parameter estimation. Simultaneously allowing the component membership probabilities to depend on fixed covariates and accommodating sampling weights in the clustering process yields new insights on the Northern Irish data. In particular, we find that school examination performance is the single most important predictor of cluster membership.
{"title":"Clustering Longitudinal Life-Course Sequences Using Mixtures of Exponential-Distance Models","authors":"Keefe Murphy, Brendan Murphy, R. Piccarreta, I. C. Gormley","doi":"10.31235/osf.io/f5n8k","DOIUrl":"https://doi.org/10.31235/osf.io/f5n8k","url":null,"abstract":"Sequence analysis is an increasingly popular approach for analysing life courses represented by ordered collections of activities experienced by subjects over time. Here, we analyse a survey data set containing information on the career trajectories of a cohort of Northern Irish youths tracked between the ages of 16 and 22. We propose a novel, model-based clustering approach suited to the analysis of such data from a holistic perspective, with the aims of estimating the number of typical career trajectories, identifying the relevant features of these patterns, and assessing the extent to which such patterns are shaped by background characteristics.Several criteria exist for measuring pairwise dissimilarities among categorical sequences. Typically, dissimilarity matrices are employed as input to heuristic clustering algorithms. The family of methods we develop instead clusters sequences directly using mixtures of exponential-distance models. Basing the models on weighted variants of the Hamming distance metric permits closed-form expressions for parameter estimation. Simultaneously allowing the component membership probabilities to depend on fixed covariates and accommodating sampling weights in the clustering process yields new insights on the Northern Irish data. In particular, we find that school examination performance is the single most important predictor of cluster membership.","PeriodicalId":186390,"journal":{"name":"arXiv: Methodology","volume":"105 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132776684","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
During the past few decades, missing-data problems have been studied extensively, with a focus on the ignorable missing case, where the missing probability depends only on observable quantities. By contrast, research into non-ignorable missing data problems is quite limited. The main difficulty in solving such problems is that the missing probability and the regression likelihood function are tangled together in the likelihood presentation, and the model parameters may not be identifiable even under strong parametric model assumptions. In this paper we discuss a semiparametric model for non-ignorable missing data and propose a maximum full semiparametric likelihood estimation method, which is an efficient combination of the parametric conditional likelihood and the marginal nonparametric biased sampling likelihood. The extra marginal likelihood contribution can not only produce efficiency gain but also identify the underlying model parameters without additional assumptions. We further show that the proposed estimators for the underlying parameters and the response mean are semiparametrically efficient. Extensive simulations and a real data analysis demonstrate the advantage of the proposed method over competing methods.
{"title":"Full-semiparametric-likelihood-based inference for non-ignorable missing data","authors":"Yukun Liu, Pengfei Li, J. Qin","doi":"10.5705/ss.202019.0243","DOIUrl":"https://doi.org/10.5705/ss.202019.0243","url":null,"abstract":"During the past few decades, missing-data problems have been studied extensively, with a focus on the ignorable missing case, where the missing probability depends only on observable quantities. By contrast, research into non-ignorable missing data problems is quite limited. The main difficulty in solving such problems is that the missing probability and the regression likelihood function are tangled together in the likelihood presentation, and the model parameters may not be identifiable even under strong parametric model assumptions. In this paper we discuss a semiparametric model for non-ignorable missing data and propose a maximum full semiparametric likelihood estimation method, which is an efficient combination of the parametric conditional likelihood and the marginal nonparametric biased sampling likelihood. The extra marginal likelihood contribution can not only produce efficiency gain but also identify the underlying model parameters without additional assumptions. We further show that the proposed estimators for the underlying parameters and the response mean are semiparametrically efficient. Extensive simulations and a real data analysis demonstrate the advantage of the proposed method over competing methods.","PeriodicalId":186390,"journal":{"name":"arXiv: Methodology","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121283531","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Confounding by unmeasured spatial variables has received some attention in the spatial statistics and causal inference literatures, but concepts and approaches have remained largely separated. In this paper, we aim to bridge these distinct strands of statistics by considering unmeasured spatial confounding within a causal inference framework, and estimating effects using outcome regression tools popular within the spatial literature. First, we show how using spatially correlated random effects in the outcome model, an approach common among spatial statisticians, does not necessarily mitigate bias due to spatial confounding, a previously published but not universally known result. Motivated by the bias term of commonly-used estimators, we propose an affine estimator which addresses this deficiency. We discuss how unbiased estimation of causal parameters in the presence of unmeasured spatial confounding can only be achieved under an untestable set of assumptions which will often be application-specific. We provide a set of assumptions which describe how the exposure and outcome of interest relate to the unmeasured variables, and which is sufficient for identification of the causal effect based on the observed data. We examine identifiability issues through the lens of restricted maximum likelihood estimation in linear models, and implement our method using a fully Bayesian approach applicable to any type of outcome variable. This work is motivated by and used to estimate the effect of county-level limited access to supermarkets on the rate of cardiovascular disease deaths in the elderly across the whole continental United States. Even though standard approaches return null or protective effects, our approach uncovers evidence of unobserved spatial confounding, and indicates that limited supermarket access has a harmful effect on cardiovascular mortality.
{"title":"Mitigating unobserved spatial confounding when estimating the effect of supermarket access on cardiovascular disease deaths","authors":"P. Schnell, Georgia Papadogeorgou","doi":"10.1214/20-aoas1377","DOIUrl":"https://doi.org/10.1214/20-aoas1377","url":null,"abstract":"Confounding by unmeasured spatial variables has received some attention in the spatial statistics and causal inference literatures, but concepts and approaches have remained largely separated. In this paper, we aim to bridge these distinct strands of statistics by considering unmeasured spatial confounding within a causal inference framework, and estimating effects using outcome regression tools popular within the spatial literature. First, we show how using spatially correlated random effects in the outcome model, an approach common among spatial statisticians, does not necessarily mitigate bias due to spatial confounding, a previously published but not universally known result. Motivated by the bias term of commonly-used estimators, we propose an affine estimator which addresses this deficiency. We discuss how unbiased estimation of causal parameters in the presence of unmeasured spatial confounding can only be achieved under an untestable set of assumptions which will often be application-specific. We provide a set of assumptions which describe how the exposure and outcome of interest relate to the unmeasured variables, and which is sufficient for identification of the causal effect based on the observed data. We examine identifiability issues through the lens of restricted maximum likelihood estimation in linear models, and implement our method using a fully Bayesian approach applicable to any type of outcome variable. This work is motivated by and used to estimate the effect of county-level limited access to supermarkets on the rate of cardiovascular disease deaths in the elderly across the whole continental United States. Even though standard approaches return null or protective effects, our approach uncovers evidence of unobserved spatial confounding, and indicates that limited supermarket access has a harmful effect on cardiovascular mortality.","PeriodicalId":186390,"journal":{"name":"arXiv: Methodology","volume":"146 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123049858","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-07-19DOI: 10.13140/RG.2.2.29926.37440
Chen Gong, D. Stoffer
The stochastic volatility model is a popular tool for modeling the volatility of assets. The model is a nonlinear and non-Gaussian state space model, and consequently is difficult to fit. Many approaches, both classical and Bayesian, have been developed that rely on numerically intensive techniques such as quasi-maximum likelihood estimation and Markov chain Monte Carlo (MCMC). Convergence and mixing problems still plague MCMC algorithms when drawing samples sequentially from the posterior distributions. While particle Gibbs methods have been successful when applied to nonlinear or non-Gaussian state space models in general, slow convergence still haunts the technique when applied specifically to stochastic volatility models. We present an approach that couples particle Gibbs with ancestral sampling and joint parameter sampling that ameliorates the slow convergence and mixing problems when fitting both univariate and multivariate stochastic volatility models. We demonstrate the enhanced method on various numerical examples.
{"title":"An Approach to Efficient Fitting of Univariate and Multivariate Stochastic Volatility Models","authors":"Chen Gong, D. Stoffer","doi":"10.13140/RG.2.2.29926.37440","DOIUrl":"https://doi.org/10.13140/RG.2.2.29926.37440","url":null,"abstract":"The stochastic volatility model is a popular tool for modeling the volatility of assets. The model is a nonlinear and non-Gaussian state space model, and consequently is difficult to fit. Many approaches, both classical and Bayesian, have been developed that rely on numerically intensive techniques such as quasi-maximum likelihood estimation and Markov chain Monte Carlo (MCMC). Convergence and mixing problems still plague MCMC algorithms when drawing samples sequentially from the posterior distributions. While particle Gibbs methods have been successful when applied to nonlinear or non-Gaussian state space models in general, slow convergence still haunts the technique when applied specifically to stochastic volatility models. We present an approach that couples particle Gibbs with ancestral sampling and joint parameter sampling that ameliorates the slow convergence and mixing problems when fitting both univariate and multivariate stochastic volatility models. We demonstrate the enhanced method on various numerical examples.","PeriodicalId":186390,"journal":{"name":"arXiv: Methodology","volume":"104 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133657659","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Randomness is one of the important key concepts of statistics. In epidemiology or medical science, we investigate our hypotheses and interpret results through this statistical randomness. We hypothesized by imposing some conditions to this randomness, interpretation of our result may be changed. In this article, we introduced the restricted re-sampling method to confirm inter-generational relations and presented an example.
{"title":"Random family method: Confirming inter-generational relations by restricted re-sampling","authors":"T. Usuzaki, M. Chiba, S. Hotta","doi":"10.31219/osf.io/h5fqn","DOIUrl":"https://doi.org/10.31219/osf.io/h5fqn","url":null,"abstract":"Randomness is one of the important key concepts of statistics. In epidemiology or medical science, we investigate our hypotheses and interpret results through this statistical randomness. We hypothesized by imposing some conditions to this randomness, interpretation of our result may be changed. In this article, we introduced the restricted re-sampling method to confirm inter-generational relations and presented an example.","PeriodicalId":186390,"journal":{"name":"arXiv: Methodology","volume":"201 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121000523","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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