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多参数线性模型中残差经验过程的弱收敛AI 解读

When fitting, by least squares, a linear model (with an intercept term) with $p$ parameters to $n$ data points, the asymptotic behavior of the residual empirical process is shown to be the same as in the single sample problem provided $p^3 \log^2 (p) /n \to 0$ for any error density having finite variance and a bounded first derivative. No further conditions are imposed on the sequence of design matrices. The result is extended to more general estimates with the property that…

三参数 Weibull 分布的估计与拟合检验AI 解读

SUMMARY Estimation techniques are given for the three-parameter Weibull distribution, with all parameters unknown. Tables are given for the empirical distribution function statistics W 2, U 2 and A 2, for testing for the distribution.

信号位置的确定：贝叶斯分析AI 解读

We study the problem of determining the location of an emergency transmitter in a downed aircraft. The observations are bearings read at fixed stations. A Bayesian approach, yielding a posterior map of probable locations, seems reasonable in this situation. We therefore develop conjugate prior distributions for the von Mises distribution, which we use to compute a posterior distribution of the location. An approximation to the posterior distribution yields accurate, rapidly…

均匀次序统计量二次型的渐近分布AI 解读

The asymptotic distribution of quadratic forms in uniform order statistics is studied under contiguous alternatives. Using minimal conditions on the sequence of forms, the limiting distribution is shown to be the convolution of a sum of weighted noncentral chi-squares and a normal variate. The results give approximate distribution theory even when no limit exists. As an example, high-order spacings statistics are shown to have trivial asymptotic power unless the order of the…

关于指定中位数的对称性检验：渐近临界值AI 解读

We examine the asymptotic distribution and give asymptotic critical values for a statistic suggested by Hill & Rao (1977) for testing the symmetry of a continuous distribution about a specified median.

关于指定中位数的对称性检验：渐近临界值AI 解读

We examine the asymptotic distribution and give asymptotic critical values for a statistic suggested by Hill & Rao (1977) for testing the symmetry of a continuous distribution about a specified median.