@article{TVP_2010_55_3_a10,
author = {M. S. Muminov},
title = {On a limit distribution of the maximal level of empirical distribution density and the regression {function.~I}},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {582--590},
year = {2010},
volume = {55},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_2010_55_3_a10/}
}
TY - JOUR AU - M. S. Muminov TI - On a limit distribution of the maximal level of empirical distribution density and the regression function. I JO - Teoriâ veroâtnostej i ee primeneniâ PY - 2010 SP - 582 EP - 590 VL - 55 IS - 3 UR - http://geodesic.mathdoc.fr/item/TVP_2010_55_3_a10/ LA - ru ID - TVP_2010_55_3_a10 ER -
M. S. Muminov. On a limit distribution of the maximal level of empirical distribution density and the regression function. I. Teoriâ veroâtnostej i ee primeneniâ, Tome 55 (2010) no. 3, pp. 582-590. http://geodesic.mathdoc.fr/item/TVP_2010_55_3_a10/
[1] Smirnov N. V., “O postroenii doveritelnoi oblasti dlya plotnosti raspredeleniya sluchainoi velichiny”, Dokl. AN SSSR, 74:2 (1950), 189–191 | Zbl
[2] Smirnov N. V., “O priblizhenii plotnostei raspredeleniya sluchainykh velichin”, Uch. zap. MGPI im. V. P. Potemkina, 16:3 (1951), 69–96
[3] Smirnov N. V., “O priblizhenii plotnostei raspredeleniya sluchainykh velichin”, Teoriya veroyatnostei i matematicheskaya statistika, Izbrannye trudy, Nauka, M., 1970, 205–223 | MR
[4] Bickel P. J., Rosenblatt M., “On some global measures of the deviations of density function estimates”, Ann. Statist., 1:6 (1973), 1071–1095 | DOI | MR | Zbl
[5] Rosenblatt M., “On the maximal deviation of $k$-dimensional density estimates”, Ann. Probab., 4:6 (1976), 1009–1015 | DOI | MR | Zbl
[6] Khashimov Sh. A., Muminov M. S., “O predelnom raspredelenii maksimalnogo ukloneniya splain-otsenok plotnosti veroyatnosti”, Veroyatnostnye raspredeleniya i matematicheskaya statistika, Fan, Tashkent, 1986, 447–467 | MR
[7] Nadaraya E. A., Neparametricheskoe otsenivanie plotnosti veroyatnostei i krivoi regressii, Tbilisi, 1983, 195 pp. | MR
[8] Johnston G. J., “Probabilities of maximal deviations for nonparametric regression function estimates”, J. Multivariate Anal., 12:3 (1982), 402–414 | DOI | MR | Zbl
[9] Révész P., “On the nonparametric estimation of the regression function”, Problems of Control and Information Theory, 8:4 (1979), 297–302 | MR | Zbl
[10] Wandl H., On kernel estimation of regression functions, Wissenschaftliche sitzungen zur stochastik, 3, Berlin, 1980 | MR
[11] Liero H., “On the maximal deviation of the kernel regression functions estimate”, Math. Operationsforsch. Statist. Ser. Statist., 13:2 (1982), 171–182 | MR
[12] Hall P., “On convergence rates of suprema”, Probab. Theory Related Fields, 89:4 (1991), 447–445 | DOI | MR
[13] Konakov V. D., Piterbarg V. I., “Skorost skhodimosti raspredelenii maksimalnykh uklonenii gaussovskikh protsessov i empiricheskikh plotnostei. I”, Teoriya veroyatn. i ee primen., 27:4 (1982), 707–724 | MR | Zbl
[14] Konakov V. D., Piterbarg V. I., “Skorost skhodimosti raspredelenii maksimalnykh uklonenii gausovskikh protsessov i empiricheskikh plotnostei. II”, Teoriya veroyatn. i ee primen., 28:1 (1983), 164–169 | MR | Zbl
[15] Konakov V. D., Piterbarg V. I., “On the convergence rate of maximal deviation distribution for kernel regression estimates”, J. Multivariate Anal., 15:3 (1984), 279–294 | DOI | MR | Zbl
[16] Konakov V. D., “Utochnenie predelnykh teorem dlya maksimuma ukloneniya neparametricheskoi otsenki regresii”, 3-ya Mezhdunarodnaya Vilnyusskaya konferentsiya po teorii veroyatnostei i matematicheskoi statistike, Tezisy dokladov, v. 1, 1981, 241–242
[17] Konakov V. D., “O maksimalnykh ukloneniyakh empiricheskoi plotnosti i regressii. Nekotorye obschie metody issledovaniya”, Seminarber. (Humboldt Univ., Berlin), 51 (1983), 106–125 | MR | Zbl
[18] Konakov V. D., On convergence rate of suprema in the presence of nonnegligible trends, Preprint No 103, Institut für Andewandte Analysis und Stochastik, Berlin, 1994
[19] Rosenblatt M., “Remarks on a multivariate transformation”, Ann. Math. Statist., 23 (1952), 470–472 | DOI | MR | Zbl
[20] Konakov V. D., “Approximations of deviations fields of some nonparametric statistical estimates by Gaussian fields, invariance principles”, Lecture Notes in Math., 1021, 1983, 302–314 | MR
[21] Mikhaleva T. L., Piterbarg V. I., “O raspredelenii maksimuma gaussovskogo polya s postoyannoi dispersiei na gladkom mnogoobrazii”, Teoriya veroyatn. i ee primen., 41:2 (1996), 438–451 | MR | Zbl