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Empirical transform estimation for indexed stochastic models

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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.
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Keywords: Diagonal optimization; Empirical transform; Growth model; Indexed stochastic model; Laplace transform; Least squares estimator; Mean-squared errors

Document Type: Original Article

Affiliations: University of Kent, Canterbury, UK

Publication date: 01 January 1999

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