Nonparametric Bayesian testing for monotonicity

Testing strict monotonicity in nonparametric regression

A new test for strict monotonicity of the regression function is proposed which is based on a composition of an estimate of the inverse of the regression function with a common regression estimate. This composition is equal to the identity if and only if the “true” regression function is strictly monotone, and a test based on an L2-distance is investigated. The asymptotic normality of the corre...

www.econstor.eu Testing strict monotonicity in nonparametric regression

A new test for strict monotonicity of the regression function is proposed which is based on a composition of an estimate of the inverse of the regression function with a common regression estimate. This composition is equal to the identity if and only if the “true” regression function is strictly monotone, and a test based on an L2-distance is investigated. The asymptotic normality of the corre...

Bayesian nonparametric multiple testing

Multiple testing, or multiplicity problems often require testing several means with the assumption that we will reject infrequently, as motivated by the need to analyze DNA microarray data. The goal is to keep the combined rate of false discoveries and non-discoveries as small as possible. We propose a discrete approximation to a Polya tree prior that enjoys fast, conjugate updating, centered a...

On Testing Positivity/Monotonicity/Convexity of nonparametric Signals

Bayesian Nonparametric Approach to Multiple Testing

Motivated by the problems in genomics, astronomy and some other emerging fields, multiple hypothesis testing has come to the forefront of statistical research in the recent years. In the context of multiple testing, new error measures such as the false discovery rate (FDR) occupy important roles comparable to the role of type I error in classical hypothesis testing. Assuming that a random mecha...