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合并检验的渐近最优方法AI 解读

A criterion for the asymptotic optimality of combined independent tests is given. Methods other than Fisher's are shown to satisfy the criterion. Certain problems call for a weighted combination of tests. It is shown that many weighted procedures are optimal. In particular, a weighted procedure based on gamma transforms is optimal. This weighted procedure has the additional advantage that critical values are easily determined. Good's weighting procedure is shown not to be…

序贯检验的渐近效率（二）AI 解读

An asymptotic expression is given for the $\log$ error probability of a sequential test based on a random walk. This may be used to compute limiting relative efficiencies of such tests. The results are illustrated for the one-sided normal testing problem with an asymptotic Bayes test due to Schwarz. Some numerical comparisons are given for five sequential tests of a normal mean.

序贯 Bahadur 效率AI 解读

The notion of Bahadur efficiency for test statistics is extended to the sequential case and illustrated in the specific context of testing one-sided hypotheses about a normal mean. An analog of Bahadur's theorem on the asymptotic optimality of the likelihood ratio statistic is seen to hold in the normal case. Some possible definitions of attained level for a sequential experiment are considered.

序贯检验的渐近效率AI 解读

Some concepts of relative and absolute efficiency for sequential tests are considered. These are sequential analogs of Hodges-Lehmann and Chernoff efficiencies. Using these criteria, several sequential tests for the mean of a normal distribution are evaluated. Among them are Wald's SPRT, Anderson's triangular boundary, Bayes and APO tests and a repeated significance test. Truncated versions of these tests are also considered. Asymptotic expressions for the (expected)…

序贯检验与非序贯检验的比较AI 解读

Sequential tests for one-sided hypotheses are compared, asymptotically, with non-sequential counterparts. An analog of Pitman efficiency is obtained, as is another comparison that has no purely non-sequential analog. With these methods of comparison, the limiting relative efficiency of the sequential test is never less than one and for most parameter values, it is infinite. An asymptotic notion of minimal relative efficiency is also considered.

序贯分析的若干渐近问题AI 解读

The asymptotic behavior is given for the error rates and ASN of the Wald SPRT and of invariant sequential tests. An asymptotic justification of Bhate's conjecture is also provided for invariant sequential tests. Expressions are obtained for the asymptotic relative efficiency of the Wald SPRT as compared with the corresponding best non-sequential test.