scholarly journals A New Class of Robust Two-Sample Wald-Type Tests

2018 ◽  
Vol 14 (2) ◽  
Author(s):  
Abhik Ghosh ◽  
Nirian Martin ◽  
Ayanendranath Basu ◽  
Leandro Pardo
Keyword(s):  
Clinical Trials ◽  
Hypothesis Testing ◽  
Real Data ◽  
Nuisance Parameters ◽  
Medical Sciences ◽  
Density Power Divergence ◽  
Minimum Density ◽  
New Class ◽  
Composite Hypotheses ◽  
Power Divergence

Abstract Parametric hypothesis testing associated with two independent samples arises frequently in several applications in biology, medical sciences, epidemiology, reliability and many more. In this paper, we propose robust Wald-type tests for testing such two sample problems using the minimum density power divergence estimators of the underlying parameters. In particular, we consider the simple two-sample hypothesis concerning the full parametric homogeneity as well as the general two-sample (composite) hypotheses involving some nuisance parameters. The asymptotic and theoretical robustness properties of the proposed Wald-type tests have been developed for both the simple and general composite hypotheses. Some particular cases of testing against one-sided alternatives are discussed with specific attention to testing the effectiveness of a treatment in clinical trials. Performances of the proposed tests have also been illustrated numerically through appropriate real data examples.

Minimum density power divergence estimator for GARCH models

Test ◽  
2008 ◽  
Vol 18 (2) ◽  
pp. 316-341 ◽  
Author(s):  
Sangyeol Lee ◽  
Junmo Song
Keyword(s):  
Garch Models ◽  
Density Power Divergence ◽  
Minimum Density ◽  
Power Divergence

A new class of regression model for a bounded response with application in the study of the incidence rate of colorectal cancer

2019 ◽  
Vol 29 (7) ◽  
pp. 2015-2033
Author(s):  
Vicente G Cancho ◽  
Jorge L Bazán ◽  
Dipak K Dey
Keyword(s):  
Colorectal Cancer ◽  
Regression Model ◽  
Incidence Rate ◽  
Regression Models ◽  
Real Data ◽  
Unit Interval ◽  
Open Unit ◽  
Medical Sciences ◽  
New Class ◽  
New Family

Response variables in medical sciences are often bounded, e.g. proportions, rates or fractions of incidence of some disease. In this work, we are interested to study if some characteristics of the population, e.g. sex and race which can explain the incidence rate of colorectal cancer cases. To accommodate such responses, we propose a new class of regression models for bounded response by considering a new distribution in the open unit interval which includes a new parameter to make a more flexible distribution. The proposal is to obtain compound power normal distribution as a base distribution with a quantile transformation of another family of distributions with the same support and then is to study some properties of the new family. In addition, the new family is extended to regression models as an alternative to the regression model with a unit interval response. We also present inferential procedures based on the Bayesian methodology, specifically a Metropolis–Hastings algorithm is used to obtain the Bayesian estimates of parameters. An application to real data to illustrate the use of the new family is considered.

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