Yao, Qiwei; Morgan, Byron J. T. Empirical transform estimation for indexed stochastic models. (English) Zbl 0913.62023 J. R. Stat. Soc., Ser. B, Stat. Methodol. 61, No. 1, 127-141 (1999). Summary: 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. Cited in 6 Documents MSC: 62F10 Point estimation 62F12 Asymptotic properties of parametric estimators Keywords:diagonal optimization; empirical transform; growth model; Laplace transform; least squares estimator; mean-squared errors; indexed stochastic models PDFBibTeX XMLCite \textit{Q. Yao} and \textit{B. J. T. Morgan}, J. R. Stat. Soc., Ser. B, Stat. Methodol. 61, No. 1, 127--141 (1999; Zbl 0913.62023) Full Text: DOI