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一种逐步上升多重检验程序AI 解读

We consider the problem of simultaneously testing k ≥ 2 hypotheses on parameters θ1, …, θk . In a typical application the θ's may be a set of contrasts, for instance, a set of orthogonal contrasts among population means or a set of differences between k treatment means and a standard treatment mean. It is assumed that least squares estimators 1, …, k are available that are jointly normally distributed with a common variance (known up to a scalar, namely the error variance σ…

利用残差检测线性回归单个异常值的札记AI 解读

Consider the usual linear regression model y = Xβ +ε, where the vector ε has E(ε) = 0, cov (ε) = σ2V, where V is known. Let e = y-ŷ be the least squares residual vector. It is shown that a test based on the transformed residual vector d* = V−1e has, in the class of linear transformations of e, certain optimal power properties for detecting the presence of a single outlier when the label of the outlier observation is unknown. The outlier model considered here is that of shift…

利用残差检测线性回归中异常值的一个注记AI 解读

Consider the usual linear regression model y = Xβ +ε, where the vector ε has E(ε) = 0, cov (ε) = σ2V, where V is known. Let e = y-ŷ be the least squares residual vector. It is shown that a test based on the transformed residual vector d* = V−1e has, in the class of linear transformations of e, certain optimal power properties for detecting the presence of a single outlier when the label of the outlier observation is unknown. The outlier model considered here is that of shift…

多个敏感属性的随机化回答技术AI 解读

Some randomized response techniques for investigating t ≧ 2 sensitive attributes are reviewed. A new technique is proposed that has the advantage of requiring only r trials per respondent (r ≦ t) if estimation of up to r-variate joint proportions is desired. The case of r = 2 is analyzed in detail. A procedure for deriving the restricted maximum likelihood estimators (MLE's) of the proportions and a test of independence between any set of pairs of attributes are given. The…

双重抽样中基于回归估计量的统计推断AI 解读

The problem of hypothesis testing using the regression estimator in double sampling is considered. Test procedures are provided when the covariance matrix between the primary and the auxiliary variables is either partially known or completely unknown. For the latter case a new ‘studentized’ version of the regression estimator is proposed as a test statistic. The exact null distribution of this statistic is derived in a special case. An approximation to the null distribution…

具有块协方差结构的多元正态积分的迭代积分表示AI 解读

It is shown that a km-variate normal probability integral over a rectangular region can be expressed as an iterated k-variate normal integral when the k sets of m variates each have a certain commonly realized block covariance structure. The latter representation is much easier to evaluate numerically than is the former. This result generalizes previous results for k= 1 of Dunnett & Sobel and Steck & Owen.

块协方差结构下多元正态积分的迭代积分表示AI 解读

It is shown that a km-variate normal probability integral over a rectangular region can be expressed as an iterated k-variate normal integral when the k sets of m variates each have a certain commonly realized block covariance structure. The latter representation is much easier to evaluate numerically than is the former. This result generalizes previous results for k= 1 of Dunnett & Sobel and Steck & Owen.