The Annals of Statistics

The transfer principle: A tool for complete case analysis

Hira L. Koul, Ursula U. Müller, and Anton Schick

Full-text: Open access

Abstract

This paper gives a general method for deriving limiting distributions of complete case statistics for missing data models from corresponding results for the model where all data are observed. This provides a convenient tool for obtaining the asymptotic behavior of complete case versions of established full data methods without lengthy proofs.

The methodology is illustrated by analyzing three inference procedures for partially linear regression models with responses missing at random. We first show that complete case versions of asymptotically efficient estimators of the slope parameter for the full model are efficient, thereby solving the problem of constructing efficient estimators of the slope parameter for this model. Second, we derive an asymptotically distribution free test for fitting a normal distribution to the errors. Finally, we obtain an asymptotically distribution free test for linearity, that is, for testing that the nonparametric component of these models is a constant. This test is new both when data are fully observed and when data are missing at random.

Article information

Source
Ann. Statist., Volume 40, Number 6 (2012), 3031-3049.

Dates
First available in Project Euclid: 8 February 2013

Permanent link to this document
https://projecteuclid.org/euclid.aos/1360332192

Digital Object Identifier
doi:10.1214/12-AOS1061

Mathematical Reviews number (MathSciNet)
MR3097968

Zentralblatt MATH identifier
1296.62040

Subjects
Primary: 62E20: Asymptotic distribution theory
Secondary: 62G05: Estimation 62G10: Hypothesis testing

Keywords
Transfer principle missing at random partially linear models efficient estimation martingale transform test for normal errors testing for linearity

Citation

Koul, Hira L.; Müller, Ursula U.; Schick, Anton. The transfer principle: A tool for complete case analysis. Ann. Statist. 40 (2012), no. 6, 3031--3049. doi:10.1214/12-AOS1061. https://projecteuclid.org/euclid.aos/1360332192


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