×
Hall, Peter

Central limit theorem for integrated square error of multivariate nonparametric density estimators. (English) Zbl 0528.62028

J. Multivariate Anal. 14, 1-16 (1984).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0528.62028

Cited in 15 Reviews
Cited in 205 Documents

MSC:

62G05 Nonparametric estimation
60F05 Central limit and other weak theorems
60G42 Martingales with discrete parameter
62H12 Estimation in multivariate analysis

Keywords:

integrated square error; variable kernels; Rosenblatt-Parzen kernel estimator; degenerate U-statistics
PDF BibTeX XML Cite
\textit{P. Hall}, J. Multivariate Anal. 14, 1--16 (1984; Zbl 0528.62028)
Full Text: DOI
  • logo of hbz
  • logo of WorldCat

References:

[1] Bickel, P.J; Rosenblatt, M, On some global measures of the deviations of density function estimates, Ann. statist., 1, 1071-1095, (1973) · Zbl 0275.62033
[2] Bowman, A.W, A comparative study of some kernel-based nonparametric density estimates, Manchester-Sheffield school of probability and statistics research report 84/AWB/1, (1982)
[3] Brown, B.M, Martingale central limit theorems, Ann. math. statist., 42, 59-66, (1971) · Zbl 0218.60048
[4] Cs̈orgö, M; Révész, P, ()
[5] Gregory, G.G, Large sample theory for U-statistics and tests of fit, Ann. statist., 5, 110-123, (1977) · Zbl 0371.62033
[6] Hall, P, On the invariance principle for U-statistics, Stochastic process. appl., 9, 163-174, (1979) · Zbl 0422.62019
[7] Hall, P, Limit theorems for stochastic measures of the accuracy of density estimators, Stochastic process. appl., 13, 11-25, (1982) · Zbl 0486.60022
[8] Hall, P, Large sample optimality of least squares cross-validation in density estimation, Ann. statist., (1982), To appear
[9] Hall, P; Heyde, C.C, ()
[10] Komlós, J; Major, P; Tusnády, G, An approximation of partial sums of independent r.v.’s and the sample d.f. I, Z. wahrsch. verw. gebiete, 32, 111-131, (1975) · Zbl 0308.60029
[11] Mack, Y.P; Rosenblatt, M, Multivariate k-nearest neighbour density estimates, J. multivar. anal., 9, 1-15, (1979) · Zbl 0406.62023
[12] Neuhaus, G, Functional limit theorems for U-statistics in the degenerate case, J. multivar. anal., 7, 424-439, (1977) · Zbl 0368.60034
[13] Rosenblatt, M, A quadratic measure of deviation of two-dimensional density estimates and a test of independence, Ann. statist., 3, 1-14, (1975) · Zbl 0325.62030
[14] Weber, N.C, Incomplete degenerate U-statistics, Scand. J. statist., 8, 120-123, (1981) · Zbl 0466.62021
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.