Self-normalized processes are of common occurrence in probabilistic and statistical studies.
A prototypical example is Student's t-statistic introduced in 1908 by Gosset, whose portrait is …

Consider $ d $ dependent change point tests, each based on a CUSUM-statistic. We
provide an asymptotic theory that allows us to deal with the maximum over all test statistics …

Cramér type moderate deviation theorems quantify the accuracy of the relative error of the
normal approximation and provide theoretical justifications for many commonly used …

Limiting behavior of weighted sums of iid random variables - ScienceDirect Skip to main
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Abstract Let X_1,X_2,..., be independent random variables with EX_i=0 and write
S_n=i=1^nX_i and V_n^2=i=1^nX_i^2. This paper provides an overview of current …

We establish the asymptotic validity of the bootstrap-based IVX estimator proposed by
Phillips and Magdalinos (2009) for the predictive regression model parameter based on a …

The present paper first shows that, without any dependent structure assumptions for a
sequence of random variables, the refined results of the complete convergence for the …

The geometry of unit $ N $-dimensional $\ell_ {p} $ balls has been intensively investigated
in the past decades. A particular topic of interest has been the study of the asymptotics of …

Let (X i) i≥ 1 be a stationary sequence. Denote m=⌊ n α⌋, 0< α< 1, and k=⌊ n∕ m⌋,
where⌊ a⌋ stands for the integer part of a. Set S j∘=∑ i= 1 m X m (j− 1)+ i, 1≤ j≤ k, and (V …

In safe offline reinforcement learning (RL), the objective is to develop a policy that
maximizes cumulative rewards while strictly adhering to safety constraints, utilizing only …