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自回归单位根的高效检验AI 解读

The asymptotic power envelope is derived for point-optimal tests of a unit root in the autoregressive representation of a Gaussian time series. The authors propose a family of tests whose asymptotic power functions are tangent to the power envelope at one point and are never far below. When the series has an unknown mean or linear trend, commonly used tests are found to be dominated by members of the family of point-optimal invariant tests. The authors propose a modified…

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若干回归系数稳健检验的近似功效函数AI 解读

Edgeworth approximations are developed for the distribution functio ns of some statistics for testing a linear hypothesis on the coefficient s in a regression model with an unknown error covariance matrix. Adjust ments to the asymptotic critical values are found to insure that the tests have correct size to second order of approximation. The power loss due to the estimation of the error covariance matrix is calculated. Some examples involving heteroskedasticity and…

误差协方差矩阵非标量时线性模型中的假设检验AI 解读

A WELL DEVELOPED EXACT STATISTICAL THEORY exists for hypothesis testing in the normal linear regression model when the errors are independent and homoscedastic. In the more general case where the error covariance matrix is nonscalar and depends on a set of unknown parameters, exact analysis is difficult and reliance is usually placed on asymptotic approximations for large sample size n. In this paper, higher-order asymptotic expansions are developed for comparing the size…

摘要暂缺

A theory of identification is developed for general stochastic model whose probability law is determined by finite number of parameters. It is shown under weak regularity conditions that local identifiability of the unknown parameter vector is equivalent to nonsingularity of the information matrix. The use of reduced-form parameters to establish identifiability is also analyzed. The general results are applied to the familiar problem of determining whether the coefficients…

柯西样本估计的一则札记AI 解读

A class of estimators is proposed for the estimation of the center of the Cauchy distribution. Each estimator in the class is the arithmetic average of a central subset of the sample order statistics. Although the sample median is a member of the proposed class, it is not the most efficient. The average of roughly the middle quarter of the ordered sample has the lowest asymptotic variance.