Electronic Journal of Statistics

Efficient parameter estimation in regression with missing responses

Ursula U. Müller and Ingrid Van Keilegom

Full-text: Open access

Abstract

We discuss efficient estimation in regression models that are defined by a finite-dimensional parametric constraint. This includes a variety of regression models, in particular the basic nonlinear regression model and quasi-likelihood regression. We are interested in the case where responses are missing at random. This is a popular research topic and various methods have been proposed in the literature. However, many of them are complicated and are not shown to be efficient. The method presented here is, in contrast, very simple – we use an estimating equation that does not impute missing responses – and we also prove that it is efficient if an appropriate weight matrix is selected. Finally, we show that this weight matrix can be replaced by a consistent estimator without losing the efficiency property.

Article information

Source
Electron. J. Statist., Volume 6 (2012), 1200-1219.

Dates
First available in Project Euclid: 29 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1340974141

Digital Object Identifier
doi:10.1214/12-EJS708

Mathematical Reviews number (MathSciNet)
MR2988444

Zentralblatt MATH identifier
1295.62022

Subjects
Primary: 62F12: Asymptotic properties of estimators 62G05: Estimation
Secondary: 62J02: General nonlinear regression

Keywords
Efficiency influence function missing at random nonlinear regression nuisance function parametric regression quantile regression quasi-likelihood regression

Citation

Müller, Ursula U.; Van Keilegom, Ingrid. Efficient parameter estimation in regression with missing responses. Electron. J. Statist. 6 (2012), 1200--1219. doi:10.1214/12-EJS708. https://projecteuclid.org/euclid.ejs/1340974141


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