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The average critical value method and the asymptotic relative efficiency of tests
平均临界值法与检验的渐近相对效率
The average critical value method of gauging the efficiency of tests may usually be represented as an approximation to a power, often the square root, of the asymptotic relative efficiency of the tests.
Gamma-Distributed Products of Independent Random Variables
Gamma-distributed products of independent random variables
Equally Correlated Variates and the Multinormal Integral
等相关随机变量与多元正态积分
Summary An n-dimensional distribution with all correlations equal to p, called an equally correlated distribution, can very simply be constructed from a set of n + 1 one-dimensional variates; these variates are uncorrelated if p is non-negative, and n of them are uncorrelated if p is negative. From this, a general relation is deduced between any problem concerning an equally correlated distribution and an equivalent problem for uncorrelated variates. Applications are (i) to…
A Singularity in the Estimation of Binomial Variance
The Efficiency of the Records Test for Trend in Normal Regression
正态回归中纪录值趋势检验的效率
Summary A test for trend based on records is found to have asymptotic relative efficiency of zero compared with several other tests against normal regression alternatives, while two other well-known tests have zero efficiency compared even to the records test.
A singularity in the estimation of binomial variance
二项分布方差估计中的奇异性
For the symmetrical binomial distribution, the limit distribution of the sample variance is non-normal and has variance of order 1/n2.
The Efficiencies of Tests of Randomness Against Normal Regression
The Efficiencies of Tests of Randomness Against Normal Regression
A Test for Homogeneity of the Marginal Distributions in a Two-Way Classification
A TEST FOR HOMOGENEITY OF THE MARGINAL DISTRIBUTIONS IN A TWO-WAY CLASSIFICATION
Sampling Methods for Censuses and Surveys.
Asymptotic Relative Efficiencies of Distribution-Free Tests of Randomness Against Normal Alternatives
分布无关随机性检验对正态备择的渐近相对效率
S EVERAL writers, notably Hotelling and Pabst [5], have explicitly assumed that the relative efficiency of two test statistics is to be measured by their estimating efficiencies. While this seems reasonable, it is by no means obvious, since if the two tests are consistent, the ratio of their powers against any fixed alternative hypothesis must tend to unity with increasing sample size n, and it may easily be shown that for any n, the less efficient estimator may provide a…
The Power of Two Difference-Sign Tests
两种差分符号检验的功效
SITUATIONS arise in which we are unable to make the assumptions necessary for the application of standard theory based on the normal distribution. Most of the distribution-free tests which have been proposed for such situations are based on statistics which are very easy to compute, and this ease of computation goes some way to compensate for any information, available in the sample, which may be ignored. Quite apart from such situations, it is interesting to investigate the…