A Semiparametric Tilt Optimality Model

Chathurangi H. Pathiravasan and Bhaskar Bhattacharya ()
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Chathurangi H. Pathiravasan: Department of Biostatistics, Boston University School of Public Health, Boston, MA 02118, USA
Bhaskar Bhattacharya: School of Mathematical and Statistical Sciences, Southern Illinois University Carbondale, Carbondale, IL 62901, USA

Stats, 2022, vol. 6, issue 1, 1-16

Abstract: Practitioners often face the situation of comparing any set of k distributions, which may follow neither normality nor equality of variances. We propose a semiparametric model to compare those distributions using an exponential tilt method. This extends the classical analysis of variance models when all distributions are unknown by relaxing its assumptions. The proposed model is optimal when one of the distributions is known. Large-sample estimates of the model parameters are derived, and the hypotheses for the equality of the distributions are tested for one-at-a-time and simultaneous comparison cases. Real data examples from NASA meteorology experiments and social credit card limits are analyzed to illustrate our approach. The proposed approach is shown to be preferable in a simulated power comparison with existing parametric and nonparametric methods.

Keywords: constraints; exponential tilt; goodness-of-fit tests; information projection; Kullback–Leibler divergence; maximum entropy (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2022
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