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Please use this identifier to cite or link to this item: http://dspace.library.iitb.ac.in/jspui/handle/10054/9979

Title: LARGE DEVIATION LOCAL LIMIT-THEOREMS FOR RATIO STATISTICS
Authors: CHAGANTY, NR
SABNIS, S
Keywords: random-variables
Issue Date: 1990
Publisher: MARCEL DEKKER INC
Citation: COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 19(11), 4083-4101
Abstract: Let {T(n), n greater-than-or-equal-to 1} be an arbitrary sequence of nonlattice random variables and let {S(n), n greater-than-or-equal-to 1} be another sequence of positive random variables. Assume that the sequences are independent. In this paper we obtain asymptotic expression for the density function of the ratio statistic R(n) = T(n)/S(n) based on simple conditions on the moment generating functions of T(n) and S(n). When S(n) = n, our main result reduces to that of Chaganty and Sethuraman[Ann. Probab. 13(1985):97-114]. We also obtain analogous results when T(n) and S(n) are both lattice random variables. We call our theorems large deviation local limit theorems for R(n), since the conditions of our theorems imply that R(n) --> c in probability for some constant c. We present some examples to illustrate our theorems.
URI: http://dx.doi.org/10.1080/03610929008830430
http://dspace.library.iitb.ac.in/xmlui/handle/10054/9979
http://hdl.handle.net/10054/9979
ISSN: 0361-0926
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