A note on the normal approximation error for randomly weighted self-normalized sums
نویسندگان
چکیده
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.
منابع مشابه
The 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.
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ورودعنوان ژورنال:
- Periodica Mathematica Hungarica
دوره 67 شماره
صفحات -
تاریخ انتشار 2013