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The problem of testing equality of means of a bivariate normal distribution on the basis of a sample of size n has been considered when the labels of the observations are either missing or not known. The problem may arise in many applied settings, especially in genetics. Classical likelihood ratio test fails here because of identifiability problems. We propose a two-stage testing procedure using a recently developed test in the context of penalized splines. The proposed testing procedure is found to outperform the tests proposed in the literature. Copyright © 2017 John Wiley & Sons, Ltd.

The problem of testing equality of means of a bivariate normal distribution on the basis of a sample of size n has been considered when the labels of the observations are either missing or not known. The problem may arise in many applied settings, especially in genetics. Classical likelihood ratio test fails here because of identifiability problems. We propose a two-stage testing procedure using a recently developed test in the context of penalized splines. The proposed testing procedure is found to outperform the tests proposed in the literature. Copyright © 2017 John WileySons, Ltd.

Inference on the difference between two binomial proportions in the paired binomial setting is often an important problem in many biomedical investigations. Tang et al. (2010, Statistics in Medicine) discussed six methods to construct confidence intervals (henceforth, we abbreviate it as CI) for the difference between two proportions in paired binomial setting using method of variance estimates recovery. In this article, we propose weighted profile likelihood-based CIs for the difference between proportions of a paired binomial distribution. However, instead of the usual likelihood, we use weighted likelihood that is essentially making adjustments to the cell frequencies of a 2 × 2 table in the spirit of Agresti and Min (2005, Statistics in Medicine). We then conduct numerical studies to compare the performances of the proposed CIs with that of Tang et al. and Agresti and Min in terms of coverage probabilities and expected lengths. Our numerical study clearly indicates that the weighted profile likelihood-based intervals and Jeffreys interval (cf. Tang et al.) are superior in terms of achieving the nominal level, and in terms of expected lengths, they are competitive. Finally, we illustrate the use of the proposed CIs with real-life examples. Copyright © 2014 John Wiley & Sons, Ltd.

The article considers regression models for binary response in a situation when the response is subject to classification error. It is also assumed that some of the covariates are unobservable, but measurements on its surrogates are available. Likelihood based analysis is developed to fit the model. A sensitivity analysis is also carried out through simulation to ascertain the effect of ignoring classification error and/or measurement error on the estimation of regression parameters. At the end, the methodology developed in this paper is illustrated through an example.