Nonparametric estimation of distributions with categorical and continuous data

Journal of Multivariate Analysis

Volumn 86, Issue 2, 2003, Pages 266-292

  Li, Qi ^a   Racine, Jeff ^b  

^a TEXAS A AND M UNIVERSITY   (United States)

^b SYRACUSE UNIVERSITY   (United States)

Author keywords

Asymptotic normality; Cross validation; Density estimation; Discrete and continuous variables; Nonparametric smoothing

Indexed keywords

EID: 0041656193     PISSN: 0047259X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0047-259X(02)00025-8     Document Type: Article

References (23)

1. M. Aerts, I. Augustyns, P. Janssen, Smoothing sparse multinomial data using local polynomial fitting, J. Nonparametric Statist. 8 (1997) 127-147.
2. M. Aerts, I. Augustyns, P. Janssen, Local polynomial estimation of contingency table cell probabilities, Statistics 30 (1997) 127-148.
3. I.A. Ahmad, P.B. Cerrito, Nonparametric estimation of joint discrete-continuous probability densities with applications, J. Statist. Plann. Inference 41 (1994) 349-364.
4. J. Aitchison, C.G.G. Aitken, Multivariate binary discrimination by the kernel method, Biometrika 63 (1976) 413-420.
5. A.W. Bowman, A note on consistency of the kernel method for the analysis of categorical data, Biometrika 67 (1980) 682-684.
6. J. Dong, J.S. Simonoff, The construction and properties of boundary kernels for sparse multinomials, J. Comput. Graph. Statist. 3 (1994) 57-66.
7. L. Fahrmeir, G. Tutz, Multivariate Statistical Modeling Based on Generalized Models, Springer, New York, 1994.
8. M. Gerfin, Parametric and semiparametric estimation of the binary response model of labour market participation, J. Appl. Econometrics 11 (3) (1996) 321-340.
9. B. Grund, Kernel estimators for cell probabilities, J. Multivariate Anal. 46 (1993) 283-308.
10. B. Grund, P. Hall, On the performance of kernel estimators for high-dimensional sparse binary data, J. Multivariate Anal. 44 (1993) 321-344.
11. P. Hall, On nonparametric multivariate binary discrimination, Biometrika 68 (1981) 287-294.
12. P. Hall, Central limit theorem for integrated square error of multivariate nonparametric density estimators, J. Multivariate Anal. 14 (1984) 1-16.
13. P. Hall, On Kullback-Leibler loss and density estimation, Ann. Statist. 15 (1987) 1491-1519.
14. P. Hall, On the use of compactly supported densities in problems of discrimination, J. Multivariate Anal. 23 (1987) 131-158.
15. P. Hall, M. Wand, On nonparametric discrimination using density differences, Biometrika 75 (1988) 541-547.
16. W. Härdle, J.S. Marron, Optimal bandwidth selection in nonparametric regression function estimation, Ann. Statist. 13 (1985) 1465-1481.
17. J.D. Hart, Nonparametric Smoothing and Lack-of-fit Tests, Springer, New York, 1997.
18. A. Izenman, Recent developments in nonparametric density estimation, J. Amer. Statist. Assoc. 413 (1991) 205-224.
19. J. Racine, Q. Li, Nonparametric estimation of regression functions with both categorical and continuous data, J. Econometrics (2001) submitted.
20. D. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization, Wiley, New York, 1992.
21. J.S. Simonoff, A penalty function approach to smoothing to smoothing large sparse contingency tables, Ann. Statist. 11 (1983) 208-218.
22. J.S. Simonoff, Smoothing Methods in Statistics, Springer, New York, 1996.
23. G. Tutz, Consistency of cross-validatory choice of smoothing parameters for direct kernel estimates, Comput. Statist. Quart. 4 (1991) 295-314.