Efficiency transfer for regression models with responses missing at random

被引:6
作者
Mueller, Ursula U. [1 ]
Schick, Anton [2 ]
机构
[1] Texas A&M Univ, Dept Stat, College Stn, TX 77843 USA
[2] Binghamton Univ, Dept Math Sci, Binghamton, NY 13902 USA
关键词
complete case analysis; efficient estimation; efficient influence function; linear and nonlinear regression; nonparametric regression; partially linear regression; random coefficient model; tangent space; transfer principle; ESTIMATING LINEAR FUNCTIONALS; NONPARAMETRIC REGRESSION; ERROR DISTRIBUTION; EMPIRICAL LIKELIHOOD; ADAPTIVE ESTIMATION; ESTIMATORS;
D O I
10.3150/16-BEJ824
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
We consider independent observations on a random pair (X, Y), where the response Y is allowed to be missing at random but the covariate vector X is always observed. We demonstrate that characteristics of the conditional distribution of Y given X can be estimated efficiently using complete case analysis, that is, one can simply omit incomplete cases and work with an appropriate efficient estimator which remains efficient. This means in particular that we do not have to use imputation or work with inverse probability weights. Those approaches will never be better (asymptotically) than the above complete case method. This efficiency transfer is a general result and holds true for all regression models for which the distribution of Y given X and the marginal distribution of X do not share common parameters. We apply it to the general homoscedastic semiparametric regression model. This includes models where the conditional expectation is modeled by a complex semiparametric regression function, as well as all basic models such as linear regression and nonparametric regression. We discuss estimation of various functionals of the conditional distribution, for example, of regression parameters and of the error distribution.
引用
收藏
页码:2693 / 2719
页数:27
相关论文
共 32 条
[1]  
[Anonymous], 2001, Monographs on Statistics and Applied Probability
[2]  
[Anonymous], 2002, STAT ANAL MISSING DA, DOI [DOI 10.1002/9781119013563, 10.1002/9781119013563]
[3]  
Bickel P. J., 1998, Efficient and Adaptive Estimation for Semiparametric Models, V1st ed.
[4]   ON ADAPTIVE ESTIMATION [J].
BICKEL, PJ .
ANNALS OF STATISTICS, 1982, 10 (03) :647-671
[6]   Efficiently estimating the error distribution in nonparametric regression with responses missing at random [J].
Chown, Justin ;
Mueller, Ursula U. .
JOURNAL OF NONPARAMETRIC STATISTICS, 2013, 25 (03) :665-677
[7]   Nonparametric regression with responses missing at random [J].
Efromovich, Sam .
JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 2011, 141 (12) :3744-3752
[8]  
Forrester J., 2003, Statistical Decisions, V21, P109
[9]   Goodness-of-fit tests for linear regression models with missing response data [J].
González-Manteiga, W ;
Pérez-González, A .
CANADIAN JOURNAL OF STATISTICS-REVUE CANADIENNE DE STATISTIQUE, 2006, 34 (01) :149-170
[10]   EMPIRICAL SMOOTHING PARAMETER SELECTION IN ADAPTIVE ESTIMATION [J].
JIN, K .
ANNALS OF STATISTICS, 1992, 20 (04) :1844-1874