We propose a projection correlation for measure of dependence between numerical multivariate variables and categorical variables. The projection correlation, defined as the maximum of the Gini correlations (i.e., MaGiC) between the categorical variable and the univariate projections of the multivariate vector, is non-parametric, and intuitively produces a high coefficient when the two variables are dependent, and zero when they are independent. We show that MaGiC possesses the property of nestedness, in that it is non-decreasing with the increasing number of features in the numerical vector, while remaining unchanged if additional numerical features are independent of the categorical variable and original features. We establish -consistency of the sample projection correlation. A powerful -sample test can be carried out via the MaGiC-based independence test. When compared with related correlation definitions for multivariate variables, MaGiC also enjoys a faster implementation, with the computational complexity where is the dimension of the numerical variable, is the sample size, and is the number of projections performed, as opposed to for Gini correlation. We demonstrate these properties through simulation and application to real datasets.
{"title":"Maximum Projection Gini Correlation (MaGiC) for mixed categorical and numerical data","authors":"Hong Xiao , Radhakrishna Adhikari , Yixin Chen , Xin Dang","doi":"10.1016/j.jspi.2025.106294","DOIUrl":"10.1016/j.jspi.2025.106294","url":null,"abstract":"<div><div>We propose a projection correlation for measure of dependence between numerical multivariate variables and categorical variables. The projection correlation, defined as the maximum of the Gini correlations (i.e., MaGiC) between the categorical variable and the univariate projections of the multivariate vector, is non-parametric, and intuitively produces a high coefficient when the two variables are dependent, and zero when they are independent. We show that MaGiC possesses the property of nestedness, in that it is non-decreasing with the increasing number of features in the numerical vector, while remaining unchanged if additional numerical features are independent of the categorical variable and original features. We establish <span><math><msqrt><mrow><mi>n</mi></mrow></msqrt></math></span>-consistency of the sample projection correlation. A powerful <span><math><mi>K</mi></math></span>-sample test can be carried out via the MaGiC-based independence test. When compared with related correlation definitions for multivariate variables, MaGiC also enjoys a faster implementation, with the computational complexity <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mi>m</mi><mi>n</mi><mrow><mo>(</mo><mi>d</mi><mo>+</mo><mo>log</mo><mi>n</mi><mo>)</mo></mrow><mo>)</mo></mrow></mrow></math></span> where <span><math><mi>d</mi></math></span> is the dimension of the numerical variable, <span><math><mi>n</mi></math></span> is the sample size, and <span><math><mi>m</mi></math></span> is the number of projections performed, as opposed to <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mi>d</mi><mspace></mspace><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span> for Gini correlation. We demonstrate these properties through simulation and application to real datasets.</div></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"239 ","pages":"Article 106294"},"PeriodicalIF":0.8,"publicationDate":"2025-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143874462","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 : 2025-03-31DOI: 10.1016/j.jspi.2025.106277
Zhihao Hu , Shyam Ranganathan , Yang Shao , Xinwei Deng
Vector autoregression (VAR) models are popular in modeling multivariate time series in data sciences and other areas. When the number of time series is large, the number of parameters in the VAR model increases dramatically, posing great challenges for proper model estimation and inference. In this work, we propose a so-called neighborhood vector autoregression (NVAR) model to efficiently analyze large-dimensional multivariate time series. We assume that the time series have underlying neighborhood relationships, e.g., spatial or network, among them based on the inherent setting of the problem. When this neighborhood information is available or can be summarized using a distance matrix, we demonstrate that our proposed NVAR method provides a computationally efficient and theoretically sound estimation of model parameters. The performance of the proposed method is compared with other existing approaches in both simulation studies and a real-data application in environmental science.
{"title":"Neighborhood VAR: Efficient estimation of multivariate timeseries with neighborhood information","authors":"Zhihao Hu , Shyam Ranganathan , Yang Shao , Xinwei Deng","doi":"10.1016/j.jspi.2025.106277","DOIUrl":"10.1016/j.jspi.2025.106277","url":null,"abstract":"<div><div>Vector autoregression (VAR) models are popular in modeling multivariate time series in data sciences and other areas. When the number of time series is large, the number of parameters in the VAR model increases dramatically, posing great challenges for proper model estimation and inference. In this work, we propose a so-called neighborhood vector autoregression (NVAR) model to efficiently analyze large-dimensional multivariate time series. We assume that the time series have underlying neighborhood relationships, e.g., spatial or network, among them based on the inherent setting of the problem. When this neighborhood information is available or can be summarized using a distance matrix, we demonstrate that our proposed NVAR method provides a computationally efficient and theoretically sound estimation of model parameters. The performance of the proposed method is compared with other existing approaches in both simulation studies and a real-data application in environmental science.</div></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"239 ","pages":"Article 106277"},"PeriodicalIF":0.8,"publicationDate":"2025-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143768174","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-03-26DOI: 10.1016/j.jspi.2025.106292
Hongqi Chen
This paper focuses on developing a robust inference procedure for the linear quantile regression estimator in the context of dyadic data structures. We investigate the asymptotic distribution of the quantile regression estimator under dependency structures arising from shared nodes in both undirected and directed networks. We establish consistency results for the covariance matrix estimator and provide asymptotic distributions for the associated -statistic and Wald statistic, particularly in both univariate and joint hypothesis testing scenarios. To showcase the effectiveness of our proposed method, we present numerical simulations and an empirical application using international trade data. Our results demonstrate the excellent performance of the robust -statistic and Wald statistic in quantile regression inference with dyadic data.
{"title":"Inference on linear quantile regression with dyadic data","authors":"Hongqi Chen","doi":"10.1016/j.jspi.2025.106292","DOIUrl":"10.1016/j.jspi.2025.106292","url":null,"abstract":"<div><div>This paper focuses on developing a robust inference procedure for the linear quantile regression estimator in the context of dyadic data structures. We investigate the asymptotic distribution of the quantile regression estimator under dependency structures arising from shared nodes in both undirected and directed networks. We establish consistency results for the covariance matrix estimator and provide asymptotic distributions for the associated <span><math><mi>t</mi></math></span>-statistic and Wald statistic, particularly in both univariate and joint hypothesis testing scenarios. To showcase the effectiveness of our proposed method, we present numerical simulations and an empirical application using international trade data. Our results demonstrate the excellent performance of the robust <span><math><mi>t</mi></math></span>-statistic and Wald statistic in quantile regression inference with dyadic data.</div></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"239 ","pages":"Article 106292"},"PeriodicalIF":0.8,"publicationDate":"2025-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143734819","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 : 2025-03-19DOI: 10.1016/j.jspi.2025.106291
Michael Kohler , Adam Krzyżak , Benjamin Walter
Image classification based on over-parametrized convolutional neural networks with a global average-pooling layer is considered. The weights of the network are learned by gradient descent. A bound on the rate of convergence of the difference between the misclassification risk of the newly introduced convolutional neural network estimate and the minimal possible value is derived.
{"title":"Analysis of the rate of convergence of an over-parametrized convolutional neural network image classifier learned by gradient descent","authors":"Michael Kohler , Adam Krzyżak , Benjamin Walter","doi":"10.1016/j.jspi.2025.106291","DOIUrl":"10.1016/j.jspi.2025.106291","url":null,"abstract":"<div><div>Image classification based on over-parametrized convolutional neural networks with a global average-pooling layer is considered. The weights of the network are learned by gradient descent. A bound on the rate of convergence of the difference between the misclassification risk of the newly introduced convolutional neural network estimate and the minimal possible value is derived.</div></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"239 ","pages":"Article 106291"},"PeriodicalIF":0.8,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143715034","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-03-13DOI: 10.1016/j.jspi.2025.106290
O.V. Chernoyarov , S. Dachian , Yu.A. Kutoyants
The problem of parameter estimation by i.i.d. observations of an inhomogeneous Poisson process is considered in situation of misspecification. The model is that of a Poissonian signal observed in presence of a homogeneous Poissonian noise. The intensity function of the process is supposed to have a cusp-type singularity at the change-point (the unknown moment of arrival of the signal), while the supposed (theoretical) and the real (observed) levels of the signal are different. The asymptotic properties of the (pseudo) MLE are described. It is shown that the estimator converges to the value minimizing the Kullback–Leibler divergence, that the normalized error of estimation converges to some limit distribution, and that its polynomial moments also converge.
{"title":"On misspecification in cusp-type change-point models","authors":"O.V. Chernoyarov , S. Dachian , Yu.A. Kutoyants","doi":"10.1016/j.jspi.2025.106290","DOIUrl":"10.1016/j.jspi.2025.106290","url":null,"abstract":"<div><div>The problem of parameter estimation by i.i.d. observations of an inhomogeneous Poisson process is considered in situation of misspecification. The model is that of a Poissonian signal observed in presence of a homogeneous Poissonian noise. The intensity function of the process is supposed to have a cusp-type singularity at the change-point (the unknown moment of arrival of the signal), while the supposed (theoretical) and the real (observed) levels of the signal are different. The asymptotic properties of the (pseudo) MLE are described. It is shown that the estimator converges to the value minimizing the Kullback–Leibler divergence, that the normalized error of estimation converges to some limit distribution, and that its polynomial moments also converge.</div></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"239 ","pages":"Article 106290"},"PeriodicalIF":0.8,"publicationDate":"2025-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143637425","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 : 2025-03-11DOI: 10.1016/j.jspi.2025.106289
Hui Ding , Mei Yao , Riquan Zhang , Zhenglong Zhang , Hanbing Zhu
In this paper we propose varying-coefficient single-index quantile regression models, which includes most existing quantile regression models. We adopt B-spline basis approximation for the estimation of nonparametric components and use the “delete-one-component” method to construct check loss function. Under some mild conditions, we establish asymptotic theory of the proposed estimators for both the parametric and nonparametric components. Moreover, we propose a rank score based test to examine whether the varying-coefficient functions are constant. The finite sample performance of the proposed estimation method is illustrated by simulation studies and an empirical analysis of two real datasets.
{"title":"Estimation and testing for varying-coefficient single-index quantile regression models","authors":"Hui Ding , Mei Yao , Riquan Zhang , Zhenglong Zhang , Hanbing Zhu","doi":"10.1016/j.jspi.2025.106289","DOIUrl":"10.1016/j.jspi.2025.106289","url":null,"abstract":"<div><div>In this paper we propose varying-coefficient single-index quantile regression models, which includes most existing quantile regression models. We adopt B-spline basis approximation for the estimation of nonparametric components and use the “delete-one-component” method to construct check loss function. Under some mild conditions, we establish asymptotic theory of the proposed estimators for both the parametric and nonparametric components. Moreover, we propose a rank score based test to examine whether the varying-coefficient functions are constant. The finite sample performance of the proposed estimation method is illustrated by simulation studies and an empirical analysis of two real datasets.</div></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"239 ","pages":"Article 106289"},"PeriodicalIF":0.8,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143629064","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 : 2025-03-04DOI: 10.1016/j.jspi.2025.106286
Gecheng Chen, Rui Tuo
This work focuses on the design of experiments of multi-fidelity computer experiments. We consider the autoregressive Gaussian process model proposed by Kennedy and O’Hagan (2000) and the optimal nested design that maximizes the prediction accuracy subject to a budget constraint. An approximate solution is identified through the idea of multi-level approximation and recent error bounds of Gaussian process regression. The proposed (approximately) optimal designs admit a simple analytical form. We prove that, to achieve the same prediction accuracy, the proposed optimal multi-fidelity design requires much lower computational cost than any single-fidelity design in the asymptotic sense. Numerical studies confirm this theoretical assertion.
{"title":"Fixed-budget optimal designs for multi-fidelity computer experiments","authors":"Gecheng Chen, Rui Tuo","doi":"10.1016/j.jspi.2025.106286","DOIUrl":"10.1016/j.jspi.2025.106286","url":null,"abstract":"<div><div>This work focuses on the design of experiments of multi-fidelity computer experiments. We consider the autoregressive Gaussian process model proposed by Kennedy and O’Hagan (2000) and the optimal nested design that maximizes the prediction accuracy subject to a budget constraint. An approximate solution is identified through the idea of multi-level approximation and recent error bounds of Gaussian process regression. The proposed (approximately) optimal designs admit a simple analytical form. We prove that, to achieve the same prediction accuracy, the proposed optimal multi-fidelity design requires much lower computational cost than any single-fidelity design in the asymptotic sense. Numerical studies confirm this theoretical assertion.</div></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"239 ","pages":"Article 106286"},"PeriodicalIF":0.8,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143579798","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 : 2025-03-01DOI: 10.1016/j.jspi.2025.106278
Tian Jiang
Nonparametric regression with missing at random (MAR) predictors, univariate regression component of interest, and the scale function depending on both the predictor and auxiliary covariates, is considered. The asymptotic theory suggests that both heteroscedasticity and MAR mechanism affect the sharp constant of the minimax mean integrated squared error (MISE) convergence. We propose a data-driven procedure adaptive to the missing mechanism and unknown smoothness of the estimated regression function. The estimator preserves the optimal convergence rate and can achieve sharp minimaxity when predictors are missing completely at random (MCAR).
{"title":"Nonparametric regression with predictors missing at random and the scale depending on auxiliary covariates","authors":"Tian Jiang","doi":"10.1016/j.jspi.2025.106278","DOIUrl":"10.1016/j.jspi.2025.106278","url":null,"abstract":"<div><div>Nonparametric regression with missing at random (MAR) predictors, univariate regression component of interest, and the scale function depending on both the predictor and auxiliary covariates, is considered. The asymptotic theory suggests that both heteroscedasticity and MAR mechanism affect the sharp constant of the minimax mean integrated squared error (MISE) convergence. We propose a data-driven procedure adaptive to the missing mechanism and unknown smoothness of the estimated regression function. The estimator preserves the optimal convergence rate and can achieve sharp minimaxity when predictors are missing completely at random (MCAR).</div></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"239 ","pages":"Article 106278"},"PeriodicalIF":0.8,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143552811","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 : 2025-02-21DOI: 10.1016/j.jspi.2025.106274
Shanchao Yang , Qi Lan , Xueyan Xu , Zhu Liang
The diffusion process is widely used in finance, and many scholars pay close attention to the statistical estimation of diffusion processes. Some literature has discussed the non parametric kernel estimation of drift and diffusion functions, and proved the consistency and asymptotic normality of the estimators, but the convergence rate of asymptotic normality has not been discussed yet. In this paper, we derive the convergence rate of uniformly asymptotic normality of the drift function estimator by using the method of large and small blocks for stationary and -mixing diffusion process. In the case of optimal bandwidth, the rate of uniformly asymptotic normality reaches . In order to prove the results, we put forward some inequalities for mixing processes with variable sampling interval, which play a key role in the study of limit theory.
{"title":"Uniformly asymptotic normality of estimation of the drift function for diffusion processes","authors":"Shanchao Yang , Qi Lan , Xueyan Xu , Zhu Liang","doi":"10.1016/j.jspi.2025.106274","DOIUrl":"10.1016/j.jspi.2025.106274","url":null,"abstract":"<div><div>The diffusion process is widely used in finance, and many scholars pay close attention to the statistical estimation of diffusion processes. Some literature has discussed the non parametric kernel estimation of drift and diffusion functions, and proved the consistency and asymptotic normality of the estimators, but the convergence rate of asymptotic normality has not been discussed yet. In this paper, we derive the convergence rate of uniformly asymptotic normality of the drift function estimator by using the method of large and small blocks for stationary and <span><math><mi>ρ</mi></math></span>-mixing diffusion process. In the case of optimal bandwidth, the rate of uniformly asymptotic normality reaches <span><math><msup><mrow><mi>n</mi></mrow><mrow><mo>−</mo><mn>2</mn><mo>/</mo><mn>15</mn></mrow></msup></math></span>. In order to prove the results, we put forward some inequalities for mixing processes with variable sampling interval, which play a key role in the study of limit theory.</div></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"239 ","pages":"Article 106274"},"PeriodicalIF":0.8,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143579797","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 : 2025-02-08DOI: 10.1016/j.jspi.2025.106276
Daniel Gaigall , Julian Gerstenberg
Conditional excess distribution modelling is a widely used technique, in financial and insurance mathematics or survival analysis, for instance. Classical theory considers the thresholds as fixed values. In contrast, the use of empirical quantiles as thresholds offers advantages with respect to the design of the statistical experiment. Either way, the modeller is in a non-standard situation and runs in the risk of improper usage of statistical procedures. From both points of view, statistical planning and inference, a detailed discussion is requested. For this purpose, we treat both methods and demonstrate the necessity taking into account the characteristics of the approaches in practice. In detail, we derive general statements for empirical processes related to the conditional excess distribution in both situations. As examples, estimating the mean excess and the conditional Value-at-Risk are given. We apply our findings for the testing problems of goodness-of-fit and homogeneity for the conditional excess distribution and obtain new results of outstanding interest.
{"title":"Fixed values versus empirical quantiles as thresholds in excess distribution modelling","authors":"Daniel Gaigall , Julian Gerstenberg","doi":"10.1016/j.jspi.2025.106276","DOIUrl":"10.1016/j.jspi.2025.106276","url":null,"abstract":"<div><div>Conditional excess distribution modelling is a widely used technique, in financial and insurance mathematics or survival analysis, for instance. Classical theory considers the thresholds as fixed values. In contrast, the use of empirical quantiles as thresholds offers advantages with respect to the design of the statistical experiment. Either way, the modeller is in a non-standard situation and runs in the risk of improper usage of statistical procedures. From both points of view, statistical planning and inference, a detailed discussion is requested. For this purpose, we treat both methods and demonstrate the necessity taking into account the characteristics of the approaches in practice. In detail, we derive general statements for empirical processes related to the conditional excess distribution in both situations. As examples, estimating the mean excess and the conditional Value-at-Risk are given. We apply our findings for the testing problems of goodness-of-fit and homogeneity for the conditional excess distribution and obtain new results of outstanding interest.</div></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"238 ","pages":"Article 106276"},"PeriodicalIF":0.8,"publicationDate":"2025-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143379110","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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