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Johnston, Gordon J.

Probabilities of maximal deviations for nonparametric regression function estimates. (English) Zbl 0497.62038

J. Multivariate Anal. 12, 402-414 (1982).
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Cited in 46 Documents

MSC:

62G05 Nonparametric estimation
62J02 General nonlinear regression
62J05 Linear regression; mixed models

Keywords:

probabilities of maximal deviations; Watson estimate; density estimates; Gaussian processes; Yang estimates

Citations:

Zbl 0275.62033; Zbl 0369.62028
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Full Text: DOI

References:

[1] Benedetti, J. K., Kernel Estimation of Regression Functions, (Ph. D. Dissertation (1974), Department of Biostatistics, University of Washington)
[2] Bhattacharya, P. K., An invariance principle in regression analysis, Ann. Statist., 4, 621-624 (1976) · Zbl 0331.62016
[3] Bickel, P. J.; Rosenblatt, M., On some global measures of the deviation of density function estimators, Ann. Math. Statist., 1, 1071-1095 (1973) · Zbl 0275.62033
[4] Billingsley, P., (Convergence of Probability Measures (1968), Wiley: Wiley New York) · Zbl 0172.21201
[5] Johnston, G., Smooth nonparametric regression analysis, (Institute of Statistics Mimeo Series 1253 (1979), University of North Carolina)
[6] Lai, S. L., Large Sample Properties of K-Nearest Neighbor Procedures, (Ph. D. Dissertation (1977), Department of Mathematics, University of California: Department of Mathematics, University of California Los Angeles)
[7] Marcondes, N. P., Estimation of Multivariate Densities, Conditional Distributions and Related Functions, (Ph. D. Dissertation (1978), Department of Statistics, University of California: Department of Statistics, University of California Berkeley)
[8] Parzen, E., On estimation of a probability density function, Ann. Math. Statist., 33, 1065-1076 (1962) · Zbl 0116.11302
[9] Priestly, M. B.; Chao, M. T., Nonparametric function fitting, J. Roy. Statist. Soc. Ser. B, 34, 385-392 (1972) · Zbl 0263.62044
[10] Revesz, P., On strong approximation of the multidimensional empirical process, Ann. Prob., 4, 729-743 (1976) · Zbl 0344.60022
[11] Rosenblatt, M., On the maximal deviation of a \(k\)-dimensional density estimator, Ann. Probab., 4, 1009-1015 (1976) · Zbl 0369.62028
[12] Schuster, E. F., Joint asymptotic distribution of the estimated regression function at a finite number of distinct points, Ann. Math. Statist., 43, 84-88 (1972) · Zbl 0248.62027
[13] Schuster, E. F.; Yakowitz, S., Contributions to the theory of nonparametric regression, with applications to system identification, Ann. Statist., 7, 139-149 (1979) · Zbl 0401.62033
[14] Stone, C. J., Consistent nonparametric regression, Ann. Statist., 5, 595-620 (1977) · Zbl 0366.62051
[15] Watson, G. S., Smooth regression analysis, Sankhyā, Ser. A. Math. Sci., 26, 359-372 (1964) · Zbl 0137.13002
[16] Watson, G. S.; Leadbetter, M. R., On the estimation of the probability density, I, Ann. Math. Statist., 34, 480-491 (1963) · Zbl 0113.34504
[17] Yang, S. S., Linear functions of concomitants of order statistics, (Technical Report No. 7 (1977), Department of Mathematics, M.I.T) · Zbl 0367.62017
[18] Yang, S. S., General distribution theory of the concomitants of order statistics, Ann. Statist., 6, 996-1002 (1977) · Zbl 0367.62017
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