Chen, Songxi and Van Keilegom, Ingrid (2012): Estimation in semiparametric models with missing data. Published in:
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Abstract
This paper considers the problem of parameter estimation in a general class of semiparametric models when observations are subject to missingness at random. The semiparametric models allow for estimating functions that are nonsmooth with respect to the parameter. We propose a nonparametric imputation method for the missing values, which then leads to imputed estimating equations for the finite dimensional parameter of interest. The asymptotic normality of the parameter estimator is proved in a general setting, and is investigated in detail for a number of specific semiparametric models. Finally, we study the small sample performance of the proposed estimator via simulations.
Item Type:  MPRA Paper 

Original Title:  Estimation in semiparametric models with missing data 
Language:  English 
Keywords:  Copulas; imputation; kernel smoothing; missing at random; nuisance function; partially linear model; semiparametric model; single index model. 
Subjects:  C  Mathematical and Quantitative Methods > C0  General C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General C  Mathematical and Quantitative Methods > C2  Single Equation Models ; Single Variables C  Mathematical and Quantitative Methods > C3  Multiple or Simultaneous Equation Models ; Multiple Variables C  Mathematical and Quantitative Methods > C4  Econometric and Statistical Methods: Special Topics C  Mathematical and Quantitative Methods > C5  Econometric Modeling C  Mathematical and Quantitative Methods > C6  Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory C  Mathematical and Quantitative Methods > C8  Data Collection and Data Estimation Methodology ; Computer Programs C  Mathematical and Quantitative Methods > C9  Design of Experiments G  Financial Economics > G0  General 
Item ID:  46277 
Depositing User:  Professor Songxi Chen 
Date Deposited:  17 Apr 2013 10:05 
Last Modified:  16 Nov 2016 09:29 
References:  1.Ai, C., Chen, X. (2003). Efficient estimation of models with conditional moment restrictions containing unknown functions. Econometrica, 71, 1795–1843. 2.Chen, Q., Zeng, D., Ibrahim, J. G. (2007). Sieve maximum likelihood estimation for regression models with covariates missing at random. Journal of the American Statistical Association, 102, 1309–1317. 3.Chen, X., Hong, H., Tarozzi, A. (2008). Semiparametric efficiency in GMM models with auxiliary data. Annals of Statistics, 36, 808–843. 4.Chen, X., Linton, O. B., Van Keilegom, I. (2003). Estimation of semiparametric models when the criterion function is not smooth. Econometrica, 71, 1591–1608. 5.Härdle, W., Hall, P., Ichimura, H. (1993). Optimal smoothing in singleindex models. Annals of Statistics, 21, 157–178. 6.Ichimura, H. (1993). Semiparametric least squares (SLS) and weighted SLS estimation of singleindex models. Journal of Econometrics, 58, 71–120. 7.Ichimura, H., Lee, L.F. (1991). Semiparametric least squares estimation of multiple index models: Single equation estimation. In W. A. Barnett, J. Powell, G. Tauchen (Eds.), Nonparametric and semiparametric methods in statistics and econometrics. Cambridge: Cambridge University Press (Chapter 1). 8.Liang, H. (2008). Generalized partially linear models with missing covariates. Journal of Multivariate Analysis, 99, 880–895. 9.Little, R. J. A., Rubin, D. B. (2002). Statistical analysis with missing data. New York: Wiley. 10.McCullagh, P., Nelder, J. A. (1983). Generalized linear models. London: Chapman & Hall. 11.Müller, U. U. (2009). Estimating linear functionals in nonlinear regression with responses missing at random. Annals of Statistics, 37, 2245–2277. 12.Müller, U. U., Schick, A., Wefelmeyer, W. (2006). Imputing responses that are not missing. In M. Nikulin, D. Commenges, C. Huber (Eds.), Probability, statistics and modelling in public health (pp. 350–363). New York: Springer. 13.Powell, J. L., Stock, J. M., Stoker, T. M. (1989). Semiparametric estimation of index coefficients. Econometrica, 57, 1403–1430. 14.Robins, J. M., Rotnitzky, A., Zhao, L. P. (1994). Estimation of regression coefficients when some regressors are not always observed. Journal of the American Statistical Association, 89, 846–866. 15.Robinson, P. M. (1988). RootNconsistent semiparametric regression. Econometrica, 56, 931–954. 16.Rubin, D. B. (1976). Inference and missing values (with discussion). Biometrika, 63, 481–592. 17.Van der Vaart, A. W., Wellner, J. A. (1996). Weak convergence and empirical processes. New York: Springer. 18.Wang, C. Y., Wang, S., Gutierrez, R. G., Carroll, R. J. (1998). Local linear regression for generalized linear models with missing data. Annals of Statistics, 26, 1028–1050. 19.Wang, D., Chen, S. X. (2009). Empirical likelihood for estimating equations with missing values. Annals of Statistics, 37, 490–517. 20.Wang, Q., Sun, Z. (2007). Estimation in partially linear models with missing responses at random. Journal of Multivariate Analysis, 98, 1470–1493. 21.Wang, Q., Linton, O., Härdle, W. (2004). Semiparametric regression analysis with missing response at random. Journal of the American Statistical Association, 99, 334–345. 22.Wang, Q.H. (2009). Statistical estimation in partial linear models with covariate data missing at random. Annals of the Institute of Statistical Mathematics, 61, 47–84. 23.Wang, Y., Shen, J., He, S., Wang, Q. (2010). Estimation of single index model with missing response at random. Journal of Statistical Planning and Inference, 140, 1671–1690. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/46277 
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Estimation in semiparametric models with missing data. (deposited 16 Apr 2013 10:13)
 Estimation in semiparametric models with missing data. (deposited 17 Apr 2013 10:05) [Currently Displayed]