Robust Hypothesis Testing and Robust Time Series Interpolation And Regression

Abstract. Recent results on minimax robust time series interpolation and regression coefficient estimation are generalized and extended through a relationship with robust hypothesis testing. The spectral uncertainty classes in the time series problems are assumed to be convex and to satisfy an integral constraint such as on the variance of the process. It is shown that robust solutions in such cases can always be obtained from the least-favourable probability density functions for corresponding hypothesis testing problems. A specific class, the bounded spectral densities from the band model, is considered to illustrate the results.