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LARGE DEVIATION LOCAL LIMIT-THEOREMS FOR RATIO STATISTICS

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Title LARGE DEVIATION LOCAL LIMIT-THEOREMS FOR RATIO STATISTICS
 
Creator CHAGANTY, NR
SABNIS, S
 
Subject random-variables
large deviations
local limit theorems
saddle point
 
Description 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.
 
Publisher MARCEL DEKKER INC
 
Date 2011-08-18T10:31:11Z
2011-12-26T12:55:42Z
2011-12-27T05:42:06Z
2011-08-18T10:31:11Z
2011-12-26T12:55:42Z
2011-12-27T05:42:06Z
1990
 
Type Article
 
Identifier COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 19(11), 4083-4101
0361-0926
http://dx.doi.org/10.1080/03610929008830430
http://dspace.library.iitb.ac.in/xmlui/handle/10054/9979
http://hdl.handle.net/10054/9979
 
Language en