Pub Date : 2023-10-11DOI: 10.1080/10485252.2023.2266740
Mohammad Mohammadi, Meng Li
AbstractWe propose a novel approach for model-free time series forecasting. Unlike most existing methods, the proposed method does not rely on parametric error distributions nor assume parametric forms of the mean function, leading to broad applicability. We achieve such generality by establishing a simple but powerful representation of a time series {Xt;t∈Z} with suptE|Xt|<∞, that is, Xt has a solution which is a linear combination of infinite past values. Then using the obtained solution a prediction algorithm is presented, with large sample theoretical guarantees. Simulation studies show favourable performance of the proposed method compared with popular parametric and neural networks methods, and suggest its superiority when the sample size is small. An application to practical time series is discussed.Keywords: Predictionnonparametric methodsneural networksα-stable distributionMSC2010 subject classifications:: Primary: 60G25Secondary: 62M20 Disclosure statementNo potential conflict of interest was reported by the author(s).Notes1 See https://www.sciencedirect.com/topics/engineering/left-inverse.
{"title":"Model-free prediction of time series: a nonparametric approach","authors":"Mohammad Mohammadi, Meng Li","doi":"10.1080/10485252.2023.2266740","DOIUrl":"https://doi.org/10.1080/10485252.2023.2266740","url":null,"abstract":"AbstractWe propose a novel approach for model-free time series forecasting. Unlike most existing methods, the proposed method does not rely on parametric error distributions nor assume parametric forms of the mean function, leading to broad applicability. We achieve such generality by establishing a simple but powerful representation of a time series {Xt;t∈Z} with suptE|Xt|<∞, that is, Xt has a solution which is a linear combination of infinite past values. Then using the obtained solution a prediction algorithm is presented, with large sample theoretical guarantees. Simulation studies show favourable performance of the proposed method compared with popular parametric and neural networks methods, and suggest its superiority when the sample size is small. An application to practical time series is discussed.Keywords: Predictionnonparametric methodsneural networksα-stable distributionMSC2010 subject classifications:: Primary: 60G25Secondary: 62M20 Disclosure statementNo potential conflict of interest was reported by the author(s).Notes1 See https://www.sciencedirect.com/topics/engineering/left-inverse.","PeriodicalId":50112,"journal":{"name":"Journal of Nonparametric Statistics","volume":"107 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":"136097527","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-19DOI: 10.1080/10485252.2023.2258999
Haiyan Liu, Jeanine Houwing-Duistermaat
In many studies on disease progression, biomarkers are restricted by detection limits, hence informatively missing. Current approaches ignore the problem by just filling in the value of the detection limit for the missing observations for the estimation of the mean and covariance function, which yield inaccurate estimation. Inspired by our recent work [Liu and Houwing-Duistermaat (2022), ‘Fast Estimators for the Mean Function for Functional Data with Detection Limits’, Stat, e467.] in which novel estimators for mean function for data subject to detection limit are proposed, in this paper, we will propose a novel estimator for the covariance function for sparse and dense data subject to a detection limit. We will derive the asymptotic properties of the estimator. We will compare our method to the standard method, which ignores the detection limit, via simulations. We will illustrate the new approach by analysing biomarker data subject to a detection limit. In contrast to the standard method, our method appeared to provide more accurate estimates of the covariance. Moreover its computation time is small.
{"title":"On estimation of covariance function for functional data with detection limits","authors":"Haiyan Liu, Jeanine Houwing-Duistermaat","doi":"10.1080/10485252.2023.2258999","DOIUrl":"https://doi.org/10.1080/10485252.2023.2258999","url":null,"abstract":"In many studies on disease progression, biomarkers are restricted by detection limits, hence informatively missing. Current approaches ignore the problem by just filling in the value of the detection limit for the missing observations for the estimation of the mean and covariance function, which yield inaccurate estimation. Inspired by our recent work [Liu and Houwing-Duistermaat (2022), ‘Fast Estimators for the Mean Function for Functional Data with Detection Limits’, Stat, e467.] in which novel estimators for mean function for data subject to detection limit are proposed, in this paper, we will propose a novel estimator for the covariance function for sparse and dense data subject to a detection limit. We will derive the asymptotic properties of the estimator. We will compare our method to the standard method, which ignores the detection limit, via simulations. We will illustrate the new approach by analysing biomarker data subject to a detection limit. In contrast to the standard method, our method appeared to provide more accurate estimates of the covariance. Moreover its computation time is small.","PeriodicalId":50112,"journal":{"name":"Journal of Nonparametric Statistics","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135106403","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-19DOI: 10.1080/10485252.2023.2259011
Stephan Clémençon, Pierre Laforgue, Robin Vogel
AbstractIn practice, and especially when training deep neural networks, visual recognition rules are often learned based on various sources of information. On the other hand, the recent deployment of facial recognition systems with uneven performances on different population segments has highlighted the representativeness issues induced by a naive aggregation of the datasets. In this paper, we show how biasing models can remedy these problems. Based on the (approximate) knowledge of the biasing mechanisms at work, our approach consists in reweighting the observations, so as to form a nearly debiased estimator of the target distribution. One key condition is that the supports of the biased distributions must partly overlap, and cover the support of the target distribution. In order to meet this requirement in practice, we propose to use a low dimensional image representation, shared across the image databases. Finally, we provide numerical experiments highlighting the relevance of our approach.Keywords: Sampling biasselection effectvisual recognitionreliable statistical learning Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThis work was partially supported by the research chair ‘Good In Tech : Rethinking innovation and technology as drivers of a better world for and by humans’, under the auspices of the ‘Fondation du Risque’ and in partnership with the Institut Mines-Télécom, Sciences Po, Afnor, Ag2r La Mondiale, CGI France, Danone and Sycomore.
在实践中，特别是在训练深度神经网络时，视觉识别规则通常是基于各种信息来源学习的。另一方面，最近部署的面部识别系统在不同人群中表现不均匀，突出了数据集幼稚聚合引起的代表性问题。在本文中，我们展示了偏置模型如何解决这些问题。基于对工作中的偏倚机制的(近似)了解，我们的方法包括重新加权观测值，从而形成目标分布的近去偏估计量。一个关键条件是有偏分布的支持必须部分重叠，并覆盖目标分布的支持。为了在实践中满足这一要求，我们建议使用低维图像表示，在图像数据库中共享。最后，我们提供了数值实验，突出了我们方法的相关性。关键词:抽样偏倚选择效应视觉识别可靠统计学习披露声明作者未报告潜在的利益冲突。这项工作得到了“科技的好处:重新思考创新和技术作为人类和人类更美好世界的驱动力”研究主席的部分支持，该研究主席由“Risque基金会”主持，并与矿业研究所、巴黎政治学院、Afnor、Ag2r La Mondiale、CGI法国、达能和Sycomore合作。
{"title":"Fighting selection bias in statistical learning: application to visual recognition from biased image databases","authors":"Stephan Clémençon, Pierre Laforgue, Robin Vogel","doi":"10.1080/10485252.2023.2259011","DOIUrl":"https://doi.org/10.1080/10485252.2023.2259011","url":null,"abstract":"AbstractIn practice, and especially when training deep neural networks, visual recognition rules are often learned based on various sources of information. On the other hand, the recent deployment of facial recognition systems with uneven performances on different population segments has highlighted the representativeness issues induced by a naive aggregation of the datasets. In this paper, we show how biasing models can remedy these problems. Based on the (approximate) knowledge of the biasing mechanisms at work, our approach consists in reweighting the observations, so as to form a nearly debiased estimator of the target distribution. One key condition is that the supports of the biased distributions must partly overlap, and cover the support of the target distribution. In order to meet this requirement in practice, we propose to use a low dimensional image representation, shared across the image databases. Finally, we provide numerical experiments highlighting the relevance of our approach.Keywords: Sampling biasselection effectvisual recognitionreliable statistical learning Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThis work was partially supported by the research chair ‘Good In Tech : Rethinking innovation and technology as drivers of a better world for and by humans’, under the auspices of the ‘Fondation du Risque’ and in partnership with the Institut Mines-Télécom, Sciences Po, Afnor, Ag2r La Mondiale, CGI France, Danone and Sycomore.","PeriodicalId":50112,"journal":{"name":"Journal of Nonparametric Statistics","volume":"181 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135106810","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper provides a necessary and sufficient condition for asymptotic efficiency of a nonparametric estimator of the generalised autocovariance function of a stationary random process. The generalised autocovariance function is the inverse Fourier transform of a power transformation of the spectral density and encompasses the traditional and inverse autocovariance functions as particular cases. A nonparametric estimator is based on the inverse discrete Fourier transform of the power transformation of the pooled periodogram. We consider two cases: the fixed bandwidth design and the adaptive bandwidth design. The general result on the asymptotic efficiency, established for linear processes, is then applied to the class of stationary ARMA processes and its implications are discussed. Finally, we illustrate that for a class of contrast functionals and spectral densities, the minimum contrast estimator of the spectral density satisfies a Yule–Walker system of equations in the generalised autocovariance estimator.
{"title":"Efficient nonparametric estimation of generalised autocovariances","authors":"Alessandra Luati, Francesca Papagni, Tommaso Proietti","doi":"10.1080/10485252.2023.2252527","DOIUrl":"https://doi.org/10.1080/10485252.2023.2252527","url":null,"abstract":"This paper provides a necessary and sufficient condition for asymptotic efficiency of a nonparametric estimator of the generalised autocovariance function of a stationary random process. The generalised autocovariance function is the inverse Fourier transform of a power transformation of the spectral density and encompasses the traditional and inverse autocovariance functions as particular cases. A nonparametric estimator is based on the inverse discrete Fourier transform of the power transformation of the pooled periodogram. We consider two cases: the fixed bandwidth design and the adaptive bandwidth design. The general result on the asymptotic efficiency, established for linear processes, is then applied to the class of stationary ARMA processes and its implications are discussed. Finally, we illustrate that for a class of contrast functionals and spectral densities, the minimum contrast estimator of the spectral density satisfies a Yule–Walker system of equations in the generalised autocovariance estimator.","PeriodicalId":50112,"journal":{"name":"Journal of Nonparametric Statistics","volume":"63 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134950151","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-02DOI: 10.1080/10485252.2023.2241572
N. Bayarassou, F. Hamrani, E. Ould Saïd
{"title":"Nonparametric relative error estimation of the regression function for left truncated and right censored time series data","authors":"N. Bayarassou, F. Hamrani, E. Ould Saïd","doi":"10.1080/10485252.2023.2241572","DOIUrl":"https://doi.org/10.1080/10485252.2023.2241572","url":null,"abstract":"","PeriodicalId":50112,"journal":{"name":"Journal of Nonparametric Statistics","volume":"30 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76728038","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-25DOI: 10.1080/10485252.2023.2250011
J. Racine, Qi Li, Qiaoyu Wang
{"title":"Boundary-adaptive kernel density estimation: the case of (near) uniform density","authors":"J. Racine, Qi Li, Qiaoyu Wang","doi":"10.1080/10485252.2023.2250011","DOIUrl":"https://doi.org/10.1080/10485252.2023.2250011","url":null,"abstract":"","PeriodicalId":50112,"journal":{"name":"Journal of Nonparametric Statistics","volume":"110 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73284507","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
MODEL CHECKS FOR TWO-SAMPLE LOCATION-SCALE by Atefeh Javidialsaadi Two-sample location-scale refers to a model that permits a pair of standardized random variables to have a common distribution. This means that if X1 and X2 are two random variables with means μ1 and μ2 and standard deviations σ1 and σ2, then (X1−μ1)/σ1 and (X2−μ2)/σ2 have some common unspecified standard or base distribution F0. Function-based hypothesis testing for these models refers to formal tests that would help determine whether or not two samples may have come from some location-scale family of distributions, without specifying the standard distribution F0. For uncensored data, Hall et al. (2013) proposed a test based on empirical characteristic functions (ECFs), but it can not be directly applied for censored data. Empirical likelihood with minimum distance (MD) plug-ins provides an alternative to the approach based on ECFs (Subramanian, 2020). However, when working with standardized data, it appeared feasible to set up plug-in empirical likelihood (PEL) with estimated means and standard deviations as plug-ins, which avoids MD estimation of location and scale parameters and (hence) quantile estimation. This project addresses two issues: (i) Set up a PEL founded testing procedure that uses sample means and standard deviations as the plug-ins for uncensored case, and Kaplan–Meier integral based estimators as plug-ins for censored case, (ii) Extend the ECF test to accommodate censoring. Large sample null distributions of the proposed test statistics are derived. Numerical studies are carried out to investigate the performance of the proposed methods. Real examples are also presented for both the uncensored and censored cases. MODEL CHECKS FOR TWO-SAMPLE LOCATION-SCALE by Atefeh Javidialsaadi A Dissertation Submitted to the Faculty of New Jersey Institute of Technology and Rutgers, The State University of New Jersey – Newark in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Mathematical Sciences Department of Mathematical Sciences Department of Mathematics and Computer Science, Rutgers-Newark
{"title":"Model checks for two-sample location-scale","authors":"Atefeh Javidialsaadi, Shoubhik Mondal, Sundarraman Subramanian","doi":"10.1080/10485252.2023.2243350","DOIUrl":"https://doi.org/10.1080/10485252.2023.2243350","url":null,"abstract":"MODEL CHECKS FOR TWO-SAMPLE LOCATION-SCALE by Atefeh Javidialsaadi Two-sample location-scale refers to a model that permits a pair of standardized random variables to have a common distribution. This means that if X1 and X2 are two random variables with means μ1 and μ2 and standard deviations σ1 and σ2, then (X1−μ1)/σ1 and (X2−μ2)/σ2 have some common unspecified standard or base distribution F0. Function-based hypothesis testing for these models refers to formal tests that would help determine whether or not two samples may have come from some location-scale family of distributions, without specifying the standard distribution F0. For uncensored data, Hall et al. (2013) proposed a test based on empirical characteristic functions (ECFs), but it can not be directly applied for censored data. Empirical likelihood with minimum distance (MD) plug-ins provides an alternative to the approach based on ECFs (Subramanian, 2020). However, when working with standardized data, it appeared feasible to set up plug-in empirical likelihood (PEL) with estimated means and standard deviations as plug-ins, which avoids MD estimation of location and scale parameters and (hence) quantile estimation. This project addresses two issues: (i) Set up a PEL founded testing procedure that uses sample means and standard deviations as the plug-ins for uncensored case, and Kaplan–Meier integral based estimators as plug-ins for censored case, (ii) Extend the ECF test to accommodate censoring. Large sample null distributions of the proposed test statistics are derived. Numerical studies are carried out to investigate the performance of the proposed methods. Real examples are also presented for both the uncensored and censored cases. MODEL CHECKS FOR TWO-SAMPLE LOCATION-SCALE by Atefeh Javidialsaadi A Dissertation Submitted to the Faculty of New Jersey Institute of Technology and Rutgers, The State University of New Jersey – Newark in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Mathematical Sciences Department of Mathematical Sciences Department of Mathematics and Computer Science, Rutgers-Newark","PeriodicalId":50112,"journal":{"name":"Journal of Nonparametric Statistics","volume":"33 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80291186","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-24DOI: 10.1080/10485252.2023.2238841
Hong-Fan Zhang
{"title":"A varying coefficient model with matrix valued covariates","authors":"Hong-Fan Zhang","doi":"10.1080/10485252.2023.2238841","DOIUrl":"https://doi.org/10.1080/10485252.2023.2238841","url":null,"abstract":"","PeriodicalId":50112,"journal":{"name":"Journal of Nonparametric Statistics","volume":"5 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74329515","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-16DOI: 10.1080/10485252.2023.2233642
Amel Azzi, Abderrahmane Belguerna, Ali Laksaci, Mustapha Rachdi
{"title":"The scalar-on-function modal regression for functional time series data","authors":"Amel Azzi, Abderrahmane Belguerna, Ali Laksaci, Mustapha Rachdi","doi":"10.1080/10485252.2023.2233642","DOIUrl":"https://doi.org/10.1080/10485252.2023.2233642","url":null,"abstract":"","PeriodicalId":50112,"journal":{"name":"Journal of Nonparametric Statistics","volume":"34 4 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87668719","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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