An Exponential Nonuniform Berry-Esseen Bound for Self-Normalized Sums
نویسندگان
چکیده
منابع مشابه
The Berry-esseen Bound for Character Ratios
Let λ be a partition of n chosen from the Plancherel measure of the symmetric group Sn, let χλ(12) be the irreducible character of the symmetric group parameterized by λ evaluated on the transposition (12), and let dim(λ) be the dimension of the irreducible representation parameterized by λ. Fulman recently obtained the convergence rate of O(n−s) for any 0 < s < 1 2 in the central limit theorem...
متن کاملA Berry - Esseen bound for the uniform multinomial occupancy model ∗
The inductive size bias coupling technique and Stein’s method yield a Berry-Esseen theorem for the number of urns having occupancy d ≥ 2 when n balls are uniformly distributed over m urns. In particular, there exists a constant C depending only on d such that sup z∈R |P (Wn,m ≤ z)− P (Z ≤ z)| ≤ C σn,m 1 + ( n m )3 for all n ≥ d and m ≥ 2, where Wn,m and σ 2 n,m are the standardized count and va...
متن کاملA Berry-Esseen Type Bound for the Kernel Density Estimator of Length-Biased Data
Length-biased data are widely seen in applications. They are mostly applicable in epidemiological studies or survival analysis in medical researches. Here we aim to propose a Berry-Esseen type bound for the kernel density estimator of this kind of data.The rate of normal convergence in the proposed Berry-Esseen type theorem is shown to be O(n^(-1/6) ) modulo logarithmic term as n tends to infin...
متن کاملA Berry-Esseen Type Bound for a Smoothed Version of Grenander Estimator
In various statistical model, such as density estimation and estimation of regression curves or hazard rates, monotonicity constraints can arise naturally. A frequently encountered problem in nonparametric statistics is to estimate a monotone density function f on a compact interval. A known estimator for density function of f under the restriction that f is decreasing, is Grenander estimator, ...
متن کاملAn Improved Mordell Type Bound for Exponential Sums
where ep(·) is the additive character ep(·) = e2πi·/p on the finite field Zp. For χ = χ0, the principal character, the sum is just a pure exponential sum S(χ0, f) = ∑p−1 x=1 ep(f(x)). Of course S(χ, f) = 0 unless χ(p−1)/d = χ0 where d = (k1, ..., kr, p− 1), as is easily seen from the change of variables x → xu if there is a u with u = 1 and χ(u) 6= 1. The classical Weil bound [12] (see [2] or [...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Annals of Probability
سال: 1999
ISSN: 0091-1798
DOI: 10.1214/aop/1022874829