Asymptotic Distributions and Berry-Esseen Bounds for Sums of Record Values
نویسندگان
چکیده
منابع مشابه
Berry-Esseen bounds for econometric time series
We derive uniform and non–uniform error bounds in the normal approximation under a general dependence assumption. Our method is tailor made for dynamic time series models employed in the econometric literature but it is also applicable for many other dependent processes. Neither stationarity nor any smoothness conditions of the underlying distributions are required. If the introduced weak depen...
متن کاملBerry Esseen Bounds for Combinatorial Central Limit
Berry Esseen type bounds to the normal, based on zeroand size-bias couplings, are derived using Stein’s method. The zero biasing bounds are illustrated with an application to combinatorial central limit theorems where the random permutation has either the uniform distribution or one which is constant over permutations with the same cycle type and having no fixed points. The size biasing bounds ...
متن کاملAsymptotic Refinement of the Berry-Esseen Constant
For sum of independent and identically distributed (i.i.d.) random variables {Xi}i=1, the Berry-Esseen theorem states that sup y∈< ∣∣∣∣Pr { 1 sn (X1 + X2 + · · ·+ Xn) ≤ y } − Φ(y) ∣∣∣∣ ≤ C ρ σ3 √ n , where σ and ρ are respectively the variance and the absolute third moment of the parent distribution, Φ(·) is the unit normal cumulative distribution function, and C is an absolute constant. In thi...
متن کاملBerry-esseen Bounds for Projections of Coordinate Symmetric Random Vectors
For a coordinate symmetric random vector (Y1, . . . ,Yn) = Y ∈ R, that is, one satisfying (Y1, . . . ,Yn) =d (e1Y1, . . . , enYn) for all (e1, . . . , en) ∈ {−1,1}, for which P(Yi = 0) = 0 for all i = 1,2, . . . ,n, the following Berry Esseen bound to the cumulative standard normal Φ for the standardized projection Wθ = Yθ/vθ of Y holds: sup x∈R |P(Wθ ≤ x)−Φ(x)| ≤ 2 n ∑ i=1 |θi |E|X i | + 8.4E(...
متن کاملAsymptotically optimal Berry-Esseen-type bounds for distributions with an absolutely continuous part
Recursive and closed form upper bounds are o¤ered for the Kolmogorov and the total variation distance between the standard normal distribution and the distribution of a standardized sum of n independent and identically distributed random variables. The approximation error in the CLT obtained from these new bounds vanishes at a rate O(n ); provided that the common distribution of the summands po...
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: Electronic Journal of Probability
سال: 2004
ISSN: 1083-6489
DOI: 10.1214/ejp.v9-210