Limit distribution of a statistic of type x2 for weakly dependent observations

1988 ◽  
Vol 43 (1) ◽  
pp. 2179-2183
Author(s):  
G. R. Abdyusheva
Keyword(s):  
Limit Distribution ◽  
Dependent Observations ◽  
Distribution Of A Statistic ◽  
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.

scholarly journals Inference Under Random Limit Bootstrap Measures

Econometrica ◽  
2020 ◽  
Vol 88 (6) ◽  
pp. 2547-2574
Author(s):  
Giuseppe Cavaliere ◽  
Iliyan Georgiev
Keyword(s):  
Limit Distribution ◽  
Linear Models ◽  
Sufficient Conditions ◽  
Conditional Inference ◽  
Specification Tests ◽  
Inference Problems ◽  
Kolmogorov Smirnov ◽  
Distribution Of A Statistic ◽  
Random Limit ◽  
Bootstrap Distribution

Asymptotic bootstrap validity is usually understood as consistency of the distribution of a bootstrap statistic, conditional on the data, for the unconditional limit distribution of a statistic of interest. From this perspective, randomness of the limit bootstrap measure is regarded as a failure of the bootstrap. We show that such limiting randomness does not necessarily invalidate bootstrap inference if validity is understood as control over the frequency of correct inferences in large samples. We first establish sufficient conditions for asymptotic bootstrap validity in cases where the unconditional limit distribution of a statistic can be obtained by averaging a (random) limiting bootstrap distribution. Further, we provide results ensuring the asymptotic validity of the bootstrap as a tool for conditional inference, the leading case being that where a bootstrap distribution estimates consistently a conditional (and thus, random) limit distribution of a statistic. We apply our framework to several inference problems in econometrics, including linear models with possibly nonstationary regressors, CUSUM statistics, conditional Kolmogorov–Smirnov specification tests and tests for constancy of parameters in dynamic econometric models.

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