Tests for Patterned Alternatives Using Logarithmic Quantile Estimation

We investigate the logarithmic quantile estimation (LQE) method using fully nonparametric rank statistics to test for known trend and umbrella patterns in the main effects of three widely used designs: a fixed-effect two-factor model, a mixed-effect repeated measures model, and a mixed-effect cross-...

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Bibliographic Details
Published inJournal of statistical theory and practice Vol. 15; no. 3
Main Authors Ledbetter, Mark K., Tabacu, Lucia
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.09.2021
Subjects
Mathematics and Statistics
Original Article
Probability Theory and Stochastic Processes
Statistical Theory and Methods
Statistics
Rank tests
62-02
62P10
Almost sure central limit theorem
Logarithmic quantile estimation
62G30
62G20
Patterned alternatives
Nonparametric factorial designs
62G10
62G99
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Summary:We investigate the logarithmic quantile estimation (LQE) method using fully nonparametric rank statistics to test for known trend and umbrella patterns in the main effects of three widely used designs: a fixed-effect two-factor model, a mixed-effect repeated measures model, and a mixed-effect cross-classification model. We also test for patterned alternatives in the interaction between the main effect and time in the repeated measures model. We determine the level and power of the test statistics using LQE with simulated and real data. The LQE procedure uses only the data to estimate quantiles of test statistics and does not require the estimation of the asymptotic variance nor the Satterthwaite–Smith degrees of freedom estimation. Our results show that the LQE method commonly yields conservative tests with high power when testing for patterned alternatives.
ISSN:1559-8608
1559-8616
DOI:10.1007/s42519-021-00194-z