### An Omnibus Test for Departures from Constant Mean

Daniel Barry and J. A. Hartigan
Source: Ann. Statist. Volume 18, Number 3 (1990), 1340-1357.

#### Abstract

Observations $y_i$ are made at points $x_i$ according to the model $y_i = F(x_i) + e_i$, where the $e_i$ are independent normals with constant variance. In order to decide whether or not $F(x)$ is constant, a likelihood ratio test is constructed, comparing $F(x) \equiv \mu$ with $F(x) = \mu + Z(x)$, where $Z(x)$ is a Brownian motion. The ratio of error variance to Brownian motion variance is chosen to maximize the likelihood, and the resulting maximum likelihood statistic $B$ is used to test departures from constant mean. Its asymptotic distribution is derived and its finite sample size behavior is compared with five other tests. The $B$-statistic is comparable or superior to each of the tests on the five alternatives considered.

First Page:
Primary Subjects: 62G10
Secondary Subjects: 62E20, 62M10
Full-text: Open access

Permanent link to this document: http://projecteuclid.org/euclid.aos/1176347753
Digital Object Identifier: doi:10.1214/aos/1176347753
Mathematical Reviews number (MathSciNet): MR1062712
Zentralblatt MATH identifier: 0706.62046