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一阶平稳马尔可夫残差下样本均值的效率AI 解读

The efficiency of the sample mean relative to the “best” linear unbiased estimator when residuals follow a first-order stationary Markoff process is studied. The minimum efficiency for correlation ρ ≧ 0 occurs at the unique root of a certain equation depending on the sample size n and decreases monotonically in n toward the value .878 obtained by Ylvisaker in the continuous case. It is tabulated for selected n ≦ 300, together with the value of p at which the minimum is…

变量平减引起的虚假相关AI 解读

Abstract : This Memorandum shows that when a homogeneous linear regression of a normally distributed variable Y on two nromally distributed variables X and Z is deflated by Z, then when X and Y are uncorrelated the deflated dependent variable Y/Z and independent variable X/Z are either uncorrelated or perfectly correlated. Thus, existing approximations to the covariance of these deflated variables are poor. A new approximation to this covariance is given which has the same…

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相关样本的齐性检验AI 解读

This paper presents techniques for testing various hypotheses related to the notion of temporal homogeneity of a population each of whose members can belong to any one of S states at any time. These hypotheses include Cochran's interchangeability hypothesis, the hypothesis of strict exchange, the usual homogeneity hypothesis for multinomial distributions in the presence of correlated samples, and the hypothesis that a first order Markov chain is in a steady state.

再论置信区间长度AI 解读

In this note we present an example where the usual method of obtaining a confidence region for a parameter, namely “inverting” the uniformly most powerful test of a related hypothesis, leads to an interval whose expected length is greater than that obtained by another method of obtaining a confidence interval for the parameter. The implications of this example are then discussed.

关于置信区间长度的进一步讨论AI 解读

In this note we present an example where the usual method of obtaining a confidence region for a parameter, namely “inverting” the uniformly most powerful test of a related hypothesis, leads to an interval whose expected length is greater than that obtained by another method of obtaining a confidence interval for the parameter. The implications of this example are then discussed.