Serial Correlation in Contingency Tables

Arbeitspapier

Pearson's chi-squared test for independence in two-way contingency tables is developed under the assumption of multinomial sampling. In this paper I consider the case where draws are not independent but exhibit serial dependence. I derive the asymptotic distribution and show that adjusting Pearson's statistic is simple and works reasonably well irrespective whether the processes are Markov chains or m-dependent. Moreover, I propose a test for independence that has a simple limiting distribution if at least one of the two processes is a Markov chain. For three-way tables I investigate the Cochrane-Mantel-Haenszel (CMH) statistic and show that there exists a closely related procedure that has power against a larger class of alternatives. This new statistic might be used to test whether a Markov chain is simple against the alternative of being a Markov chain of higher order. Monte Carlo experiments are used to illustrate the small sample properties.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: Working Paper ; No. 228

Classification and Topics

• Classification: Wirtschaft ; Hypothesis Testing: General ; Semiparametric and Nonparametric Methods: General ; Model Evaluation, Validation, and Selection
• Subject: Goodness of Fit ; Independence Tests ; Cochrane-Mantel-Haenszel Test ; Markov chain

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Elsinger, Helmut
• Event: Veröffentlichung
• (who): Oesterreichische Nationalbank (OeNB)
• (where): Vienna
• (when): 2020

Further information

• Handle: http://hdl.handle.net/10419/264820
• Last update: 10.03.2025, 11:41 AM CET