Empirical transform estimation for indexed stochastic models

Q. Yao and B. J. T. Morgan

Journal of the Royal Statistical Society Series B, 1999, vol. 61, issue 1, 127-141

Abstract: We present a method for estimating the parameters in indexed stochastic models via a least squares approach based on empirical transforms. Asymptotic approximations are derived for the distribution of the resulting estimators. An explicit expression for the mean‐squared error provides a natural way of selecting the transform variable, and a numerical example illustrates the performance of the resulting method. A common finding, which we term ‘diagonal optimization’, occurs when multiparameter models are fitted by using transforms. Diagonal optimization arises when optimal performance results from equating the elements of the transform vector, and we provide a heuristic explanation of why this occurs.

Date: 1999
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