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In this paper we derive the asymptotic distribution of normalized residual empirical autocovariances and autocorrelations under weak assumptions on the noise. We propose new portmanteau statistics for vector autoregressive moving-average…

Statistics Theory · Mathematics 2024-04-22 Yacouba Boubacar Maïnassara , Bruno Saussereau

In this paper, we consider the usual linear regression model in the case where the error process is assumed strictly stationary. We use a result from Hannan, who proved a Central Limit Theorem for the usual least squares estimator under…

Statistics Theory · Mathematics 2019-06-18 Emmanuel Caron , Sophie Dede

In this paper, we analyze the asymptotic behavior of the main characteristics of the mean-variance efficient frontier employing random matrix theory. Our particular interest covers the case when the dimension $p$ and the sample size $n$…

Statistical Finance · Quantitative Finance 2024-09-24 Taras Bodnar , Nikolaus Hautsch , Yarema Okhrin , Nestor Parolya

Sample correlation matrices are employed ubiquitously in statistics. However, quite surprisingly, little is known about their asymptotic spectral properties for high-dimensional data, particularly beyond the case of "null models" for which…

Statistics Theory · Mathematics 2019-03-13 David Morales-Jimenez , Iain M. Johnstone , Matthew R. McKay , Jeha Yang

Although asymptotic analyses of undirected network models based on degree sequences have started to appear in recent literature, it remains an open problem to study statistical properties of directed network models. In this paper, we…

Statistics Theory · Mathematics 2016-01-13 Ting Yan , Chenlei Leng , Ji Zhu

The asymptotic normality for a large family of eigenvalue statistics of a general sample covariance matrix is derived under the ultra-high dimensional setting, that is, when the dimension to sample size ratio $p/n \to \infty$. Based on this…

Methodology · Statistics 2021-09-15 Jiaxin Qiu , Zeng Li , Jianfeng Yao

We consider high-dimensional estimation problems where the number of parameters diverges with the sample size. General conditions are established for consistency, uniqueness, and asymptotic normality in both unpenalized and penalized…

Statistics Theory · Mathematics 2025-04-08 Jana Gauss , Thomas Nagler

Robust estimators of large covariance matrices are considered, comprising regularized (linear shrinkage) modifications of Maronna's classical M-estimators. These estimators provide robustness to outliers, while simultaneously being…

Statistics Theory · Mathematics 2018-07-04 Nicolas Auguin , David Morales-Jimenez , Matthew R. McKay , Romain Couillet

Prediction, in regression and classification, is one of the main aims in modern data science. When the number of predictors is large, a common first step is to reduce the dimension of the data. Sufficient dimension reduction (SDR) is a well…

Methodology · Statistics 2023-06-21 Liliana Forzani , Daniela Rodriguez , Mariela Sued

Distance correlation has become an increasingly popular tool for detecting the nonlinear dependence between a pair of potentially high-dimensional random vectors. Most existing works have explored its asymptotic distributions under the null…

Statistics Theory · Mathematics 2021-10-06 Lan Gao , Yingying Fan , Jinchi Lv , Qi-Man Shao

We consider the problem of subspace estimation in situations where the number of available snapshots and the observation dimension are comparable in magnitude. In this context, traditional subspace methods tend to fail because the…

Information Theory · Computer Science 2016-11-15 Pascal Vallet , Philippe Loubaton , Xavier Mestre

This work is concerned with the estimation of multidimensional regression and the asymptotic behaviour of the test involved in selecting models. The main problem with such models is that we need to know the covariance matrix of the noise to…

Statistics Theory · Mathematics 2008-02-20 Joseph Rynkiewicz

We study estimation and inference on causal parameters under finely stratified rerandomization designs, which use baseline covariates to match units into groups (e.g. matched pairs), then rerandomize within-group treatment assignments until…

Econometrics · Economics 2025-01-07 Max Cytrynbaum

Split-Plot or Repeated Measures Designs with multiple groups occur naturally in sciences. Their analysis is usually based on the classical Repeated Measures ANOVA. Roughly speaking, the latter can be shown to be asymptotically valid for…

Statistics Theory · Mathematics 2020-03-11 Paavo Sattler

We develop an asymptotic theory for $L^2$ norms of sample mean vectors of high-dimensional data. An invariance principle for the $L^2$ norms is derived under conditions that involve a delicate interplay between the dimension $p$, the sample…

Statistics Theory · Mathematics 2015-03-13 Mengyu Xu , Danna Zhang , Wei Biao Wu

A recent article on generalised linear mixed model asymptotics, Jiang et al. (2022), derived the rates of convergence for the asymptotic variances of maximum likelihood estimators. If $m$ denotes the number of groups and $n$ is the average…

Statistics Theory · Mathematics 2023-04-03 Luca Maestrini , Aishwarya Bhaskaran , Matt P. Wand

In repeated Measure Designs with multiple groups, the primary purpose is to compare different groups in various aspects. For several reasons, the number of measurements and therefore the dimension of the observation vectors can depend on…

Statistics Theory · Mathematics 2022-07-20 Paavo Sattler , Markus Pauly

High dimensionality comparable to sample size is common in many statistical problems. We examine covariance matrix estimation in the asymptotic framework that the dimensionality $p$ tends to $\infty$ as the sample size $n$ increases.…

Statistics Theory · Mathematics 2007-06-13 Jianqing Fan , Yingying Fan , Jinchi Lv

Estimating some mathematical expectations from partially observed data and in particular missing outcomes is a central problem encountered in numerous fields such as transfer learning, counterfactual analysis or causal inference. Matching…

Statistics Theory · Mathematics 2025-05-01 Simon Viel , Lionel Truquet , Ikko Yamane

This study investigates the dynamics of alternating minimization applied to a bilinear regression task with normally distributed covariates, under the asymptotic system size limit where the number of parameters and observations diverge at…

Optimization and Control · Mathematics 2025-02-03 Koki Okajima , Takashi Takahashi