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Abstract:

In this paper strong consistency and uniform complete consistency of the nonparametric density estimator proposed by D. O. Loftsgaarden and C. D. Quesenberry (Ann. Math. Statist. 36 (1965), 1049-1051) is proved for φ{symbol}-mixing and α-mixing processes. © 1988.

Registro:

Documento: Artículo
Título:Consistency of a nonparametric estimate of a density function for dependent variables
Autor:Boente, G.; Fraiman, R.
Filiación:CONICET, U.B.A., Buenos Aires, Argentina
Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, U.B.A., Buenos Aires, Argentina
Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, U.B.A., Buenos Aires, Argentina
Palabras clave:nearest neighbor method; nonparametric density estimators; α-mixing processes; φ{symbol}-mixing
Año:1988
Volumen:25
Número:1
Página de inicio:90
Página de fin:99
DOI: http://dx.doi.org/10.1016/0047-259X(88)90154-6
Título revista:Journal of Multivariate Analysis
Título revista abreviado:J. Multivariate Anal.
ISSN:0047259X
CODEN:JMVAA
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0047259X_v25_n1_p90_Boente

Referencias:

  • Billingsley, (1968) Convergence of Probability Measures, , Wiley, New York
  • Collomb, Propriétés de convergence presque complète du prédicteur à noyau (1984) Z. Wahrsch. Verw. Gebiete, 66, pp. 441-460
  • Devroye, Wagner, The strong uniform consistency of nearest neighbor density estimates (1977) The Annals of Statistics, 5, pp. 536-540
  • Doukhan, Leon, Portal, Vitesse de convergence dans le théorème central limite pour des variables aléatoires mélangeantes à valeurs dans un espace de Hilbert (1984) C. R. Acad. Sci. Paris, 289, pp. 305-308
  • Loftsgaarden, Quesenberry, A nonparametric estimate of a multivariate density function (1965) The Annals of Mathematical Statistics, 36, pp. 1049-1051
  • Mack, Rosenblatt, Multivariate k-nearest neighbor density estimates (1979) J. Multivariate Anal., 9, pp. 1-15
  • Moore, Henrichon, Uniform consistency of some estimates of a density function (1969) The Annals of Mathematical Statistics, 40, pp. 1499-1502
  • Moore, Yackel, Consistency properties of nearest neighbor density estimates (1977) The Annals of Statistics, 5, pp. 143-154
  • Moore, Yackel, Large sample properties of nearest neighbor density function estimators (1977) Statistical Decision Theory and Related Topics, , S.S Gupta, D.S Moore, Academic Press, New York
  • Rosenblatt, A central limit theorem and a strong mixing condition (1956) Proceedings of the National Academy of Sciences, 42, pp. 43-47
  • Wagner, Strong consistency of a nonparametric estimate of a density function (1973) IEEE Trans. Systems Man Cybernet., 3, pp. 289-290
  • Wheeden, Zygmund, (1977) Measure and Integral, , Dekker, New York

Citas:

---------- APA ----------
Boente, G. & Fraiman, R. (1988) . Consistency of a nonparametric estimate of a density function for dependent variables. Journal of Multivariate Analysis, 25(1), 90-99.
http://dx.doi.org/10.1016/0047-259X(88)90154-6
---------- CHICAGO ----------
Boente, G., Fraiman, R. "Consistency of a nonparametric estimate of a density function for dependent variables" . Journal of Multivariate Analysis 25, no. 1 (1988) : 90-99.
http://dx.doi.org/10.1016/0047-259X(88)90154-6
---------- MLA ----------
Boente, G., Fraiman, R. "Consistency of a nonparametric estimate of a density function for dependent variables" . Journal of Multivariate Analysis, vol. 25, no. 1, 1988, pp. 90-99.
http://dx.doi.org/10.1016/0047-259X(88)90154-6
---------- VANCOUVER ----------
Boente, G., Fraiman, R. Consistency of a nonparametric estimate of a density function for dependent variables. J. Multivariate Anal. 1988;25(1):90-99.
http://dx.doi.org/10.1016/0047-259X(88)90154-6