Kernel density estimation with missing data and auxiliary variables

Australian and New Zealand Journal of Statistics

Volumn 51, Issue 3, 2009, Pages 247-270

  Dubnicka, Suzanne R ^a,b  

^a KANSAS STATE UNIVERSITY   (United States)

^b 101 Dickens Hall ^*  (United States)

Author keywords

Horvitz Thompson estimator; Integrated squared error; Kernel smoothing; Missing at random

Indexed keywords

EID: 69949107089     PISSN: 13691473     EISSN: 1467842X     Source Type: Journal    
DOI: 10.1111/j.1467-842X.2009.00541.x     Document Type: Article

References (31)

1. Bowman, A.W. (1984). An alternative method of cross-validation for the smoothing of density estimates. Biometrika 71, 353 360.
2. Bowman, A.W. Azzalini, A. (2005). sm: Smoothing methods for nonparametric regression and density estimation. R package version 2.1-0; Ported to R by B. D. Ripley up to version 2.0 and later versions by Adrian W. Bowman and Adelchi Azzalini/. Available from URL : http://www.stats.gla.ac.uk/∼adrian/sm
3. Davidian, M., Tsiatis, A.A. Leon, S. (2005). Semiparametric estimation of treatment effect in a pretest-posttest study with missing data. Statist. Sci. 20, 261 301.
4. Dempster, A.P., Laird, N.M. Rubin, D.B. (1977). Maximum likelihood from incomplete data via the EM algorithm. J. R. Statist. Soc. Ser. B Statist. Methodol. 39, 1 22.
5. Elmore, R.T., Hall, P. Troynikov, V.S. (2006). Nonparametric density estimation from covariate information. J. Amer. Statist. Assoc. 101, 701 711.
6. Fan, J., Heckmann, N.E. Wand, M.P. (1995). Local polynomial kernel regression for generalized linear models and quasi likelihood functions. J. Amer. Statist. Assoc. 90, 141 150.
7. Hall, P., Marron, J.S. Park, B.U. (1991). Smoothed cross-validation. Probab. Theory Related Fields 92, 1 20.
8. Hammer, S.M., Katzenstein, D.A., Hughes, M.D. et al. 1996). A trial comparing nucleoside monotherapy with combination therapy in HIV-infected adults with CD4 cell counts from 200 to 500 per cubic millimeter. New England J. Medicine 335, 1081 1090.
9. Hayfield, T. Racine, J.S. (2008). Nonparametric econometrics: The np package. J. of Statist. Software 27. Available from URL : http://www.jstatsoft. org/v27/i05/.
10. Horvitz, D.G. Thompson, D.J. (1952). A generalization of sampling without replacement from a finite universe. J. Amer. Statist. Assoc. 47, 663 685.
11. Hurvich, C.M., Simonoff, J.S. Tsai, C.L. (1998). Smoothing parameter selection in nonparametric regression using an improved Akaike information criterion. J. R. Statist. Soc. Ser. B Statist. Methodol. 60, 271 293.
12. Hyndman, R.J., Bashtannyk, D.M. Grunwald, G.K. (1996). Estimating and visualizing conditional densities. J. Comput. Graph. Statist. 5, 315 336.
13. Jones, M.C., Marron, J.S. Sheather, S.J. (1996). A brief survey of bandwidth selection for density estimation. J. Amer. Statist. Assoc. 91, 401 407.
14. Kennedy, K.F. (2007). A weighted estimating equation approach to local linear regression with missing covariate data (MSc Thesis). Kansas State University, Manhattan, Kansas, USA.
15. Little, R.J.A. Rubin, D.B. (2002). Statistical Analysis with Missing Data, 2nd edn. Hoboken, John Wiley & Sons.
16. Marron, J.S. Wand, M.P. (1992). Exact mean integrated squared error. Ann. Statist. 20, 712 736.
17. Müller, H.-G. (1987). Empirical bandwidth choice for nonparametric kernel regression by means of pilot estimators. Statist. Decisions Supplement no. 2, 193 206.
18. Nadaraya, E.A. (1964). On estimating regression. Theory Probab. Appl. 10, 186 190.
19. Nottingham, Q.J., Birch, J.B. Bodt, B.A. (2000). Local logistic regression: an application to army penetration data. J. Statist. Comput. Simul. 66, 35 50.
20. Park, B.U. Marron, J.S. (1990). Comparison of data-driven bandwidth selectors. J. Amer. Statist. Assoc. 85, 66 72.
21. Qi, L., Wang, C.Y. Prentice, R.L. (2005). Weighted estimators for proportional hazards regression with missing covariates. J. Amer. Statist. Assoc. 100, 1250 1263.
22. R Development Core Team (2006). R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria. Available from URL : http://www.R-project.org
23. Robins, J.M., Rotnitzky, A. Zhao, L.P. (1994). Estimation of regression coefficients when some regressors are not always observed. J. Amer. Statist. Assoc. 89, 846 866.
24. Rosenbaum, P.R. Rubin, D.B. (1983). The central role of the propensity score in observational studies for causal effects. Biometrika 70, 41 55.
25. Rudemo, M. (1982). Empirical choice of histograms and kernel density estimators. Scand. J. Statist. 9, 65 78.
26. Scott, D.W. Terrell, G.R. (1987). Biased and unbiased cross-validation in density estimation. J. Amer. Statist. Assoc. 82, 1131 1146.
27. Sheather, S.J. Jones, M.C. (1991). A reliable data-based bandwidth selection method for kernel density estimation. J. R. Statist. Soc. Ser. B Statist. Methodol. 53, 683 690.
28. Silverman, B.W. (1986). Density Estimation for Statistics and Data Analysis. London : Chapman & Hall/CRC.
29. Staniswalis, J.G. (1989). Local bandwidth selection for kernel estimates. J. Amer. Statist. Assoc. 86, 284 288.
30. Tibshirani, R. Hastie, T. (1987). Local likelihood estimation. J. Amer. Statist. Assoc. 82, 559 567.
31. Watson, G.S. (1964). Smooth regression analysis. Sankhyā, Series A 26, 359 372.