On one homogeneity test based on quadratic deviations between kernel estimators of a distribution density in $p\geq 2$ independent samples
Teoriâ veroâtnostej i ee primeneniâ, Tome 63 (2018) no. 4, pp. 654-668 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A homogeneity test is constructed based on kernel-type estimators of a distribution density. The limit power of the test thus constructed is found for Pitman-type close alternatives.
Keywords: homogeneity hypothesis, test power, kernel estimator of density, limit theorem, Brownian bridges.
@article{TVP_2018_63_4_a1,
     author = {P. Babilua and E. A. Nadaraya},
     title = {On one homogeneity test based on quadratic deviations between kernel estimators of a distribution density in $p\geq 2$ independent samples},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {654--668},
     year = {2018},
     volume = {63},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2018_63_4_a1/}
}
TY  - JOUR
AU  - P. Babilua
AU  - E. A. Nadaraya
TI  - On one homogeneity test based on quadratic deviations between kernel estimators of a distribution density in $p\geq 2$ independent samples
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 2018
SP  - 654
EP  - 668
VL  - 63
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/TVP_2018_63_4_a1/
LA  - ru
ID  - TVP_2018_63_4_a1
ER  - 
%0 Journal Article
%A P. Babilua
%A E. A. Nadaraya
%T On one homogeneity test based on quadratic deviations between kernel estimators of a distribution density in $p\geq 2$ independent samples
%J Teoriâ veroâtnostej i ee primeneniâ
%D 2018
%P 654-668
%V 63
%N 4
%U http://geodesic.mathdoc.fr/item/TVP_2018_63_4_a1/
%G ru
%F TVP_2018_63_4_a1
P. Babilua; E. A. Nadaraya. On one homogeneity test based on quadratic deviations between kernel estimators of a distribution density in $p\geq 2$ independent samples. Teoriâ veroâtnostej i ee primeneniâ, Tome 63 (2018) no. 4, pp. 654-668. http://geodesic.mathdoc.fr/item/TVP_2018_63_4_a1/

[1] N. H. Anderson, P. Hall, D. M. Titterington, “Two-sample test statistics for measuring discrepancies between two multivariate probability density functions using kernel-based density estimates”, J. Multivariate Anal., 50:1 (1994), 41–54 | DOI | MR | Zbl

[2] E. A. Nadaraya, “Predelnoe raspredelenie kvadraticheskogo raskhozhdeniya dvukh neparametricheskikh otsenok plotnosti raspredeleniya”, Soobsch. AN GSSR, 78:1 (1975), 25–28 | MR | Zbl

[3] J. Komlós, P. Major, G. Tusnády, “An approximation of partial sums of independent $\mathrm{RV}$'s and the sample $\mathrm{DF}$. I”, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 32:1-2 (1975), 111–131 | DOI | MR | Zbl

[4] P. Hall, “Limit theorems for stochastic measures of the accuracy of density estimators”, Stochastic Process. Appl., 13:1 (1982), 11–25 | DOI | MR | Zbl

[5] E. A. Nadaraya, Nonparametric estimation of probability densities and regression curves, Math. Appl. (Soviet Ser.), 20, Kluwer Acad. Publ., Dordrecht, 1989, x+213 pp. | DOI | MR | MR | Zbl | Zbl

[6] P. J. Bickel, M. Rosenblatt, “On some global measures of the deviations of density function estimates”, Ann. Statist., 1:6 (1973), 1071–1095 | DOI | MR | Zbl

[7] G. K. Bhattacharyya, G. G. Roussas, “Estimation of a certain functional of a probability density function”, Skand. Aktuarietidskr., 1969 (1969), 201–206 | MR | Zbl

[8] D. M. Mason, E. Nadaraya, G. Sokhadze, “Integral functionals of the density”, Nonparametrics and robustness in modern statistical inference and time series analysis: a Festschrift in honor of Professor Jana Jurečková, Inst. Math. Stat. (IMS) Collect., 7, Inst. Math. Statist., Beachwood, OH, 2010, 153–168 | DOI | MR

[9] E. A. Nadaraya, “On non-parametric estimates of density functions and regression curves”, Theory Probab. Appl., 10:1 (1965), 186–190 | DOI | MR | Zbl