Marcinkiewicz–Zygmund strong laws for -statistics of weakly dependent observations

2009 ◽  
Vol 79 (19) ◽  
pp. 2028-2036 ◽  
Author(s):  
Herold G. Dehling ◽  
Olimjon Sh. Sharipov
Keyword(s):  
Strong Laws ◽  
Dependent Observations ◽  
Weakly Dependent

BICKEL–ROSENBLATT TEST FOR WEAKLY DEPENDENT DATA

2012 ◽  
Vol 17 (3) ◽  
pp. 383-395 ◽  
Author(s):  
Janis Valeinis ◽  
Audris Locmelis
Keyword(s):  
Goodness Of Fit ◽  
Simulation Analysis ◽  
Dependent Data ◽  
Practical Implementation ◽  
Test Statistic ◽  
Goodness Of Fit Test ◽  
Dependent Observations ◽  
Simple Hypothesis ◽  
Weakly Dependent Data ◽  
Weakly Dependent

The aim of this paper is to analyze the Bickel–Rosenblatt test for simple hypothesis in case of weakly dependent data. Although the test has nice theoretical properties, it is not clear how to implement it in practice. Choosing different band-width sequences first we analyze percentage rejections of the test statistic under H0 by some empirical simulation analysis. This can serve as an approximate rule for choosing the bandwidth in case of simple hypothesis for practical implementation of the test. In the recent paper [12] a version of Neyman goodness-of-fit test was established for weakly dependent data in the case of simple hypotheses. In this paper we also aim to compare and discuss the applicability of these tests for both independent and dependent observations.

Strong Laws for Dependent Heterogeneous Processes

1991 ◽  
Vol 7 (2) ◽  
pp. 213-221 ◽  
Author(s):  
Bruce E. Hansen
Keyword(s):  
Law Of Large Numbers ◽  
Strong Mixing ◽  
Strong Law ◽  
Strong Laws ◽  
Maximal Inequalities ◽  
Large Numbers ◽  
Heterogeneous Processes ◽  
Mixing Sequences ◽  
Strong Mixing Sequences ◽  
Weakly Dependent

This paper presents maximal inequalities and strong law of large numbers for weakly dependent heterogeneous random variables. Specifically considered are Lr mixingales for r > 1, strong mixing sequences, and near epoch dependent (NED) sequences. We provide the first strong law for Lr-bounded Lr mixingales and NED sequences for 1 > r > 2. The strong laws presented for α-mixing sequences are less restrictive than the laws of McLeish [8].

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