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带移入的临界分枝过程中 Bootstrap 的无效性AI 解读

This article considers a case of parametric bootstrap when the observations consist of generation sizes of the branching process with immigration together with the immigration component of each generation. Suppose we estimate the offspring mean $m$ by the maximum likelihood estimator (m.l.e.). It is then shown that the bootstrap version of the standardized m.l.e. does not have the same limiting distribution as the standardized m.l.e., under the assumption that $m = 1$ (critic…

对称误差回归模型中回归参数估计的改进序贯程序AI 解读

A sequential procedure for estimating the regression parameter $\beta \in R^k$ in a regression model with symmetric errors is proposed. This procedure is shown to have asymptotically smaller regret than the procedure analyzed by Martinsek when $\mathbf{\beta} = \mathbf{0}$, and the same asymptotic regret as that procedure when $\mathbf{\beta} \neq \mathbf{0}$. Consequently, even when the errors are normally distributed, it follows that the asymptotic regret can be negative…

带迁入分枝过程的序贯估计AI 解读

For the critical and subcritical Galton-Watson processes with immigration, it is shown that if the data were collected according to an appropriate stopping rule, the natural sequential estimator of the offspring mean $m$ is asymptotically normally distributed for each fixed $m \in (0, 1\rbrack.$ Furthermore, the sequential estimator is shown to be asymptotically normally distributed uniformly over a class of offspring distributions with $m \in (0, 1\rbrack$ bounded variance…

一阶平稳自回归过程均值的序贯估计AI 解读

This paper considers the problem of sequential point and fixed-width confidence interval estimation of the location parameter when the errors form an autoregressive process with unknown scale and autoregressive parameters. The sequential point estimator considered here is based on sample mean and is shown to be asymptotically risk efficient as the cost per observation tends to zero. The sequential interval estimator is shown to be asymptotically consistent and the…