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Exact Distribution of Argmax (Argmin)

Author

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  • Habibi Reza

    (Department of Statistics, Central Bank of Iran, Ferdowsi Ave., 1135931496 Tehran, Iran.)

Abstract

This paper is concerned with the exact distribution of argmax (argmin) of a sequence of random variables. By argmax (argmin), we mean the random variable which attains the maximum (minimum) of the sequence. Change point estimators are of this type and the asymptotic distribution of this kind of estimator is studied extensively in literature. However, the exact distributions is generally not considered. Therefore, this paper is devoted to the exact distributions of the argmax in case of several examples. Finally, an approximation method is proposed.

Suggested Citation

  • Habibi Reza, 2011. "Exact Distribution of Argmax (Argmin)," Stochastics and Quality Control, De Gruyter, vol. 26(2), pages 155-162, January.
    • Handle: RePEc:bpj:ecqcon:v:26:y:2011:i:2:p:155-162:n:7
    DOI: 10.1515/EQC.2011.015
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    References listed on IDEAS

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    1. Jushan Bai, 1994. "Least Squares Estimation Of A Shift In Linear Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(5), pages 453-472, September.
    2. Ferger, Dietmar, 2009. "Argmax-stable marked empirical processes," Statistics & Probability Letters, Elsevier, vol. 79(9), pages 1203-1206, May.
    3. Dietmar Ferger, 2004. "A continuous mapping theorem for the argmax‐functional in the non‐unique case," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 58(1), pages 83-96, February.
    4. Bhattacharya, P.K., 1987. "Maximum likelihood estimation of a change-point in the distribution of independent random variables: General multiparameter case," Journal of Multivariate Analysis, Elsevier, vol. 23(2), pages 183-208, December.
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