Simultaneous estimation of the mean and the variance in heteroscedastic Gaussian regression


Abstract: Let Y be a Gaussian vector of R of mean s and diagonal covariance matrix Γ. Our aim is to estimate both s and the entries σi = Γi,i, for i = 1, . . . , n, on the basis of the observation of two independent copies of Y . Our approach is free of any prior assumption on s but requires that we know some upper bound γ on the ratio maxi σi/mini σi. For… (More)


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