Semiparametric density estimation under a two-sample density ratio model

Bernoulli

Volumn 10, Issue 4, 2004, Pages 583-604

  Cheng, K F ^a   Chu, C K ^b  

^a NATIONAL CENTRAL UNIVERSITY   (Taiwan)

^b NATIONAL DONG HWA UNIVERSITY   (Taiwan)

Author keywords

Asymptotic relative efficiency; Biased sampling problem; Case control data; Density estimation; Goodness of fit test; Logistic regression; Semiparametric maximum likelihood estimation

Indexed keywords

EID: 8644266252     PISSN: 13507265     EISSN: None     Source Type: Journal    
DOI: 10.3150/bj/1093265631     Document Type: Article

References (22)

1. Cheng, K.F. and Chen, L.C. (2003) Testing goodness-of-fit of a logistic regression model with case-control data. J. Statist. Plann. Inference. To appear.
2. de Jong, P. (1987) A central limit theorem for generalized quadratic forms. Probab. Theory Related Fields, 75, 261-277.
3. Efron, B. and Tibshirani, R. (1996) Using specially designed exponential families for density estimation. Ann. Statist., 24, 2431-2461.
4. Epanechnikov, V.A. (1969) Nonparametric estimation of a multidimensional probability density. Theory Probab. Appl., 14, 153-158.
5. Fokianos, K. (2002) Merging information for semiparametric density estimation. Technical report, Department of Mathematics and Statistics, University of Cyprus.
6. Fokianos, K., Kedem, B., Qin, J. and Short, D.A. (2001) A semiparametric approach to the one-way layout. Technometrics, 43, 56-64.
7. Glovsky, L. and Rigrodsky, S. (1964) A developmental analysis of mentally deficient children with early histories of aphasis. Training School Bull., 61, 76-96.
8. Hjort, N.L. and Glad, I.K. (1995) Nonparametric density estimation with a parametric start. Ann. Statist., 23, 882-904.
9. Hosmer, D.J. and Lemeshow, S. (1989) Applied Logistic Regression. New York: Wiley.
10. Jones, M.C. (1991) Kernel density estimation for length biased data. Biometrika, 78, 511-519.
11. Marron, J.S. and Wand, M.P. (1992) Exact mean integrated square error. Ann. Statist., 20, 712-736.
12. Prentice, R.L. and Pyke, R. (1979). Logistic disease incidence models and case-control studies. Biometrika, 66, 403-411.
13. Qin, J. (1998) Inferences for case-control and semiparametric two-sample density ratio model. Biometrika, 85, 619-630.
14. Qin, J. and Zhang, B. (1997) A goodness-of-fit test for logistic regression models based on case-control data. Biometrika, 84, 609-618.
15. Silverman, B.W. (1986) Density Estimation for Statistics and Data Analysis. New York: Chapman & Hall.
16. Vardi, Y. (1982) Nonparametric estimation in the presence of length bias. Ann. Statist., 10, 616-620.
17. Vardi, Y. (1985) Empirical distributions in selection bias models. Ann. Statist., 13, 178-203.
18. White, H. (1982) Maximum likelihood estimation of misspecified models. Econometrica, 50, 1-16.
19. Zhang, B. (1999) A chi-squared goodness-of-fit test for logistic regression models based on case-control data. Biometrika, 86, 531-539.
20. Zhang, B. (2000) M-estimation under a two-sample semiparametric model. Scand. J. Statist., 27, 263-280.
21. Zhang, B. (2001) An information matrix test for logistic regression models based on case-control data. Biometrika, 88, 921-932.
22. Zhao, L.P., Kristal, A.R. and White, E. (1996) Estimating relative risk functions in case-control studies using a nonparametric logistic regression. Amer. J. Epidemiology, 144, 598-609.