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March, 1993 Testing for Additivity of a Regression Function
Daniel Barry
Ann. Statist. 21(1): 235-254 (March, 1993). DOI: 10.1214/aos/1176349024


Observations $y_{ij}$ are made at points $(x_{1i},x_{2j})$ according to the model $y_{iy}=F(x_{1i},x_{2j})+e_{ij}$, where the $e_{ij}$ are independent normals with constant variance. In order to test that $F(x_1,x_2)$ is an additive function of $x_1$ and $x_2$, a likelihood ratio test is constructed comparing $F(x_1,x_2)=\mu+Z_1 (x_1)+Z_2(x_2)$ with $F(x_1,x_2)=\mu+Z_1(x_1)+Z_2(x_2)+Z(x_1,x_2)$, where $Z_1$, $Z_2$ are Brownian motions and Z is a Brownian sheet. The ratio of Brownian sheet variance to error variance $\infty$ is chosen by maximum likelihood and the likelihood ratio test statistic W of $H_0:\infty=0$ used to test for departures from additivity. The asymptotic null distribution of W is derived, and its finite sample size behaviour is compared with two standard tests in a simulation study. The W test performs well on the five alternatives considered.


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Daniel Barry. "Testing for Additivity of a Regression Function." Ann. Statist. 21 (1) 235 - 254, March, 1993.


Published: March, 1993
First available in Project Euclid: 12 April 2007

zbMATH: 0771.62033
MathSciNet: MR1212175
Digital Object Identifier: 10.1214/aos/1176349024

Primary: 62G10
Secondary: 62E20, 62M10

Rights: Copyright © 1993 Institute of Mathematical Statistics


Vol.21 • No. 1 • March, 1993
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