ALMOST SURE CONVERGENCE RATES FOR THE ESTIMATION OF A COVARIANCE OPERATOR FOR NEGATIVELY ASSOCIATED SAMPLES

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JABARI H.; AZARNOUSH H.A.

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ISSN: 2588-4824

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Journal: JOURNAL OF THE IRANIAN STATISTICAL SOCIETY (JIRSS) Year:2006 | Volume:5 | Issue:1-2 Page(s): 53-67

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Title

ALMOST SURE CONVERGENCE RATES FOR THE ESTIMATION OF A COVARIANCE OPERATOR FOR NEGATIVELY ASSOCIATED SAMPLES

Author(s)

JABARI H. | AZARNOUSH H.A. | Issue Writer Certificate

Keywords

EMPIRICAL PROCESS

HISTOGRAM ESTIMATOR

NEGATIVE ASSOCIATION

STATIONARITY

Abstract

Let {Xn, n³1} be a strictly stationary sequence of negatively associated random variables, with common continuous and bounded distribution function F. In this paper, we consider the estimation of the two-dimensional distribution function of (X1, Xk+1) based on histogram type estimators as well as the estimation of the covariance function of the limit EMPIRICAL PROCESS induced by the sequence {Xn, n³1}. Then, we derive uniform strong convergence rates for two-dimensional distribution function of (X1,Xk+1) without any condition on the covariance structure of the variables. Finally, assuming a convenient decrease rate of the covariance’s Cov (X1,Xn+1), n³1we introduce uniform strong convergence rate for covariance function of the limit EMPIRICAL PROCESS.

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APA: Copy

JABARI, H., & AZARNOUSH, H.A.. (2006). ALMOST SURE CONVERGENCE RATES FOR THE ESTIMATION OF A COVARIANCE OPERATOR FOR NEGATIVELY ASSOCIATED SAMPLES. JOURNAL OF THE IRANIAN STATISTICAL SOCIETY (JIRSS), 5(1-2), 53-67. SID. https://sid.ir/paper/567630/en

Vancouver: Copy

JABARI H., AZARNOUSH H.A.. ALMOST SURE CONVERGENCE RATES FOR THE ESTIMATION OF A COVARIANCE OPERATOR FOR NEGATIVELY ASSOCIATED SAMPLES. JOURNAL OF THE IRANIAN STATISTICAL SOCIETY (JIRSS)[Internet]. 2006;5(1-2):53-67. Available from: https://sid.ir/paper/567630/en

IEEE: Copy

H. JABARI, and H.A. AZARNOUSH, “ALMOST SURE CONVERGENCE RATES FOR THE ESTIMATION OF A COVARIANCE OPERATOR FOR NEGATIVELY ASSOCIATED SAMPLES,” JOURNAL OF THE IRANIAN STATISTICAL SOCIETY (JIRSS), vol. 5, no. 1-2, pp. 53–67, 2006, [Online]. Available: https://sid.ir/paper/567630/en

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