WeiYa's Work Yard

A dog, who fell into the ocean of statistics, tries to write down his ideas and notes to save himself.

Test of Monotonicity by Calibrating for Linear Functions

Posted on (Update: )
Tags: Monotone Function

This note is for Hall, P., & Heckman, N. E. (2000). Testing for Monotonicity of a Regression Mean by Calibrating for Linear Functions. The Annals of Statistics, 28(1), 20–39.

The bandwidth test will generally perform well if the regression function does not have any flat or nearly flat parts,

Let $0 \le r\le s-2\le n-2$ be integers, let $a, b$ be constants and put

\[S(a, b\mid r,s) = \sum_{i=r+1}^s[Y_i-(a+bx_i)]^2\]

For each choice of $(r, s)$, define $\hat a = \hat a(r, s)$ and $\hat b = \hat b(r, s)$ by

\[(\hat a, \hat b) = \argmin_{(a, b)} S(a, b\mid r, s)\]

Published in categories Note