Integer-Valued, Minimax Robust Designs for Estimation and Extrapolation in Heteroscedastic, Approximately Linear Models
提出一种新的稳健回归设计方法，在有限设计空间内使用模拟退火寻找整数值设计，适用于近似多项式响应和异方差情况，并扩展到外推场景，通过案例研究验证其有效性。
Abstract We present our findings on a new approach to robust regression design. This approach differs from previous investigations into this area in three respects: The use of a finite design space, the use of simulated annealing to carry out the numerical minimization problems, and in our search for integer-valued, rather than continuous, designs. We present designs for the situation in which the response is thought to be approximately polynomial. We also discuss the cases of approximate first- and second-order multiple regression. In each case we allow for possible heteroscedasticity and also obtain minimax regression weights. The results are extended to cover extrapolation of the regression response to regions outside of the design space. A case study involving dose-response experimentation is undertaken. The optimal robust designs, which protect against bias as well as variance, can be roughly described as being obtained from the classical variance-minimizing designs by replacing replicates with clusters of observations at nearby but distinct sites. Key Words: BioassayCarcinogenDose responseEfficient roundingFinite design spaceFisher consistencyLogistic modelPolynomial regressionProbit modelQuota roundingSecond-order designSimulated annealingWeighted least squares