Title Upper Expectation Parametric Regression Complete List of Authors Lixing Zhu Upper Expectation Parametric Regression
نویسندگان
چکیده
In regression analysis, some predictors might be unobservable, not observed, or ignored. These factors actually affect the response randomly. The observed data thus follows a conditional distribution when these factors are given. This phenomenon is called the distribution randomness. For such a working model, we propose an upper expectation regression and a two-step penalized maximum least squares procedure to estimate parameters in the mean function and the upper expectation of the error. The resulting estimators are consistent and asymptotically normal under certain conditions. Simulation studies and a data example are used to show that the classical least squares estimation fails but the proposed estimation performs well.
منابع مشابه
Variational Inference for Nonparametric Bayesian Quantile Regression
Quantile regression deals with the problem of computing robust estimators when the conditional mean and standard deviation of the predicted function are inadequate to capture its variability. The technique has an extensive list of applications, including health sciences, ecology and finance. In this work we present a nonparametric method of inferring quantiles and derive a novel Variational Bay...
متن کاملOn the Approximation of a Conditional Expectation
In this paper, we discuss how to approximate the conditional expectation of a random variable Y given a random variable X, i.e. E(Y|X). We propose and compare two different non parametric methodologies to approximate E(Y|X). The first approach (namely the OLP method) is based on a suitable approximation of the σ-algebra generated by X. A second procedure is based on the well known kernel non-pa...
متن کاملMinimum complexity regression estimation with weakly dependent observations
The minimum complexity regression estimation framework, due to Andrew Barron, is a general data-driven methodology for estimating a regression function from a given list of parametric models using independent and identically distributed (i.i.d.) observations. We extend Barron’s regression estimationframework tom-dependent observations and to stronglymixing observations. In particular, we propos...
متن کاملInterval Censored Survival Data : A Review of Recent
We review estimation in interval censoring models, including nonparametric estimation of a distribution function and estimation of regression models. In the non-parametric setting, we describe computational procedures and asymptotic properties of the nonparametric maximum likelihood estimators. In the regression setting, we focus on the proportional hazards, the proportional odds and the accele...
متن کاملEstimating covariate functions associated to multivariate risks: a level set approach
The aim of this paper is to study the behavior of a covariate function in a multivariate risks scenario. The first part of this paper deals with the problem of estimating the c-upper level sets L(c) = {F (x) ≥ c}, with c ∈ (0, 1), of an unknown distribution function F on R+. A plug-in approach is followed. We state consistency results with respect to the volume of the symmetric difference. In t...
متن کامل