Semiparametric regression analysis under imputation for missing response data
AbstractWe develop inference tools in a semiparametric regression model with missing response data. A semiparametric regression imputation estimator and an empirical likelihood based one for the mean of the response variable are defined. Both the estimators are proved to be asymptotically normal, with asymptotic variances estimated with Jackknife method. The empirical likelihood method is developed. It is shown that when missing responses are imputed using the semiparametric regression method the empirical log-likelihood is asymptotically a scaled chi-square variable or a weighted sum of chi-square variables with unknown weights in the absence of auxiliary information or in the presence of auxiliary information. An adjusted empirical log-likelihood ratio, which is asymptotically standard chi-square, is obtained. Also, a bootstrap empirical log-likelihood ratio is also derived and its distribution is used to approximate that of the imputed empirical log-likelihood ratio. A simulation study is conducted to compare the imputed, adjusted and bootstrap empirical likelihood with the normal approximation based methods in terms of coverage accuracies and average lengths of confidence intervals. Based on biases and standard errors, a comparison is also made by simulation between the proposed two estimators. The simulation indicates that the empirical likelihood methods developed perform competitively and the use of auxiliary information provides improved inference. --
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Bibliographic InfoPaper provided by Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes in its series SFB 373 Discussion Papers with number 2002,6.
Date of creation: 2002
Date of revision:
Asymptotic normality; Empirical likelihood; Semiparametric imputation;
Other versions of this item:
- Wolfgang Haerdle & Oliver Linton & Qihua Wang, 2003. "Semiparametric Regression Analysis under Imputation for Missing Response Data," STICERD - Econometrics Paper Series /2003/454, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Keisuke Hirano & Guido W. Imbens & Geert Ridder, 2003.
"Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score,"
Econometric Society, vol. 71(4), pages 1161-1189, 07.
- Guido Imbens, 2000. "Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score," Econometric Society World Congress 2000 Contributed Papers 1166, Econometric Society.
- Keisuke Hirano & Guido W. Imbens & Geert Ridder, 2000. "Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score," NBER Technical Working Papers 0251, National Bureau of Economic Research, Inc.
- Newey, Whitney K & Powell, James L & Walker, James R, 1990.
"Semiparametric Estimation of Selection Models: Some Empirical Results,"
American Economic Review,
American Economic Association, vol. 80(2), pages 324-28, May.
- Linton, Oliver, 1995.
"Second Order Approximation in the Partially Linear Regression Model,"
Econometric Society, vol. 63(5), pages 1079-1112, September.
- Oliver Linton, 1993. "Second Order Approximation in the Partially Linear Regression Model," Cowles Foundation Discussion Papers 1065, Cowles Foundation for Research in Economics, Yale University.
- Jinyong Hahn, 1998. "On the Role of the Propensity Score in Efficient Semiparametric Estimation of Average Treatment Effects," Econometrica, Econometric Society, vol. 66(2), pages 315-332, March.
- Oliver Linton & E. Mammen & J. Nielsen, 1997.
"The Existence and Asymptotic Properties of a Backfitting Projection Algorithm Under Weak Conditions,"
Cowles Foundation Discussion Papers
1160, Cowles Foundation for Research in Economics, Yale University.
- Oliver Linton & Enno Mammen & N Nielsen, 2000. "The Existence and Asymptotic Properties of a Backfitting Projection Algorithm under Weak Conditions," STICERD - Econometrics Paper Series /2000/386, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
- Heckman, James J & Ichimura, Hidehiko & Todd, Petra, 1998. "Matching as an Econometric Evaluation Estimator," Review of Economic Studies, Wiley Blackwell, vol. 65(2), pages 261-94, April.
- Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
- Rice, John, 1986. "Convergence rates for partially splined models," Statistics & Probability Letters, Elsevier, vol. 4(4), pages 203-208, June.
- Ahn, Hyungtaik & Powell, James L., 1993. "Semiparametric estimation of censored selection models with a nonparametric selection mechanism," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 3-29, July.
- Yuichi Kitamura & Michael Stutzer, 1997. "An Information-Theoretic Alternative to Generalized Method of Moments Estimation," Econometrica, Econometric Society, vol. 65(4), pages 861-874, July.
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