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When estimating area means, direct estimators based on area-specific data, are usually consistent under the sampling design without model assumptions. However, they are inefficient if the area sample size is small. In small area estimation,…
In this paper we study the least squares (LS) estimator in a linear panel regression model with unknown number of factors appearing as interactive fixed effects. Assuming that the number of factors used in estimation is larger than the true…
Best linear unbiased prediction is well known for its wide range of applications including small area estimation. While the theory is well established for mixed linear models and under normality of the error and mixing distributions, the…
We develop a new approach for the estimation of a multivariate function based on the economic axioms of quasiconvexity (and monotonicity). On the computational side, we prove the existence of the quasiconvex constrained least squares…
The optimization problem that arises out of the least median of squared residuals method in linear regression is analyzed. To simplify the analysis, the problem is replaced by an equivalent one of minimizing the median of absolute…
Misspecified models often provide useful information about the true data generating distribution. For example, if $y$ is a non-linear function of $x$ the least squares estimator $\hat{\beta}$ is an estimate of $\beta$, the slope of the best…
In this paper, we consider the normalized least squares estimator of the parameter in a mildly-explosive first-order autoregressive model with dependent errors which are modeled as a mildly-explosive AR(1) process. We prove that the…
The LASSO is a variable subset selection procedure in statistical linear regression based on $\ell_1$ penalization of the least-squares operator. Uniqueness of the LASSO is an important issue, especially for the study of the LASSO path. The…
Linear regression is a fundamental and popular statistical method. There are various kinds of linear regression, such as mean regression and quantile regression. In this paper, we propose a new one called distribution regression, which…
We present a novel iterative algorithm for approximating the linear least squares solution with low complexity. After a motivation of the algorithm we discuss the algorithm's properties including its complexity, and we present theoretical…
Shuffled linear regression (SLR) seeks to estimate latent features through a linear transformation, complicated by unknown permutations in the measurement dimensions. This problem extends traditional least-squares (LS) and Least Absolute…
This paper introduces a local linear smoother for regression surfaces on the simplex. The estimator solves a least-squares regression problem weighted by a locally adaptive Dirichlet kernel, ensuring good boundary properties. Asymptotic…
We consider the least-squares regression problem and provide a detailed asymptotic analysis of the performance of averaged constant-step-size stochastic gradient descent (a.k.a. least-mean-squares). In the strongly-convex case, we provide…
In a previous article, a least square regression estimation procedure was proposed: first, we condiser a family of functions and study the properties of an estimator in every unidimensionnal model defined by one of these functions; we then…
We study the optimal linear prediction of a random function that takes values in an infinite dimensional Hilbert space. We begin by characterizing the mean square prediction error (MSPE) associated with a linear predictor and discussing the…
We consider the problem of robustly predicting as well as the best linear combination of $d$ given functions in least squares regression, and variants of this problem including constraints on the parameters of the linear combination. For…
Under distribution uncertainty, on the basis of discrete data we investigate the consistency of the least squares estimator (LSE) of the parameter for the stochastic differential equation (SDE) where the noise are characterized by…
The aim of the paper is to derive for the negative correlation function with a time parameter an asymptotic disjunction of the numerical generalized least-squares estimator of an unknown constant mean of random field in fact the correct…
Estimating Kullback-Leibler divergence from identical and independently distributed samples is an important problem in various domains. One simple and effective estimator is based on the k nearest neighbor distances between these samples.…
Consider a regression model with infinitely many parameters and time series errors. We are interested in choosing weights for averaging across generalized least squares (GLS) estimators obtained from a set of approximating models. However,…