C. Tommasi, A. Lanteri, S. Leorato, J. López Fidalgo
The goal of this study is to design an experiment to detect a specific heteroscedasticity in a regression model $y_i=\eta(x_i;\beta)+\varepsilon_i$, $\varepsilon_i\sim N(0;\sigma^2 h(x_i;\gamma)), i=1,...,n$, where $\eta(x_i;\beta)$ is the mean response, $\bm{\beta}$ is a vector of coefficients and $\sigma^2 h(\bm{x}_i;\bm{\gamma})$ is the error variance depending on an unknown constant $\sigma^2$ and on a continuous positive function $h$, completely known except for a parameter vector $\gamma$. Let $\gamma_0$ such that $h(x;\gamma_0) = 1$ (homoscedastic case). To test $H_0 :\, \gamma=\gamma_0$ against a local alternative $H_1:\gamma=\gamma_0+\lambda/\sqrt{n}$ (with $\lambda\neq 0$), a likelihood-based test is usually applied. Suitable design criteria for this task are $D_s$- and KL-criteria, which are related to the noncentrality parameter of the chi-squared distribution of the likelihood-based test, and thus they maximize the asymptotic power of the test.
Keywords: $D_s$-optimality; KL-optimality; local alternatives; asymptotic power
Scheduled
GT07 Design of Experiments I
June 8, 2022 12:40 PM
Conference hall
