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A class of procedures is proposed for testing the stationarity of a Gaussian process or the homogeneity of independent processes. Requiring very limited prior knowledge of model structure, the methods can detect changes or differences in mean, in variance, in covariances and even in law. Although the theory of the stationarity test is worked out only for processes whose realizations are stationary over "epochs" separated by known change points, Monte Carlo evidence indicates…

检验平稳时间序列是否为高斯过程AI 解读

A class of procedures is proposed for testing the composite hypothesis that a stationary stochastic process is Gaussian. Requiring very limited prior knowledge about the structure of the process, the tests rely on quadratic forms in deviations of certain sample statistics from their population counterparts, minimized with respect to the unknown parameters. A specific test is developed, which employs differences between components of the sample and Gaussian characteristic…

基于经验特征函数的指数分布对单调风险率备择检验AI 解读

SUMMARY A test of exponentiality is proposed which is consistent for alternatives with monotone failure rate. Derived as a weighted integral of the difference between the characteristic functions of the sample and of the exponential distribution, the scale-invariant statistic depends on the mean value of the exponential density function, evaluated at the sample observations. The power of the test is similar to that of the Gini test of Gail and Gastwirth (1978b), and both…

基于经验特征函数的正态性检验AI 解读

An omnibus test of normality is proposed, which has high power against many alternative hypotheses. The test uses a weighted integral of the squared modulus of the difference between the characteristic functions of the sample and of the normal distribution.

基于经验矩母函数的分离分布族检验AI 解读

In testing an hypothesis that a population has a specified distribution against the alternative that its distribution belongs to a separate family it is well known that the likelihood ratio test does not apply. We propose a test based on the difference between the sample moment generating function and its theoretical counterpart under Ho. The argument of the moment generating function is chosen to maximize the test's large-sample power. Small-sample properties of the test in…

基于经验矩母函数的分离分布族检验AI 解读

In testing an hypothesis that a population has a specified distribution against the alternative that its distribution belongs to a separate family it is well known that the likelihood ratio test does not apply. We propose a test based on the difference between the sample moment generating function and its theoretical counterpart under Ho. The argument of the moment generating function is chosen to maximize the test's large-sample power. Small-sample properties of the test in…