Invariance under Dependence by Mixing

Invariance under Dependence by Mixing

This paper is concerned with arrays of conditionally independent random elements that become dependent by mixing. The principal focus is the preservation of properties known to hold under independence. Findings are reported in the context of limit theory, including laws of large numbers and central...

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Veröffentlicht in:Lecture Notes-Monograph Series. - Institute of Mathematical Statistics, 1982. - 16(1990) vom: Jan., Seite 283-293
1. Verfasser: Jensen, D. R. (VerfasserIn)
Format: Online-Aufsatz
Sprache:English
Veröffentlicht: 1990
Zugriff auf das übergeordnete Werk:Lecture Notes-Monograph Series
Schlagworte:Conditional independence Models for dependence Limit theory Unconditional inference Mathematics Behavioral sciences
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520 |a This paper is concerned with arrays of conditionally independent random elements that become dependent by mixing. The principal focus is the preservation of properties known to hold under independence. Findings are reported in the context of limit theory, including laws of large numbers and central limit theory, and topics in statistical inference. Several standard results, ranging from Berry-Esseén bounds in central limit theory to the use of Friedman's (1937) test in the analysis of two-way data, are seen to remain valid under certain models for dependence. The class of limit laws for standardized sums is expanded to include dependent cases, as are bounds on rates of convergence to these limits. 
540 |a Copyright 1990 Institute of Mathematical Statistics 
650 4 |a Conditional independence 
650 4 |a Models for dependence 
650 4 |a Limit theory 
650 4 |a Unconditional inference 
650 4 |a Mathematics  |x Applied mathematics  |x Statistics  |x Applied statistics  |x Descriptive statistics  |x Statistical distributions  |x Distribution functions  |x Probability distributions  |x Mathematical moments 
650 4 |a Mathematics  |x Applied mathematics  |x Statistics  |x Statistical theories  |x Law of large numbers 
650 4 |a Mathematics  |x Applied mathematics  |x Statistics 
650 4 |a Mathematics  |x Pure mathematics  |x Probability theory  |x Probabilities 
650 4 |a Mathematics  |x Mathematical objects  |x Mathematical series  |x Series convergence  |x Conditional convergence 
650 4 |a Behavioral sciences  |x Psychology  |x Cognitive psychology  |x Cognitive processes  |x Thought processes  |x Reasoning  |x Inference 
650 4 |a Mathematics  |x Pure mathematics  |x Linear algebra  |x Matrix theory  |x Matrices 
650 4 |a Mathematics  |x Pure mathematics  |x Linear algebra  |x Vector analysis  |x Mathematical vectors 
650 4 |a Mathematics  |x Pure mathematics  |x Linear algebra  |x Vector analysis  |x Vector operations  |x Scalars 
650 4 |a Mathematics  |x Pure mathematics  |x Probability theory 
655 4 |a research-article 
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