Minimum Distance Estimates with Rates under ø-mixing

George G. Roussas and Yannis G. Yatracos
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George G. Roussas: University of California
Yannis G. Yatracos: University of California, Santa Barbara, and Université de Montréal

Chapter 22 in Festschrift for Lucien Le Cam, 1997, pp 337-344 from Springer

Abstract: Abstract On the basis of the segment of observations X1,…, Xn from a ∅-mixing sequence of random variables, a minimum distance estimate $$ {{\hat{P}}_{n}} $$ of the probability measure P,governing the process, is constructed. Under suitable regularity conditions, it is shown that $$ {{\hat{P}}_{n}} $$ is weakly uniformly consistent, within the class P of assumed probability measures, at the same rate as in the independent identically distributed case. Strengthening of the underlying assumptions provides for strong consistency.

Keywords: Probability Measure; Strong Consistency; Hellinger Distance; Total Variation Distance; Kolmogorov Entropy (search for similar items in EconPapers)
Date: 1997
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-1880-7_22

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DOI: 10.1007/978-1-4612-1880-7_22

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