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存在干扰参数时基于估计方程的序贯估计AI 解读

Let $(X_1, X_2, \cdots)$ be a sequence of random variables and let the p.d.f. of $\mathbf{X}_n = (X_1, \cdots, X_n)$ be $p(\mathbf{x}_n, \theta)$, where $\theta = (\theta_1, \theta_2)$. An estimating equation rule for $\theta_1$ is a sequence of functions $g(x_1, \theta_1), g(x_1, x_2, \theta_1), \cdots$. If the random sample size $N = n$, we estimate $\theta_1$ through the estimating equation $g(\mathbf{X}_n, \theta_1) = 0$. In this paper, optimum estimation rules are…

已知状态数量的切换回归模型：贝叶斯分析AI 解读

Some aspects of Bayesian methods of inference relative to switching regression models are analyzed. It is shown that Bayesian confidence intervals and tests may be obtained by using Student's t and χ2 distributions. Mean biases and MSE of some Bayesian estimates are compared by Monte Carlo methods with those of the ML estimate. The MSE of the Bayesian estimates were uniformly smaller than those of the ML estimate. An experiment designed by Quandt [11] is also analyzed.