Related papers: Bivariate least squares linear regression: towards…
The functional linear model is an important extension of the classical regression model allowing for scalar responses to be modeled as functions of stochastic processes. Yet, despite the usefulness and popularity of the functional linear…
We study low-rank matrix regression in settings where matrix-valued predictors and scalar responses are observed across multiple individuals. Rather than assuming a fully homogeneous coefficient matrices across individuals, we accommodate…
Linear regression and classification methods with repeated functional data are considered. For each statistical unit in the sample, a real-valued parameter is observed over time under different conditions related by some neighborhood…
We present a new and general method of weighted least square univariate regression where the dependent variable is expanded as a series of suitably chosen functions of the independent variables. Each term of the series is obtained by an…
Two-sample testing is a fundamental problem in statistics. Despite its long history, there has been renewed interest in this problem with the advent of high-dimensional and complex data. Specifically, in the machine learning literature,…
Collected data, which is used for analysis or prediction tasks, often have a hierarchical structure, for example, data from various people performing the same task. Modeling the data's structure can improve the reliability of the derived…
Traditionally, the least squares regression is mainly concerned with studying the effects of individual predictor variables, but strongly correlated variables generate multicollinearity which makes it difficult to study their effects.…
Regression models with both high-dimensional responses and covariates have attracted growing attention. Standard multivariate regression models become inadequate when the response variables depend not only on observed covariates but also on…
This paper analyses the use of bootstrap methods to test for parameter change in linear models estimated via Two Stage Least Squares (2SLS). Two types of test are considered: one where the null hypothesis is of no change and the alternative…
Segmented regression models offer model flexibility and interpretability as compared to the global parametric and the nonparametric models, and yet are challenging in both estimation and inference. We consider a four-regime segmented model…
Constrained approaches to maximum likelihood estimation in the context of finite mixtures of normals have been presented in the literature. A fully data-dependent constrained method for maximum likelihood estimation of clusterwise linear…
With the violation of the assumption of homoskedasticity, least squares estimators of the variance become inefficient and statistical inference conducted with invalid standard errors leads to misleading rejection rates. Despite a vast…
A linear multiple regression model in function spaces is formulated, under temporal correlated errors. This formulation involves kernel regressors. A generalized least-squared regression parameter estimator is derived. Its asymptotic…
The spatial linear mixed model (SLMM) consists of fixed and spatial random effects that may be linearly dependent. Partially motivated as a means to address potential issues with confounding, the Restricted spatial regression (RSR) model…
Clustering of large-scale structure provides significant cosmological information through the power spectrum of density perturbations. Additional information can be gained from higher-order statistics like the bispectrum, especially to…
Most of the non-asymptotic theoretical work in regression is carried out for the square loss, where estimators can be obtained through closed-form expressions. In this paper, we use and extend tools from the convex optimization literature,…
The function-on-function linear regression model in which the response and predictors consist of random curves has become a general framework to investigate the relationship between the functional response and functional predictors.…
Seemingly unrelated linear regression models are introduced in which the distribution of the errors is a finite mixture of Gaussian components. Identifiability conditions are provided. The score vector and the Hessian matrix are derived.…
Supervised learning by extreme learning machines resp. neural networks with random weights is studied under a non-stationary spatial-temporal sampling design which especially addresses settings where an autonomous object moving in a…
Small area estimation has become an important tool in official statistics, used to construct estimates of population quantities for domains with small sample sizes. Typical area-level models function as a type of heteroscedastic regression,…