Abstract Mediation analysis aims to assess if, and how, a certain exposure influences an outcome of interest through intermediate variables. This problem has recently gained a surge of attention due to the tremendous need for such analyses in scientific fields. Testing for the mediation effect (ME) is greatly challenged by the fact that the underlying null hypothesis (i.e. the absence of MEs) is composite. Most existing mediation tests are overly conservative and thus underpowered. To overcome this significant methodological hurdle, we develop an adaptive bootstrap testing framework that can accommodate different types of composite null hypotheses in the mediation pathway analysis. Applied to the product of coefficients test and the joint significance test, our adaptive testing procedures provide type I error control under the composite null, resulting in much improved statistical power compared to existing tests. Both theoretical properties and numerical examples of the proposed methodology are discussed.
{"title":"Adaptive bootstrap tests for composite null hypotheses in the mediation pathway analysis","authors":"Yinqiu He, Peter X K Song, Gongjun Xu","doi":"10.1093/jrsssb/qkad129","DOIUrl":"https://doi.org/10.1093/jrsssb/qkad129","url":null,"abstract":"Abstract Mediation analysis aims to assess if, and how, a certain exposure influences an outcome of interest through intermediate variables. This problem has recently gained a surge of attention due to the tremendous need for such analyses in scientific fields. Testing for the mediation effect (ME) is greatly challenged by the fact that the underlying null hypothesis (i.e. the absence of MEs) is composite. Most existing mediation tests are overly conservative and thus underpowered. To overcome this significant methodological hurdle, we develop an adaptive bootstrap testing framework that can accommodate different types of composite null hypotheses in the mediation pathway analysis. Applied to the product of coefficients test and the joint significance test, our adaptive testing procedures provide type I error control under the composite null, resulting in much improved statistical power compared to existing tests. Both theoretical properties and numerical examples of the proposed methodology are discussed.","PeriodicalId":49982,"journal":{"name":"Journal of the Royal Statistical Society Series B-Statistical Methodology","volume":"2 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134957034","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Space-filling designs are widely used in computer experiments. A minimum aberration-type space-filling criterion was recently proposed to rank and assess a family of space-filling designs including orthogonal array-based Latin hypercubes and strong orthogonal arrays. However, it is difficult to apply the criterion in practice because it requires intensive computation for determining the space-filling pattern, which measures the stratification properties of designs on various subregions. In this article, we propose a stratification pattern enumerator to characterise the stratification properties. The enumerator is easy to compute and can efficiently rank space-filling designs. We show that the stratification pattern enumerator is a linear combination of the space-filling pattern. Based on the connection, we develop efficient algorithms for calculating the space-filling pattern. In addition, we establish a lower bound for the stratification pattern enumerator and present construction methods for designs that achieve the lower bound using multiplication tables over Galois fields. The constructed designs have good space-filling properties in low-dimensional projections and are robust under various criteria.
{"title":"Stratification pattern enumerator and its applications","authors":"Ye Tian, Hongquan Xu","doi":"10.1093/jrsssb/qkad125","DOIUrl":"https://doi.org/10.1093/jrsssb/qkad125","url":null,"abstract":"Abstract Space-filling designs are widely used in computer experiments. A minimum aberration-type space-filling criterion was recently proposed to rank and assess a family of space-filling designs including orthogonal array-based Latin hypercubes and strong orthogonal arrays. However, it is difficult to apply the criterion in practice because it requires intensive computation for determining the space-filling pattern, which measures the stratification properties of designs on various subregions. In this article, we propose a stratification pattern enumerator to characterise the stratification properties. The enumerator is easy to compute and can efficiently rank space-filling designs. We show that the stratification pattern enumerator is a linear combination of the space-filling pattern. Based on the connection, we develop efficient algorithms for calculating the space-filling pattern. In addition, we establish a lower bound for the stratification pattern enumerator and present construction methods for designs that achieve the lower bound using multiplication tables over Galois fields. The constructed designs have good space-filling properties in low-dimensional projections and are robust under various criteria.","PeriodicalId":49982,"journal":{"name":"Journal of the Royal Statistical Society Series B-Statistical Methodology","volume":"116 18","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134957609","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Proposer of the vote of thanks to Waudby-Smith and Ramdas and contribution to the Discussion of “Estimating the means of bounded random variables by betting”","authors":"Peter Gürnwald","doi":"10.1093/jrsssb/qkad128","DOIUrl":"https://doi.org/10.1093/jrsssb/qkad128","url":null,"abstract":"","PeriodicalId":49982,"journal":{"name":"Journal of the Royal Statistical Society Series B-Statistical Methodology","volume":" 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135291847","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Motivated by evaluating the effects of air pollution alerts on air quality, we propose the dynamic synthetic control method for micro-level data with time-varying confounders and spatial dependence under an auto-regressive model setting. We employ the empirical likelihood to define the synthetic control weights, which ensures a unique solution and permits theoretical analysis. The dynamic matching increases the feasibility of matching and enables us to assess the unconfoundedness assumption using pre-treatment data. For statistical inference, we develop a normalised placebo test to address the asymmetry issue. The method is illustrated and evaluated on numerical simulations and a case study on air pollution alerts.
{"title":"Dynamic synthetic control method for evaluating treatment effects in auto-regressive processes","authors":"Xiangyu Zheng, Song Xi Chen","doi":"10.1093/jrsssb/qkad103","DOIUrl":"https://doi.org/10.1093/jrsssb/qkad103","url":null,"abstract":"Abstract Motivated by evaluating the effects of air pollution alerts on air quality, we propose the dynamic synthetic control method for micro-level data with time-varying confounders and spatial dependence under an auto-regressive model setting. We employ the empirical likelihood to define the synthetic control weights, which ensures a unique solution and permits theoretical analysis. The dynamic matching increases the feasibility of matching and enables us to assess the unconfoundedness assumption using pre-treatment data. For statistical inference, we develop a normalised placebo test to address the asymmetry issue. The method is illustrated and evaluated on numerical simulations and a case study on air pollution alerts.","PeriodicalId":49982,"journal":{"name":"Journal of the Royal Statistical Society Series B-Statistical Methodology","volume":"11 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136234037","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Decision-guided perspectives on model uncertainty expand traditional statistical thinking about managing, comparing, and combining inferences from sets of models. Bayesian predictive decision synthesis (BPDS) advances conceptual and theoretical foundations, and defines new methodology that explicitly integrates decision-analytic outcomes into the evaluation, comparison, and potential combination of candidate models. BPDS extends recent theoretical and practical advances based on both Bayesian predictive synthesis and empirical goal-focused model uncertainty analysis. This is enabled by the development of a novel subjective Bayesian perspective on model weighting in predictive decision settings. Illustrations come from applied contexts including optimal design for regression prediction and sequential time series forecasting for financial portfolio decisions.
{"title":"Bayesian predictive decision synthesis","authors":"Emily Tallman, Mike West","doi":"10.1093/jrsssb/qkad109","DOIUrl":"https://doi.org/10.1093/jrsssb/qkad109","url":null,"abstract":"Abstract Decision-guided perspectives on model uncertainty expand traditional statistical thinking about managing, comparing, and combining inferences from sets of models. Bayesian predictive decision synthesis (BPDS) advances conceptual and theoretical foundations, and defines new methodology that explicitly integrates decision-analytic outcomes into the evaluation, comparison, and potential combination of candidate models. BPDS extends recent theoretical and practical advances based on both Bayesian predictive synthesis and empirical goal-focused model uncertainty analysis. This is enabled by the development of a novel subjective Bayesian perspective on model weighting in predictive decision settings. Illustrations come from applied contexts including optimal design for regression prediction and sequential time series forecasting for financial portfolio decisions.","PeriodicalId":49982,"journal":{"name":"Journal of the Royal Statistical Society Series B-Statistical Methodology","volume":"95 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135219925","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The bandwidth-free tests for a multi-dimensional parameter have attracted considerable attention in econometrics and statistics literature. These tests can be conveniently implemented due to their tuning-parameter free nature and possess more accurate size as compared to the traditional heteroskedasticity and autocorrelation consistent-based approaches. However, when sample size is small/medium, these bandwidth-free tests exhibit large size distortion when both the dimension of the parameter and the magnitude of temporal dependence are moderate, making them unreliable to use in practice. In this paper, we propose a sample splitting-based approach to reduce the dimension of the parameter to one for the subsequent bandwidth-free inference. Our SS–SN (sample splitting plus self-normalisation) idea is broadly applicable to many testing problems for time series, including mean testing, testing for zero autocorrelation, and testing for a change point in multivariate mean, among others. Specifically, we propose two types of SS–SN test statistics and derive their limiting distributions under both the null and alternatives and show their effectiveness in alleviating size distortion via simulations. In addition, we obtain the limiting distributions for both SS–SN test statistics in the multivariate mean testing problem when the dimension is allowed to diverge.
{"title":"Another look at bandwidth-free inference: a sample splitting approach","authors":"Yi Zhang, Xiaofeng Shao","doi":"10.1093/jrsssb/qkad108","DOIUrl":"https://doi.org/10.1093/jrsssb/qkad108","url":null,"abstract":"Abstract The bandwidth-free tests for a multi-dimensional parameter have attracted considerable attention in econometrics and statistics literature. These tests can be conveniently implemented due to their tuning-parameter free nature and possess more accurate size as compared to the traditional heteroskedasticity and autocorrelation consistent-based approaches. However, when sample size is small/medium, these bandwidth-free tests exhibit large size distortion when both the dimension of the parameter and the magnitude of temporal dependence are moderate, making them unreliable to use in practice. In this paper, we propose a sample splitting-based approach to reduce the dimension of the parameter to one for the subsequent bandwidth-free inference. Our SS–SN (sample splitting plus self-normalisation) idea is broadly applicable to many testing problems for time series, including mean testing, testing for zero autocorrelation, and testing for a change point in multivariate mean, among others. Specifically, we propose two types of SS–SN test statistics and derive their limiting distributions under both the null and alternatives and show their effectiveness in alleviating size distortion via simulations. In addition, we obtain the limiting distributions for both SS–SN test statistics in the multivariate mean testing problem when the dimension is allowed to diverge.","PeriodicalId":49982,"journal":{"name":"Journal of the Royal Statistical Society Series B-Statistical Methodology","volume":"5 7","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135567546","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Authors’ reply to the Discussion of “Estimating means of bounded random variables by betting” by Ian Waudby-Smith and Aaditya Ramdas","authors":"Ian Waudby-Smith, Aaditya Ramdas","doi":"10.1093/jrsssb/qkad127","DOIUrl":"https://doi.org/10.1093/jrsssb/qkad127","url":null,"abstract":"","PeriodicalId":49982,"journal":{"name":"Journal of the Royal Statistical Society Series B-Statistical Methodology","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135730157","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
I congratulate the authors on some very interesting work making connections between likelihood, betting and martingales. What caught my eye was the connection to the empirical likelihood (EL) (Owen, 2001) and the dual likelihood (Mykland, 1995). The hindsight optimal λ solves 0 = (cid:80) ti =1 ( x i − m ) / (1+ λ T ( x i − m )) = 0 corresponding to the observation weights w i ∝ 1 / (1 + λ T ( x i − m )) used in empirical likelihood. Two common alternatives use weights w i ∝ (cid:0) 1 − λ T ( x i − m ) (cid:1) and w i ∝ exp( − λ T ( x i − m )) arising from L 2 and entropy criteria, respectively (for different vectors λ ). The entropy weights connect to exponential tilting and logistic regression; see for instance Hainmueller (2012). The EL weights perform a kind of reciprocal tilting that gives them some special power properties. Kitamura (2003) shows that empirical likelihood tests cannot be dominated by other regular tests for moment restrictions, in a large deviations sense. His result is a nonparametric counterpart to the likelihood test optimality result of Hoeffding (1965) for multinomial distributions. Lazar and Mykland (1998) find that for true parametric models, empirical likelihood matches their power to second order and at third order either the empirical or the parametric tests could have greater power. In some overspecified moment models, empirical likelihood has such high power for detecting lack of fit that, under lack of fit, there cannot exist any pseudo-true value of the parameter for which the maximum EL estimate is root-n consistent (Schennach, 2007). We can now add that authors’ hindsight optimality to this list of power properties.
{"title":"Art Owen's contribution to the Discussion of “Estimating means of bounded random variables by betting” by Ian Waudby-Smith and Aaditya Ramdas","authors":"Art B Owen","doi":"10.1093/jrsssb/qkad116","DOIUrl":"https://doi.org/10.1093/jrsssb/qkad116","url":null,"abstract":"I congratulate the authors on some very interesting work making connections between likelihood, betting and martingales. What caught my eye was the connection to the empirical likelihood (EL) (Owen, 2001) and the dual likelihood (Mykland, 1995). The hindsight optimal λ solves 0 = (cid:80) ti =1 ( x i − m ) / (1+ λ T ( x i − m )) = 0 corresponding to the observation weights w i ∝ 1 / (1 + λ T ( x i − m )) used in empirical likelihood. Two common alternatives use weights w i ∝ (cid:0) 1 − λ T ( x i − m ) (cid:1) and w i ∝ exp( − λ T ( x i − m )) arising from L 2 and entropy criteria, respectively (for different vectors λ ). The entropy weights connect to exponential tilting and logistic regression; see for instance Hainmueller (2012). The EL weights perform a kind of reciprocal tilting that gives them some special power properties. Kitamura (2003) shows that empirical likelihood tests cannot be dominated by other regular tests for moment restrictions, in a large deviations sense. His result is a nonparametric counterpart to the likelihood test optimality result of Hoeffding (1965) for multinomial distributions. Lazar and Mykland (1998) find that for true parametric models, empirical likelihood matches their power to second order and at third order either the empirical or the parametric tests could have greater power. In some overspecified moment models, empirical likelihood has such high power for detecting lack of fit that, under lack of fit, there cannot exist any pseudo-true value of the parameter for which the maximum EL estimate is root-n consistent (Schennach, 2007). We can now add that authors’ hindsight optimality to this list of power properties.","PeriodicalId":49982,"journal":{"name":"Journal of the Royal Statistical Society Series B-Statistical Methodology","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136079630","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"David Siegmund's contribution to the Discussion of “Estimating the means of bounded random variables by betting” by Ian Waudby-Smith and Aaditya Ramdas","authors":"David Siegmund","doi":"10.1093/jrsssb/qkad117","DOIUrl":"https://doi.org/10.1093/jrsssb/qkad117","url":null,"abstract":"","PeriodicalId":49982,"journal":{"name":"Journal of the Royal Statistical Society Series B-Statistical Methodology","volume":"73 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135853317","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Davison and Rodionov's contribution to the discussion of “Estimating means of bounded random variables by betting” by Ian Waudby-Smith and Aaditya Ramdas","authors":"Anthony C Davison, Igor Rodionov","doi":"10.1093/jrsssb/qkad118","DOIUrl":"https://doi.org/10.1093/jrsssb/qkad118","url":null,"abstract":"","PeriodicalId":49982,"journal":{"name":"Journal of the Royal Statistical Society Series B-Statistical Methodology","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136063697","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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