In population-based cancer survival analysis, the net survival is important for government to assess health care programs. For decades, it is observed that the net survival reaches a plateau after long-term follow-up, this is so called ``statistical cure''. Several methods were proposed to address the statistical cure. Besides, the cure time can be used to evaluate the time period of a health care program for a specific patient population, and it also can be helpful for a clinician to explain the prognosis for patients, therefore the cure time is an important health care index. However, those proposed methods assume the cure time to be infinity, thus it is inconvenient to make inference on the cure time. In this dissertation, we define a more general concept of statistical cure via conditional survival. Based on the newly defined statistical cure, the cure time is well defined. We develop cure time model methodologies and show a variety of properties through simulation. In data analysis, cure times are estimated for 22 major cancers in Taiwan, we further use colorectal cancer data as an example to conduct statistical inference via cure time model with covariate sex, age group, and stage. This dissertation provides a methodology to obtain cure time estimate, which can contribute to public health policy making.
{"title":"Statistical Inference on the Cure Time","authors":"Yueh Wang, Hung Hung","doi":"10.6342/NTU201904221","DOIUrl":"https://doi.org/10.6342/NTU201904221","url":null,"abstract":"In population-based cancer survival analysis, the net survival is important for government to assess health care programs. For decades, it is observed that the net survival reaches a plateau after long-term follow-up, this is so called ``statistical cure''. Several methods were proposed to address the statistical cure. Besides, the cure time can be used to evaluate the time period of a health care program for a specific patient population, and it also can be helpful for a clinician to explain the prognosis for patients, therefore the cure time is an important health care index. However, those proposed methods assume the cure time to be infinity, thus it is inconvenient to make inference on the cure time. In this dissertation, we define a more general concept of statistical cure via conditional survival. Based on the newly defined statistical cure, the cure time is well defined. We develop cure time model methodologies and show a variety of properties through simulation. In data analysis, cure times are estimated for 22 major cancers in Taiwan, we further use colorectal cancer data as an example to conduct statistical inference via cure time model with covariate sex, age group, and stage. This dissertation provides a methodology to obtain cure time estimate, which can contribute to public health policy making.","PeriodicalId":186390,"journal":{"name":"arXiv: Methodology","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134620431","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}
We propose a novel generalisation to the Student-t Probabilistic Principal Component methodology which: (1) accounts for an asymmetric distribution of the observation data; (2) is a framework for grouped and generalised multiple-degree-of-freedom structures, which provides a more flexible approach to modelling groups of marginal tail dependence in the observation data; and (3) separates the tail effect of the error terms and factors. The new feature extraction methods are derived in an incomplete data setting to efficiently handle the presence of missing values in the observation vector. We discuss various special cases of the algorithm being a result of simplified assumptions on the process generating the data. The applicability of the new framework is illustrated on a data set that consists of crypto currencies with the highest market capitalisation.
{"title":"Parsimonious Feature Extraction Methods: Extending Robust Probabilistic Projections with Generalized Skew-t","authors":"Dorota Toczydlowska, G. Peters, P. Shevchenko","doi":"10.2139/ssrn.3678383","DOIUrl":"https://doi.org/10.2139/ssrn.3678383","url":null,"abstract":"We propose a novel generalisation to the Student-t Probabilistic Principal Component methodology which: (1) accounts for an asymmetric distribution of the observation data; (2) is a framework for grouped and generalised multiple-degree-of-freedom structures, which provides a more flexible approach to modelling groups of marginal tail dependence in the observation data; and (3) separates the tail effect of the error terms and factors. The new feature extraction methods are derived in an incomplete data setting to efficiently handle the presence of missing values in the observation vector. We discuss various special cases of the algorithm being a result of simplified assumptions on the process generating the data. The applicability of the new framework is illustrated on a data set that consists of crypto currencies with the highest market capitalisation.","PeriodicalId":186390,"journal":{"name":"arXiv: Methodology","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128654223","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 : 2020-09-23DOI: 10.1101/2020.09.21.20198762
E. T. Tchetgen, Andrew Ying, Yifan Cui, Xu Shi, Wang Miao
A standard assumption for causal inference from observational data is that one has measured a sufficiently rich set of covariates to ensure that within covariate strata, subjects are exchangeable across observed treatment values. Skepticism about the exchangeability assumption in observational studies is often warranted because it hinges on investigators' ability to accurately measure covariates capturing all potential sources of confounding. Realistically, confounding mechanisms can rarely if ever, be learned with certainty from measured covariates. One can therefore only ever hope that covariate measurements are at best proxies of true underlying confounding mechanisms operating in an observational study, thus invalidating causal claims made on basis of standard exchangeability conditions. Causal learning from proxies is a challenging inverse problem which has to date remained unresolved. In this paper, we introduce a formal potential outcome framework for proximal causal learning, which while explicitly acknowledging covariate measurements as imperfect proxies of confounding mechanisms, offers an opportunity to learn about causal effects in settings where exchangeability on the basis of measured covariates fails. Sufficient conditions for nonparametric identification are given, leading to the proximal g-formula and corresponding proximal g-computation algorithm for estimation. These may be viewed as generalizations of Robins' foundational g-formula and g-computation algorithm, which account explicitly for bias due to unmeasured confounding. Both point treatment and time-varying treatment settings are considered, and an application of proximal g-computation of causal effects is given for illustration.
{"title":"An Introduction to Proximal Causal Learning","authors":"E. T. Tchetgen, Andrew Ying, Yifan Cui, Xu Shi, Wang Miao","doi":"10.1101/2020.09.21.20198762","DOIUrl":"https://doi.org/10.1101/2020.09.21.20198762","url":null,"abstract":"A standard assumption for causal inference from observational data is that one has measured a sufficiently rich set of covariates to ensure that within covariate strata, subjects are exchangeable across observed treatment values. Skepticism about the exchangeability assumption in observational studies is often warranted because it hinges on investigators' ability to accurately measure covariates capturing all potential sources of confounding. Realistically, confounding mechanisms can rarely if ever, be learned with certainty from measured covariates. One can therefore only ever hope that covariate measurements are at best proxies of true underlying confounding mechanisms operating in an observational study, thus invalidating causal claims made on basis of standard exchangeability conditions. Causal learning from proxies is a challenging inverse problem which has to date remained unresolved. In this paper, we introduce a formal potential outcome framework for proximal causal learning, which while explicitly acknowledging covariate measurements as imperfect proxies of confounding mechanisms, offers an opportunity to learn about causal effects in settings where exchangeability on the basis of measured covariates fails. Sufficient conditions for nonparametric identification are given, leading to the proximal g-formula and corresponding proximal g-computation algorithm for estimation. These may be viewed as generalizations of Robins' foundational g-formula and g-computation algorithm, which account explicitly for bias due to unmeasured confounding. Both point treatment and time-varying treatment settings are considered, and an application of proximal g-computation of causal effects is given for illustration.","PeriodicalId":186390,"journal":{"name":"arXiv: Methodology","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123629812","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}
We consider a binary response which is potentially affected by a set of continuous variables. Of special interest is the causal effect on the response due to an intervention on a specific variable. The latter can be meaningfully determined on the basis of observational data through suitable assumptions on the data generating mechanism. In particular we assume that the joint distribution obeys the conditional independencies (Markov properties) inherent in a Directed Acyclic Graph (DAG), and the DAG is given a causal interpretation through the notion of interventional distribution. We propose a DAG-probit model where the response is generated by discretization through a random threshold of a continuous latent variable and the latter, jointly with the remaining continuous variables, has a distribution belonging to a zero-mean Gaussian model whose covariance matrix is constrained to satisfy the Markov properties of the DAG. Our model leads to a natural definition of causal effect conditionally on a given DAG. Since the DAG which generates the observations is unknown, we present an efficient MCMC algorithm whose target is the posterior distribution on the space of DAGs, the Cholesky parameters of the concentration matrix, and the threshold linking the response to the latent. Our end result is a Bayesian Model Averaging estimate of the causal effect which incorporates parameter, as well as model, uncertainty. The methodology is assessed using simulation experiments and applied to a gene expression data set originating from breast cancer stem cells.
{"title":"Bayesian Causal Inference in Probit Graphical Models","authors":"F. Castelletti, G. Consonni","doi":"10.1214/21-BA1260","DOIUrl":"https://doi.org/10.1214/21-BA1260","url":null,"abstract":"We consider a binary response which is potentially affected by a set of continuous variables. Of special interest is the causal effect on the response due to an intervention on a specific variable. The latter can be meaningfully determined on the basis of observational data through suitable assumptions on the data generating mechanism. In particular we assume that the joint distribution obeys the conditional independencies (Markov properties) inherent in a Directed Acyclic Graph (DAG), and the DAG is given a causal interpretation through the notion of interventional distribution. We propose a DAG-probit model where the response is generated by discretization through a random threshold of a continuous latent variable and the latter, jointly with the remaining continuous variables, has a distribution belonging to a zero-mean Gaussian model whose covariance matrix is constrained to satisfy the Markov properties of the DAG. Our model leads to a natural definition of causal effect conditionally on a given DAG. Since the DAG which generates the observations is unknown, we present an efficient MCMC algorithm whose target is the posterior distribution on the space of DAGs, the Cholesky parameters of the concentration matrix, and the threshold linking the response to the latent. Our end result is a Bayesian Model Averaging estimate of the causal effect which incorporates parameter, as well as model, uncertainty. The methodology is assessed using simulation experiments and applied to a gene expression data set originating from breast cancer stem cells.","PeriodicalId":186390,"journal":{"name":"arXiv: Methodology","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121625492","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}
S. Tamang, A. Ebtehaj, P. V. van Leeuwen, Dongmian Zou, Gilad Lerman
Abstract. In this paper, we present an ensemble data assimilation paradigm over a Riemannian manifold equipped with the Wasserstein metric. Unlike the Eulerian penalization of error in the Euclidean space, the Wasserstein metric can capture translation and difference between the shapes of square-integrable probability distributions of the background state and observations – enabling to formally penalize geophysical biases in state-space with non-Gaussian distributions. The new approach is applied to dissipative and chaotic evolutionary dynamics and its potential advantages and limitations are highlighted compared to the classic variational and filtering data assimilation approaches under systematic and random errors.
{"title":"Ensemble Riemannian Data Assimilation over the Wasserstein\u0000Space","authors":"S. Tamang, A. Ebtehaj, P. V. van Leeuwen, Dongmian Zou, Gilad Lerman","doi":"10.5194/NPG-2021-11","DOIUrl":"https://doi.org/10.5194/NPG-2021-11","url":null,"abstract":"Abstract. In this paper, we present an ensemble data assimilation paradigm over a Riemannian manifold equipped with the Wasserstein metric. Unlike the Eulerian penalization of error in the Euclidean space, the Wasserstein metric can capture translation and difference between the shapes of square-integrable probability distributions of the background state and observations – enabling to formally penalize geophysical biases in state-space with non-Gaussian distributions. The new approach is applied to dissipative and chaotic evolutionary dynamics and its potential advantages and limitations are highlighted compared to the classic variational and filtering data assimilation approaches under systematic and random errors.\u0000","PeriodicalId":186390,"journal":{"name":"arXiv: Methodology","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129540574","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 : 2020-09-01DOI: 10.1002/essoar.10504066.1
S. Khatami, T. Peterson, M. Peel, A. Western
To evaluate models as hypotheses, we developed the method of Flux Mapping to construct a hypothesis space based on dominant runoff generating mechanisms. Acceptable model runs, defined as total simulated flow with similar (and minimal) model error, are mapped to the hypothesis space given their simulated runoff components. In each modeling case, the hypothesis space is the result of an interplay of factors: model structure and parameterization, chosen error metric, and data information content. The aim of this study is to disentangle the role of each factor in model evaluation. We used two model structures (SACRAMENTO and SIMHYD), two parameter sampling approaches (Latin Hypercube Sampling of the parameter space and guided-search of the solution space), three widely used error metrics (Nash-Sutcliffe Efficiency - NSE, Kling-Gupta Efficiency skill score - KGEss, and Willmott refined Index of Agreement - WIA), and hydrological data from a large sample of Australian catchments. First, we characterized how the three error metrics behave under different error types and magnitudes independent of any modeling. We then conducted a series of controlled experiments to unpack the role of each factor in runoff generation hypotheses. We show that KGEss is a more reliable metric compared to NSE and WIA for model evaluation. We further demonstrate that only changing the error metric -- while other factors remain constant -- can change the model solution space and hence vary model performance, parameter sampling sufficiency, and or the flux map. We show how unreliable error metrics and insufficient parameter sampling impair model-based inferences, particularly runoff generation hypotheses.
{"title":"Evaluating Catchment Models as Multiple Working Hypotheses: on the Role of Error Metrics, Parameter Sampling, Model Structure, and Data Information Content","authors":"S. Khatami, T. Peterson, M. Peel, A. Western","doi":"10.1002/essoar.10504066.1","DOIUrl":"https://doi.org/10.1002/essoar.10504066.1","url":null,"abstract":"To evaluate models as hypotheses, we developed the method of Flux Mapping to construct a hypothesis space based on dominant runoff generating mechanisms. Acceptable model runs, defined as total simulated flow with similar (and minimal) model error, are mapped to the hypothesis space given their simulated runoff components. In each modeling case, the hypothesis space is the result of an interplay of factors: model structure and parameterization, chosen error metric, and data information content. The aim of this study is to disentangle the role of each factor in model evaluation. We used two model structures (SACRAMENTO and SIMHYD), two parameter sampling approaches (Latin Hypercube Sampling of the parameter space and guided-search of the solution space), three widely used error metrics (Nash-Sutcliffe Efficiency - NSE, Kling-Gupta Efficiency skill score - KGEss, and Willmott refined Index of Agreement - WIA), and hydrological data from a large sample of Australian catchments. First, we characterized how the three error metrics behave under different error types and magnitudes independent of any modeling. We then conducted a series of controlled experiments to unpack the role of each factor in runoff generation hypotheses. We show that KGEss is a more reliable metric compared to NSE and WIA for model evaluation. We further demonstrate that only changing the error metric -- while other factors remain constant -- can change the model solution space and hence vary model performance, parameter sampling sufficiency, and or the flux map. We show how unreliable error metrics and insufficient parameter sampling impair model-based inferences, particularly runoff generation hypotheses.","PeriodicalId":186390,"journal":{"name":"arXiv: Methodology","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121393771","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 : 2020-08-25DOI: 10.1007/978-3-030-69944-4_12
Eduardo Garc'ia-Portugu'es, Paula Navarro-Esteban, J. A. Cuesta-Albertos
{"title":"A Cramér–von Mises Test of Uniformity on the Hypersphere","authors":"Eduardo Garc'ia-Portugu'es, Paula Navarro-Esteban, J. A. Cuesta-Albertos","doi":"10.1007/978-3-030-69944-4_12","DOIUrl":"https://doi.org/10.1007/978-3-030-69944-4_12","url":null,"abstract":"","PeriodicalId":186390,"journal":{"name":"arXiv: Methodology","volume":"355 14‐15","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"113956083","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}
Experimental designs for a generalized linear model (GLM) often depend on the specification of the model, including the link function, the predictors, and unknown parameters, such as the regression coefficients. To deal with uncertainties of these model specifications, it is important to construct optimal designs with high efficiency under such uncertainties. Existing methods such as Bayesian experimental designs often use prior distributions of model specifications to incorporate model uncertainties into the design criterion. Alternatively, one can obtain the design by optimizing the worst-case design efficiency with respect to uncertainties of model specifications. In this work, we propose a new Maximin $Phi_p$-Efficient (or Mm-$Phi_p$ for short) design which aims at maximizing the minimum $Phi_p$-efficiency under model uncertainties. Based on the theoretical properties of the proposed criterion, we develop an efficient algorithm with sound convergence properties to construct the Mm-$Phi_p$ design. The performance of the proposed Mm-$Phi_p$ design is assessed through several numerical examples.
{"title":"A Maximin $Phi_{p}$-Efficient Design for Multivariate GLM","authors":"Yiou Li, Lulu Kang, Xinwei Deng","doi":"10.5705/ss.202020.0278","DOIUrl":"https://doi.org/10.5705/ss.202020.0278","url":null,"abstract":"Experimental designs for a generalized linear model (GLM) often depend on the specification of the model, including the link function, the predictors, and unknown parameters, such as the regression coefficients. To deal with uncertainties of these model specifications, it is important to construct optimal designs with high efficiency under such uncertainties. Existing methods such as Bayesian experimental designs often use prior distributions of model specifications to incorporate model uncertainties into the design criterion. Alternatively, one can obtain the design by optimizing the worst-case design efficiency with respect to uncertainties of model specifications. In this work, we propose a new Maximin $Phi_p$-Efficient (or Mm-$Phi_p$ for short) design which aims at maximizing the minimum $Phi_p$-efficiency under model uncertainties. Based on the theoretical properties of the proposed criterion, we develop an efficient algorithm with sound convergence properties to construct the Mm-$Phi_p$ design. The performance of the proposed Mm-$Phi_p$ design is assessed through several numerical examples.","PeriodicalId":186390,"journal":{"name":"arXiv: Methodology","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133549712","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}
Factor models are widely used across diverse areas of application for purposes that include dimensionality reduction, covariance estimation, and feature engineering. Traditional factor models can be seen as an instance of linear embedding methods that project multivariate observations onto a lower dimensional Euclidean latent space. This paper discusses a new class of geometric embedding models for multivariate binary data in which the embedding space correspond to a spherical manifold, with potentially unknown dimension. The resulting models include traditional factor models as a special case, but provide additional flexibility. Furthermore, unlike other techniques for geometric embedding, the models are easy to interpret, and the uncertainty associated with the latent features can be properly quantified. These advantages are illustrated using both simulation studies and real data on voting records from the U.S. Senate.
{"title":"A Bayesian Approach to Spherical Factor Analysis for Binary Data","authors":"Xingchen Yu, Abel Rodríguez","doi":"10.2139/ssrn.3672055","DOIUrl":"https://doi.org/10.2139/ssrn.3672055","url":null,"abstract":"Factor models are widely used across diverse areas of application for purposes that include dimensionality reduction, covariance estimation, and feature engineering. Traditional factor models can be seen as an instance of linear embedding methods that project multivariate observations onto a lower dimensional Euclidean latent space. This paper discusses a new class of geometric embedding models for multivariate binary data in which the embedding space correspond to a spherical manifold, with potentially unknown dimension. The resulting models include traditional factor models as a special case, but provide additional flexibility. Furthermore, unlike other techniques for geometric embedding, the models are easy to interpret, and the uncertainty associated with the latent features can be properly quantified. These advantages are illustrated using both simulation studies and real data on voting records from the U.S. Senate.","PeriodicalId":186390,"journal":{"name":"arXiv: Methodology","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128182722","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 : 2020-07-19DOI: 10.1080/01621459.2022.2096619
S. Perreault, J. Nešlehová, T. Duchesne
Joint modeling of a large number of variables often requires dimension reduction strategies that lead to structural assumptions of the underlying correlation matrix, such as equal pair-wise correlations within subsets of variables. The underlying correlation matrix is thus of interest for both model specification and model validation. In this paper, we develop tests of the hypothesis that the entries of the Kendall rank correlation matrix are linear combinations of a smaller number of parameters. The asymptotic behaviour of the proposed test statistics is investigated both when the dimension is fixed and when it grows with the sample size. We pay special attention to the restricted hypothesis of partial exchangeability, which contains full exchangeability as a special case. We show that under partial exchangeability, the test statistics and their large-sample distributions simplify, which leads to computational advantages and better performance of the tests. We propose various scalable numerical strategies for implementation of the proposed procedures, investigate their finite sample behaviour through simulations, and demonstrate their use on a real dataset of mean sea levels at various geographical locations.
{"title":"Hypothesis tests for structured rank correlation matrices","authors":"S. Perreault, J. Nešlehová, T. Duchesne","doi":"10.1080/01621459.2022.2096619","DOIUrl":"https://doi.org/10.1080/01621459.2022.2096619","url":null,"abstract":"Joint modeling of a large number of variables often requires dimension reduction strategies that lead to structural assumptions of the underlying correlation matrix, such as equal pair-wise correlations within subsets of variables. The underlying correlation matrix is thus of interest for both model specification and model validation. In this paper, we develop tests of the hypothesis that the entries of the Kendall rank correlation matrix are linear combinations of a smaller number of parameters. The asymptotic behaviour of the proposed test statistics is investigated both when the dimension is fixed and when it grows with the sample size. We pay special attention to the restricted hypothesis of partial exchangeability, which contains full exchangeability as a special case. We show that under partial exchangeability, the test statistics and their large-sample distributions simplify, which leads to computational advantages and better performance of the tests. We propose various scalable numerical strategies for implementation of the proposed procedures, investigate their finite sample behaviour through simulations, and demonstrate their use on a real dataset of mean sea levels at various geographical locations.","PeriodicalId":186390,"journal":{"name":"arXiv: Methodology","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115813299","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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