A note on the normal approximation error for randomly weighted self-normalized sums
نویسندگان
چکیده
منابع مشابه
A note on the normal approximation error for randomly weighted self-normalized sums
Let X = {Xn}n≥1 and Y = {Yn}n≥1 be two independent random sequences. We obtain rates of convergence to the normal law of randomly weighted self-normalized sums ψn(X,Y) = n ∑ i=1 XiYi/Vn, Vn = √ Y 2 1 + · · ·+ Y 2 n . These rates are seen to hold for the convergence of a number of important statistics, such as for instance Student’s t-statistic or the empirical correlation coefficient.
متن کاملThe asymptotic distribution of randomly weighted sums and self - normalized sums ∗
We consider the self-normalized sums Tn = ∑n i=1 XiYi/ ∑n i=1 Yi, where {Yi : i ≥ 1} are non-negative i.i.d. random variables, and {Xi : i ≥ 1} are i.i.d. random variables, independent of {Yi : i ≥ 1}. The main result of the paper is that each subsequential limit law of Tn is continuous for any non-degenerate X1 with finite expectation, if and only if Y1 is in the centered Feller class.
متن کاملNormal approximation for random sums
In this paper, we adapt the very effective Berry–Esseen theorems of Chen and Shao (2004), which apply to sums of locally dependent random variables, for use with randomly indexed sums. Our particular interest is in random variables resulting from integrating a random field with respect to a point process. We illustrate the use of our theorems in three examples; in a rather general model of the ...
متن کاملA Limit Theorem for the Moment of Self-Normalized Sums
Qing-pei Zang Department of Mathematics, Huaiyin Teachers College, Huaian 223300, China Correspondence should be addressed to Qing-pei Zang, [email protected] Received 25 December 2008; Revised 30 March 2009; Accepted 18 June 2009 Recommended by Jewgeni Dshalalow Let {X,Xn;n ≥ 1} be a sequence of independent and identically distributed i.i.d. random variables and X is in the domain of attra...
متن کاملApproximation of the tail probability of randomly weighted sums and applications
Consider the problem of approximating the tail probability of randomly weighted sums ∑n i=1 ΘiXi and their maxima, where {Xi, i ≥ 1} is a sequence of identically distributed but not necessarily independent random variables from the extended regular variation class and {Θi, i ≥ 1} is a sequence of nonnegative random variables, independent of {Xi, i ≥ 1} and satisfying certain moment conditions. ...
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: Periodica Mathematica Hungarica
سال: 2013
ISSN: 0031-5303,1588-2829
DOI: 10.1007/s10998-013-4789-8