Nonparametric estimation of quadratic regression fimctionals

Bernoulli

Volumn 5, Issue 5, 1999, Pages 927-949

  Huang, Li Shan ^a,b   Jianqing, F A N ^a,b  

^a FLORIDA STATE UNIVERSITY   (United States)

^b University of North Carolina at Chapel Hill   (United States)

Author keywords

Asymptotic normality; Equivalent kernel; Local polynomial regression

Indexed keywords

EID: 0007195209     PISSN: 13507265     EISSN: None     Source Type: Journal    
DOI: 10.2307/3318450     Document Type: Article

References (21)

1. Birgé, L. and Massart, P. (1995) Estimation of integral functionals of a density. Ann. Statist., 23, 11 29.
2. Bickel, P.J. and Ritov, Y. (1988) Estimating integrated squared density derivatives: sharp best order of convergence estimates. Sankhyâ Ser. A, 50, 381-393.
3. Doksum, K. and Samarov, A. (1995) Nonparametric estimation of global functionals and a measure of the explanatory power of covariates in regression. -Ann. Statist., 23, 1443-1473.
4. Donoho, D.L. and Nussbaum, M. (1990) Minimax quadratic estimation of a quadratic functional. J. Complexity, 6, 290-323.
5. Efromovich, S. and Low, M. (1996) On Bickel and Ritov's conjecture about adaptive estimation of the integral of the square of density derivative. Ann. Statist., 24, 682-686.
6. Fan, J. (1991) On the estimation of quadratic functionals. Ann. Statist., 19, 1273-1294.
7. Fan, J. and Gijbels, I. (1995) Data-driven bandwidth selection in local polynomial fitting: variable bandwidth and spatial adaptation. J. Roy. Statist. Soc. Ser. B, 57, 371-394.
8. Fan, J. and Gijbels, I. (1996) Local Polynomial Modelling and Its Applications. London: Chapman & Hall.
9. Fan, J. and Huang, L.-S. (1996) Rates of convergence for the pre-asymptotic substitution bandwidth selector. Technical report no. 912, Department of Statistics, Florida State University.
10. Hall, P. and Marron, J.S. (1987) Estimation of integrated squared density derivatives. Statist. Probab. Lett., 6, 109-115.
11. Hall, P. and Marron, J.S. (1991) Lower bounds for bandwidth Selection in density estimation. Probab. Ttieory Related Fields, 90, 149-173.
12. Hall, P., Kay, J.W. and Titterington, D.M. (1990) Asymptotically optimal difference-based estimation of variance in nonparametric regression. Biometrika, 77, 521-528.
13. Jones, M.C. and Sheather, S.J. (1991) Using non-stochastic terms to advantage in kernel-based estimation of integrated squared density derivatives. Statist. Probab. Lett., 11, 511-514.
14. Khatri, C.G. (1980) Quadratic forms in normal variables. In P.R. Krishnaiah (ed.), Handbook of Statistics, Vol. I, pp. 443-469. New York: North-Holland
15. Laurent, B. (1996) Efficient estimation of integral functionals of a density. Ann. Statist., 24, 659-681.
16. Laurent, B. (1997) Estimation of integral functionals of a density and its derivatives. Bernoulli, 3, 181-211
17. Rice, J. (1984) Bandwidth choice for nonparametric regression. Ann. Statist., 12, 1215-1230.
18. Ruppert, D. and Wand, M.P. (1994) Multivariate locally weighted least squares regression. Ann. Statist., 22, 1346-1370.
19. Ruppert, D., Sheather, S.J. and Wand, M.P. (1995) An effective bandwidth selector for local least squares regression. J. Amer. Statist. Assoc., 90, 1257-1270.
20. Stone, C.J. (1980) Optimal rates of convergence for nonparametric estimators. Ann. Statist., 8, 13481360.
21. Whittle, P. (1964) On the convergence to normality of quadratic forms in independent random variables. Tlieory Probab. Appl, 9, 103-108.