Sparse consistency and smoothing for multinomial data

Statistics and Probability Letters

Volumn 33, Issue 1, 1997, Pages 41-48

  Aerts, Marc ^a   Augustyns, Ilse ^a   Janssen, Paul ^a  

^a HASSELT UNIVERSITY   (Belgium)

Author keywords

Frequency estimators; Local polynomial smoothers; Sparse consistency; Sparse multinomial data

Indexed keywords

EID: 0031569656     PISSN: 01677152     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-7152(96)00108-3     Document Type: Article

References (17)

1. Aerts, M., I. Augustyns and P. Janssen (1995a), Smoothing sparse multinomial data using local polynomial fitting, Technical Report, submitted.
2. Aerts, M., I. Augustyns and P. Janssen (1995b), Local polynomial estimation of contingency table cell probabilities, Technical Report, submitted.
3. Burman, P. (1987), Smoothing sparse contingency tables, Sankhyā Ser. A. 49, 24-36.
4. Cheng, M.Y. (1994), A bandwidth selector for local linear density estimators, Technical Report, Univ. North Carolina.
5. Dong, J. and J.S. Simonoff (1994), The construction and properties of boundary kernels for smoothing sparse multinomials, J. Comp. Graphical Statist. 3, 57-66.
6. Dong, J. and J.S. Simonoff (1995), A geometric combination estimator for d-dimensional ordinal contingency tables, Ann. Statist. 23, 1143-1153.
7. Grund, B. and P. Hall (1993), On the performance of kernel estimators for high-dimensional sparse binary data, J. Multivariate Anal. 44, 321-344.
8. Hall, P. and D.M. Titterington (1987), On smoothing sparse multinomial data, Austral. J. Statist. 29, 19-37.
9. Mason, D.M., G.R. Shorack and J. Wellner (1983), Strong limit theorems for oscillation moduli of the uniform empirical process, Z. Wahrscheinlichkeitstheorie verw. Gebiete 65, 83-97.
10. Pollard, D. (1984), Convergence of Stochastic Processes (Springer, New York).
11. Ruppert, D. and M. Wand (1994), Multivariate locally weighted least squares regression, Ann. Statist. 22, 1346-1370.
12. Santner, T.J. and D.E. Duffy (1989), The Statistical Analysis of Discrete Data (Springer, New York).
13. Simonoff, J.S. (1983), A penalty function approach to smoothing large sparse contingency tables, Ann. Statist. 11, 208-218.
14. Simonoff, J.S. (1995), Smoothing categorical data, J. Statist. Plann. Inference 47, 41-69.
15. Stone, C.-J. (1988), Optimal global rates of convergence for nonparametric regression, Ann. Statist. 10, 1040-1053.
16. Stute, W. (1982), The oscillation behavior of empirical processes, Ann. Probab. 10, 86-107.
17. Stute, W. (1984), The oscillation behavior of empirical processes: The multivariate case, Ann. Probab. 12, 361-379.