General lemmas on large deviations for the distribution density of a random vector

1991 ◽  
Vol 30 (4) ◽  
pp. 385-394
Author(s):  
L. Saulis
Keyword(s):  
Large Deviations ◽  
Random Vector ◽  
Distribution Density

The probabilities of large deviations for a certain class of statistics associated with multinomial distribution

2020 ◽  
Vol 24 ◽  
pp. 581-606
Author(s):  
Sherzod M. Mirakhmedov
Keyword(s):  
Large Deviations ◽  
Random Vector ◽  
Large Deviation ◽  
Multinomial Distribution ◽  
Negative Integer ◽  
Probabilities Of Large Deviations ◽  
Divergence Statistics ◽  
Power Divergence

Let η = (η1, …, ηN) be a multinomial random vector with parameters n = η1 + ⋯ + ηN and pm > 0, m = 1, …, N, p1 + ⋯ + pN = 1. We assume that N →∞ and maxpm → 0 as n →∞. The probabilities of large deviations for statistics of the form h1(η1) + ⋯ + hN(ηN) are studied, where hm(x) is a real-valued function of a non-negative integer-valued argument. The new large deviation results for the power-divergence statistics and its most popular special variants, as well as for several count statistics are derived as consequences of the general theorems.

scholarly journals The discounted local limit theorems for large deviations

2008 ◽  
Vol 48 ◽  
Author(s):  
Leonas Saulis ◽  
Dovilė Deltuvienė
Keyword(s):  
Large Deviations ◽  
Density Function ◽  
Limit Theorems ◽  
Distribution Density ◽  
Normal Approximation ◽  
Random Variables ◽  
Local Limit ◽  
Distribution Density Function ◽  
Local Limit Theorems

Theorems of large deviations, both in the Cramer zone and the Linnik power zones, for the normal approximation of the distribution density function of normalized sum Sv = \sum∞ k=0 vkXk, 0 < v < 1, of i.i.d. random variables (r.v.) X0, X1, . . . satisfying the generalized Bernstein’s condition are obtained.

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