Risk bounds are derived for regression estimation based on model selection over an unrestricted number of models. While a large list of models provides more flexibility, significant selection bias may occur with model selection criteria like AIC. We incorporate a model complexity penalty term in AIC to handle selection bias. Resulting estimators are shown to achieve a trade-off among approximat...

This paper provides a regression model in which both covariates and responses are angular variables. The regression curve is expressed as a form of the Möbius circle transformation. The angular error is assumed to follow a wrapped Cauchy or, equivalently, circular Cauchy distribution. A bivariate circular distribution is proposed to model our circular regression. Some properties of the regressi...

Logistic regression analysis is used to model categorical dependent variable. It is usually used in social sciences and clinical research. Human thoughts and disease diagnosis in clinical research contain vagueness. This situation leads researchers to combine fuzzy set and statistical theories. Fuzzy logistic regression analysis is one of the outcomes of this combination and it is used in situa...