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Complete consistency for recursive probability density estimator of widely orthant dependent samples

Wybrane pełne teksty z tego czasopisma
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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, we will study the recursive density estimators of the probability density function for widely orthant dependent (WOD) random variables. The complete consistency and complete convergence rate are established under some general conditions.
Rocznik
Strony
127--138
Opis fizyczny
Bibliogr. 22 poz.
Twórcy
  • School of Mathematical Sciences, Anhui University, P.R. China
autor
  • Department of Mathematics and Computer Sciences, Chizhou University, P.R. China
Bibliografia
  • [1] Y. Chen, L. Wang, and Y. Wang, Uniform asymptotics for the finite-time ruin probabilities of two kinds of nonstandard bidimensional risk models, J. Math. Anal. Appl. 401 (2013), pp. 114-129.
  • [2] T. Hu, Negatively superadditive dependence of random variables with applications, Chinese J. Appl. Probab. Statist. 16 (2000), pp. 133-144.
  • [3] K. Joag-Dev and F. Proschan, Negative association of random variables with applications, Ann. Statist. 11 (1983), pp. 286-295.
  • [4] E. Lehmann, Some concepts of dependence, Ann. Math. Statist. 37 (1966), pp. 1137-1153.
  • [5] Y. Li, On the rate of strong convergence for a recursive probability density estimator of END samples and its applications, J. Math. Inequal. 11 (2) (2017), pp. 335-343.
  • [6] Y. Li, C. Wei, and S. Yang, The recursive kernel distribution function estimator based on negatively and positively associated sequences, Comm. Statist. Theory Methods 39 (20) (2010), pp. 3585-3595.
  • [7] Y. Li and S. Yang, Strong convergence rate of recursive probability density estimators for NA sequences, Chinese J. Engrg. Math. 22 (4) (2005), pp. 659-665.
  • [8] H. Liang and J. Baek, Asymptotic normality of recursive density estimates under some dependence assumptions, Metrika 60 (2004), pp. 155-166.
  • [9] L. Liu, Precise large deviations for dependent random variables with heavy tails, Statist. Probab. Lett. 79 (2009), pp. 1290-1298.
  • [10] E. Masry, Recursive probability density estimation for weakly dependent stationary processes, IEEE Trans. Inform. Theory 32 (2) (1986), pp. 254-267.
  • [11] E. Parzen, On estimation of a probability density function and mode, Ann. Math. Statist. 33 (1962), pp. 1065-1076.
  • [12] D. Qiu and P. Chen, Complete and complete moment convergence for weighted sums of widely orthant dependent random variables, Acta Math. Sin. (Engl. Ser.) 30 (2014), pp. 1539-1548.
  • [13] M. Rosenblatt, A central limit theorem and a strong mixing condition, Proc. Natl. Acad. Sci. USA 42 (1956), pp. 43-47.
  • [14] A. Shen, Bernstein-type inequality for widely dependent sequence and its application to nonparametric regression models, Abstr. Appl. Anal. (2013), Article ID 862602.
  • [15] A. Shen, On asymptotic approximation of inverse moments for a class of nonnegative random variables, Statistics 48 (2014), pp. 1371-1379.
  • [16] K. Wang, Y. Wang, and Q. Gao, Uniform asymptotics for the finite-time ruin probability of a new dependent risk model with a constant interest rate, Methodol. Comput. Appl. Probab. 15 (2013), pp. 109-124.
  • [17] X. Wang, Y. Wu, and A. Rosalsky, Complete convergence for arrays of rowwise widely orthant dependent random variables and its applications, Stochastics 89 (8) (2017), pp. 1228-1252.
  • [18] X. Wang, C. Xu, T.-C. Hu, A. Volodin, and S. Hu, On complete convergence for widely orthant-dependent random variables and its applications in nonparametric regression models, TEST 23 (2014), pp. 607-629.
  • [19] Y. Wang and D. Cheng, Basic renewal theorems for random walks with widely dependent increments, J. Math. Anal. Appl. 384 (2011), pp. 597-606.
  • [20] C. Wolverton and T. Wagner, Asymptotically optimal discriminant functions for pattern classification, IEEE Trans. Inform. Theory 15 (1969), pp. 258-265.
  • [21] S. Yang, Consistency of nearest neighbor estimator of density function for negative associated samples, Acta Math. Appl. Sin. 26 (3) (2003), pp. 385-395.
  • [22] W. Yang, T. Liu, X. Wang, and S. Hu, On the Bahadur representation of sample quantiles for widely orthant dependent sequences, Filomat 28 (2014), pp. 1333-1343.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-815cf01e-9b63-4d0c-9471-280254d8d704
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