Related papers: Asymptotics of Linear Regression with Linearly Dep…

We consider covariance parameter estimation for Gaussian processes with functional inputs. From an increasing-domain asymptotics perspective, we prove the asymptotic consistency and normality of the maximum likelihood estimator. We extend…

We apply the concept of distance covariance for testing independence of two long-range dependent time series. As test statistic we propose a linear combination of empirical distance cross-covariances. We derive the asymptotic distribution…

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…

Asymptotic equivalence theory developed in the literature so far are only for bounded loss functions. This limits the potential applications of the theory because many commonly used loss functions in statistical inference are unbounded. In…

This paper characterizes the impact of covariate serial dependence on the non-asymptotic estimation error bound of penalized regressions (PRs). Focusing on the direct relationship between the degree of cross-correlation between covariates…

The estimation of the covariance structure from a discretely observed multivariate Gaussian process under asynchronicity and noise is analysed under high-frequency asymptotics. Asymptotic lower and upper bounds are established for a general…

We prove a universality theorem for learning with random features. Our result shows that, in terms of training and generalization errors, a random feature model with a nonlinear activation function is asymptotically equivalent to a…

We develop a uniform inference theory for high-dimensional slope parameters in threshold regression models, allowing for either cross-sectional or time series data. We first establish oracle inequalities for prediction errors, and L1…

We address the inference problem concerning regression coefficients in a classical linear regression model using least squares estimates. The analysis is conducted under circumstances where network dependency exists across units in the…

Asymptotic equivalence in Le Cam's sense for nonparametric regression experiments is extended to the case of non-regular error densities, which have jump discontinuities at their endpoints. We prove asymptotic equivalence of such regression…

A desirable property of an autocovariance estimator is to be robust to the presence of additive outliers. It is well-known that the sample autocovariance, being based on moments, does not have this property. Hence, the use of an…

In this paper we analyze, for a model of linear regression with gaussian covariates, the performance of a Bayesian estimator given by the mean of a log-concave posterior distribution with gaussian prior, in the high-dimensional limit where…

This article carries out a large dimensional analysis of standard regularized discriminant analysis classifiers designed on the assumption that data arise from a Gaussian mixture model with different means and covariances. The analysis…

In this study, we develop an asymptotic theory of nonparametric regression for locally stationary random fields (LSRFs) $\{{\bf X}_{{\bf s}, A_{n}}: {\bf s} \in R_{n} \}$ in $\mathbb{R}^{p}$ observed at irregularly spaced locations in…

In this paper we study covariance estimation with missing data. We consider missing data mechanisms that can be independent of the data, or have a time varying dependency. Additionally, observed variables may have arbitrary (non uniform)…

We establish a rigorous asymptotic theory for the joint estimation of roughness and scale parameters in two-dimensional Gaussian random fields with power-law generalized covariances \cite{Matheron1973, Stein1999, Yaglom1987}. Our main…

Rerandomization is an effective treatment allocation procedure to control for baseline covariate imbalance. For estimating the average treatment effect, rerandomization has been previously shown to improve the precision of the unadjusted…

In this paper, we consider a weighted local linear estimator based on the inverse selection probability for nonparametric regression with missing covariates at random. The asymptotic distribution of the maximal deviation between the…

We propose a series-based nonparametric specification test for a regression function when data are spatially dependent, the `space' being of a general economic or social nature. Dependence can be parametric, parametric with increasing…

We prove theorems about the Gaussian asymptotics of an empirical bridge built from linear model regressors with multiple regressor ordering. We study the testing of the hypothesis of a linear model for the components of a random vector: one…