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估计量偏离目标值的最后时点与累计次数AI 解读

Suppose $\hat{\theta}_n$ is a strongly consistent estimator for $\theta_0$ in some i.i.d. situation. Let $N_\varepsilon$ and $Q_\varepsilon$ be, respectively, the last $n$ and the total number of $n$ for which $\hat{\theta}_n$ is at least $\varepsilon$ away from $\theta_0$. The limit distributions for $\varepsilon^2N_\varepsilon$ and $\varepsilon^2Q_\varepsilon$ as $\varepsilon$ goes to zero are obtained under natural and weak conditions. The theory covers both parametric…

对称性的图形诊断与检验AI 解读

We consider plots which can be used to check whether a distribution is symmetric about some point and which give information about possible deviations from symmetry. Simultaneous confidence bands for checking the accuracy of the plots are derived and compared. Tests that are related to the plots and confidence bands are considered and their power functions are compared using Monte Carlo methods. As tests of normality, the powers of two of these tests compare favourably with…

分布对称性的图示与检验AI 解读

We consider plots which can be used to check whether a distribution is symmetric about some point and which give information about possible deviations from symmetry. Simultaneous confidence bands for checking the accuracy of the plots are derived and compared. Tests that are related to the plots and confidence bands are considered and their power functions are compared using Monte Carlo methods. As tests of normality, the powers of two of these tests compare favourably with…