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Suppose x( n) = ( x 1, …, x n ) is a sample from a stochastic process x = { x 1, x 2, …}. Let p n ( x( n); θ) denote the joint density function of x( n), where \(\theta \epsilon \Omega \subset \mathcal {R}^k\) is a parameter. Define the log-likelihood ratio \(\Lambda _n = [\frac {p_n(x(n);\theta _n)}{p_n(x(n);\theta )}]\) , where \(\theta _n = \theta +n^{-\frac {1}{2}}h\) , and h is a ( k × 1) vector.

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Local Asymptotic Mixed Normal Family

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  • 发表日期：

    2025年

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  • Ishwar V. Basawa

摘要

Suppose x( n) = ( x 1, …, x n ) is a sample from a stochastic process x = { x 1, x 2, …}. Let p n ( x( n); θ) denote the joint density function of x( n), where \(\theta \epsilon \Omega \subset \mathcal {R}^k\) is a parameter. Define the log-likelihood ratio \(\Lambda _n = [\frac {p_n(x(n);\theta _n)}{p_n(x(n);\theta )}]\) , where \(\theta _n = \theta +n^{-\frac {1}{2}}h\) , and h is a ( k × 1) vector.