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高斯白噪声中不连续信号最大似然估计渐近效率的精确计算AI 解读

In this paper, the problem of computing the exact value of the asymptotic efficiency of maximum likelihood estimators of a discontinuous signal in a Gaussian white noise is considered. A method based on constructing difference equations for the appropriate moments is presented and used to show that the exact variance of the Pitman estimator is $16\zeta(3)$, where $\zeta$ is the Riemann zeta function.

选择包含最优总体的子集：贝叶斯方法AI 解读

The problem of selecting a subset of $k$ populations $\pi_1, \cdots, \pi_k,$ which contains the "best" population, is considered. The unknown values $\theta_1, \cdots, \theta_k$ are the characteristics associated with $\pi_1, \cdots, \pi_k$ and the unknown population associated with $\theta_{\lbrack k\rbrack} = \max_i\theta_i$ is called the "best." It is assumed that, given $\mathbf{\theta} = (\theta_1, \cdots, \theta_k)$ the $\operatorname{pdf}$ of the independent random…

稳健估计量在相依数据中的表现AI 解读

This paper investigates the effect of serial dependence in the data on the efficiency of some robust estimators. When the observations are from a stationary process satisfying certain mixing conditions, linear combinations of order statistics and the Hodges-Lehmann estimator are shown to be asymptotically normally distributed. Gaussian processes are studied in detail and it is shown that when all the serial correlations $(\rho_n)$ are $\geqq 0$, the efficiency of the robust…

混合随机过程经验累积分布函数的渐近分布理论AI 解读

This paper introduces a new mixing condition for stationary processes which is weaker than $\phi$-mixing but stronger than strong mixing. Many processes arising in applications, e.g., first order autoregressive processes, obey the conditions. The main result is that the empiric cdf of a sample from such processes converges to a Gaussian process.