On maximum likelihood estimation of cell probabilities in 2 × k contingency tables under negative dependence restrictions with various sampling schemes

Abstract

It is well known that dependence concepts are related to concepts of various types of stochastic orderings. Using estimation techniques developed for order restricted statistical inference we find maximum likelihood estimates of cell probabilities of 2 × k contingency table under negative dependence restrictions. Four types of sampling schemes, namely single multinomial, product multinomial, binomial and Poisson models, are considered.

Keywords:

• contingency table
• cell probabilities
• odds ratios
• negative dependence concepts
• stochastic orderings
• maximum likelihood estimate
• isotonic regression

¹current mailing address: Hyundai Villa A-206, Jayang 2 Dong 694-2, Seoul 133-192 Korea

¹current mailing address: Hyundai Villa A-206, Jayang 2 Dong 694-2, Seoul 133-192 Korea

Notes

¹current mailing address: Hyundai Villa A-206, Jayang 2 Dong 694-2, Seoul 133-192 Korea