Dewan, Isha ; Prakasa Rao, B. L. S.
(1999)
*A general method of density estimation for associated random variables*
Journal of Nonparametric Statistics, 10
(4).
pp. 405-420.
ISSN 1048-5252

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Official URL: http://www.tandfonline.com/doi/abs/10.1080/1048525...

Related URL: http://dx.doi.org/10.1080/10485259908832769

## Abstract

Let {X_{n};n≥1} be a sequence of stationary associated random variables having a common marginal density function f(x). Let Φ_{n}(x, y), n=1,2,..., be a sequence of Borel-measurable functions defined on R^{2}. Let f_{n}(x)=1/nΣ^{n}_{k=1}Φ_{n}(x, X_{k}) be the empirical density function. Here we study a set of sufficient conditions under which the probability Pr(sup_{a+δ≤x≤b-δ}|f_{n}(x)-f(x)|>ε→0 at an exponential rate as n → ∞ where the rate possibly depends on ε, δ and f and [a, b] is a finite or an infinite interval.

Item Type: | Article |
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Source: | Copyright of this article belongs to Taylor and Francis Group. |

Keywords: | Density Estimation; Associated Random Variables; Uniform Consistency; Exponential Rate |

ID Code: | 73748 |

Deposited On: | 07 Dec 2011 05:35 |

Last Modified: | 07 Dec 2011 05:35 |

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