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Discrete minimax designs for regression models with autocorrelated MA errors. (English) Zbl 1115.62075

Summary: Minimax robust designs for regression models with possible misspecification in the response and possible autocorrelated errors are investigated on discrete design spaces. The designs minimize the maximum value of the trace of the mean squared error (MSE) matrix, and the maximum is obtained over a class of departure functions from the regression response and a class of autocorrelated errors. In particular, classes of moving average error processes are studied. The maximum value of the trace of MSE is obtained analytically, and the minimax designs can be computed through an annealing algorithm. Several examples are given to show robust designs for polynomial regression.

MSC:

62K05 Optimal statistical designs
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62K25 Robust parameter designs
62F35 Robustness and adaptive procedures (parametric inference)
62J05 Linear regression; mixed models

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