Estimator of a parameter

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Let $J(y_1:n)$ a parameter such that $$J(y_1:n)=mathbbE left( prodlimits_i=1^n frace^-y^2/(-2X_i^2)sqrt2pi X_i right),$$ and $(X_i)$ is a sequence of independent and identically distributed random variables that follow an exponential law of parameter $lambda$.
How can i find an $textbfunbiased$ estimator of $e^-beta J(y_1:n) $ or $e^-beta log(1+J(y_1:n))$?




statistics estimation




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    Let $J(y_1:n)$ a parameter such that $$J(y_1:n)=mathbbE left( prodlimits_i=1^n frace^-y^2/(-2X_i^2)sqrt2pi X_i right),$$ and $(X_i)$ is a sequence of independent and identically distributed random variables that follow an exponential law of parameter $lambda$.
    How can i find an $textbfunbiased$ estimator of $e^-beta J(y_1:n) $ or $e^-beta log(1+J(y_1:n))$?




    statistics estimation




    share|cite|improve this question























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      up vote
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      down vote

      favorite











      Let $J(y_1:n)$ a parameter such that $$J(y_1:n)=mathbbE left( prodlimits_i=1^n frace^-y^2/(-2X_i^2)sqrt2pi X_i right),$$ and $(X_i)$ is a sequence of independent and identically distributed random variables that follow an exponential law of parameter $lambda$.
      How can i find an $textbfunbiased$ estimator of $e^-beta J(y_1:n) $ or $e^-beta log(1+J(y_1:n))$?




      statistics estimation




      share|cite|improve this question













      Let $J(y_1:n)$ a parameter such that $$J(y_1:n)=mathbbE left( prodlimits_i=1^n frace^-y^2/(-2X_i^2)sqrt2pi X_i right),$$ and $(X_i)$ is a sequence of independent and identically distributed random variables that follow an exponential law of parameter $lambda$.
      How can i find an $textbfunbiased$ estimator of $e^-beta J(y_1:n) $ or $e^-beta log(1+J(y_1:n))$?





      statistics estimation





      share|cite|improve this question












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      edited Jul 24 at 23:50









      Michael Hardy

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      asked Jul 24 at 13:50









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