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Nonparametric regression models offer a way to understand and quantify relationships between variables without having to identify an appropriate family of possible regression functions. Although many estimation methods for these models have…
Nonparametric estimators of a regression function with circular response and Rd-valued predictor are considered in this work. Local polynomial type estimators are proposed and studied. Expressions for their asymptotic biases and variances…
This paper presents tests to formally choose between regression models using different derivatives of a functional covariate in scalar-on-function regression. We demonstrate that for linear regression, models using different derivatives can…
In a regression model with multiple response variables and multiple explanatory variables, if the difference of the mean vectors of the response variables for different values of explanatory variables is always in the direction of the first…
In this paper we study the effective degrees of freedom of a general class of reduced rank estimators for multivariate regression in the framework of Stein's unbiased risk estimation (SURE). We derive a finite-sample exact unbiased…
High-dimensional covariates often admit linear factor structure. To effectively screen correlated covariates in high-dimension, we propose a conditional variable screening test based on non-parametric regression using neural networks due to…
We construct an efficient estimator for the error distribution function of the nonparametric regression model Y = r(Z) + e. Our estimator is a kernel smoothed empirical distribution function based on residuals from an under-smoothed local…
Nonparametric regression with random design is considered. Estimates are defined by minimzing a penalized empirical $L_2$ risk over a suitably chosen class of neural networks with one hidden layer via gradient descent. Here, the gradient…
The linear regression models are widely used statistical techniques in numerous practical applications. The standard regression model requires several assumptions about the regres- sors and the error term. The regression parameters are…
Distribution regression seeks to estimate the conditional distribution of a multivariate response given a continuous covariate. This approach offers a more complete characterization of dependence than traditional regression methods.…
For the last two decades, high-dimensional data and methods have proliferated throughout the literature. Yet, the classical technique of linear regression has not lost its usefulness in applications. In fact, many high-dimensional…
A least product relative error criterion is proposed for multiplicative regression models. It is invariant under scale transformation of the outcome and covariates. In addition, the objective function is smooth and convex, resulting in a…
Expectile regression is a useful tool for exploring the relation between the response and the explanatory variables beyond the conditional mean. This article develops a continuous threshold expectile regression for modeling data in which…
Estimation is a critical component of synchronization in wireless and signal processing systems. There is a rich body of work on estimator derivation, optimization, and statistical characterization from analytic system models which are used…
We present large sample results for partitioning-based least squares nonparametric regression, a popular method for approximating conditional expectation functions in statistics, econometrics, and machine learning. First, we obtain a…
This paper deals with estimation with functional covariates. More precisely, we aim at estimating the regression function $m$ of a continuous outcome $Y$ against a standard Wiener coprocess $W$. Following Cadre and Truquet (2015) and Cadre,…
Penalized smoothing is a standard tool in regression analysis. Classical approaches often rely on basis or kernel expansions, which constrain the estimator to a fixed span and impose smoothness assumptions that may be restrictive for…
Observations which are realizations from some continuous process are frequent in sciences, engineering, economics, and other fields. We consider linear models, with possible random effects, where the responses are random functions in a…
Weighting estimators based on propensity scores are widely used for causal estimation in a variety of contexts, such as observational studies, marginal structural models and interference. They enjoy appealing theoretical properties such as…
In this paper, we study finite-sample properties of the least squares estimator in first order autoregressive processes. By leveraging a result from decoupling theory, we derive upper bounds on the probability that the estimate deviates by…