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Empirical transform estimation for indexed stochastic models

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  • Q. Yao
  • B. J. T. Morgan

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.

Suggested Citation

  • Q. Yao & B. J. T. Morgan, 1999. "Empirical transform estimation for indexed stochastic models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 127-141.
    • Handle: RePEc:bla:jorssb:v:61:y:1999:i:1:p:127-141
    DOI: 10.1111/1467-9868.00167
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    Cited by:

    1. Besbeas, Panagiotis & J.T. Morgan, Byron, 2004. "Efficient and robust estimation for the one-sided stable distribution of index," Statistics & Probability Letters, Elsevier, vol. 66(3), pages 251-257, February.
    2. Narayanaswamy Balakrishnan & Chengwei Qin, 2019. "First Passage Time of a Lévy Degradation Model with Random Effects," Methodology and Computing in Applied Probability, Springer, vol. 21(1), pages 315-329, March.
    3. Maria P. Braun & Simos G. Meintanis & Viatcheslav B. Melas, 2008. "Optimal Design Approach to GMM Estimation of Parameters Based on Empirical Transforms," International Statistical Review, International Statistical Institute, vol. 76(3), pages 387-400, December.

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