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Research & Reviews : Journal of Statistics

A Density Version of A Local Limit Theorem for Properly Normalised Weighted Sums

  1. KN Raviprakash
  2. K. Vidyalaxmi
  3. Gooty Divanji

Abstract

Let   n X ,n 1 be a sequence of i.i.d. random variables with a common distribution function F with1 EX  0 . Let nn kk 1S X , n 1  andnn kk 1kT f Xn      , where f is positive, non -decreasing and continuous on [0,1] with f(1) 1. Let   k n be an integer sequence suchthat,1n n n nk k k kZ B T A    , where nk(A ) and nk(B  0) are sequences of normingconstants with nkB  as k. We obtain a moment convergence result for nkZ anda density version of a local limit theorem when distribution function F belongs to the domainof partial attraction of a semistable law.

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