Introduction to the Theory of Hypothesis Testing

As already mentioned, the procedures discussed in Chapter II for the testing of an hypothesis possess without doubt a certain intuitiveness and are rather convincing. However, we have already pointed out that it is desirable to develop a general test theory which depends on few basic assumptions. In particular, we have given no clear definition of the notion of a “test”. We also want to develop criteria for deciding when one of two tests can be viewed as the “better” one.

[1]  Oscar Wesler Invariance Theory and a Modified Minimax Principle , 1959 .

[2]  H. Witting,et al.  Optimale Tests und ungünstigste Verteilungen , 1967 .

[3]  S. Kakutani On Equivalence of Infinite Product Measures , 1948 .

[4]  R. R. Bahadur Stochastic comparison of tests , 1960 .

[5]  A. Wald Tests of statistical hypotheses concerning several parameters when the number of observations is large , 1943 .

[6]  Henry B. Mann,et al.  The Algebra of a Linear Hypothesis , 1960 .

[7]  J. L. Hodges,et al.  The Efficiency of Some Nonparametric Competitors of the t-Test , 1956 .

[8]  J. Wolfowitz,et al.  Optimum Character of the Sequential Probability Ratio Test , 1948 .

[9]  J L Denny,et al.  Sufficient conditions for a family of probabilities to be exponential. , 1967, Proceedings of the National Academy of Sciences of the United States of America.

[10]  J. Pfanzagl überall trennscharfe Tests und monotone Dichtequotienten , 1962 .

[11]  A. Wald,et al.  On the Choice of the Number of Class Intervals in the Application of the Chi Square Test , 1942 .

[12]  L. J. Savage,et al.  Application of the Radon-Nikodym Theorem to the Theory of Sufficient Statistics , 1949 .

[13]  H. Scheffé The Analysis of Variance , 1960 .

[14]  J. Neyman,et al.  Consistent Estimates Based on Partially Consistent Observations , 1948 .

[15]  Paul G. Hoel,et al.  Testing the Homogeneity of Poisson Frequencies , 1945 .

[16]  S. Isaacson On the Theory of Unbiased Tests of Simple Statistical Hypotheses Specifying the Values of Two or More Parameters , 1951 .

[17]  H. Scheffé A Useful Convergence Theorem for Probability Distributions , 1947 .

[18]  G. Nölle Zur Theorie der bedingten Tests , 1969 .

[19]  G. Dantzig On the Non-Existence of Tests of "Student's" Hypothesis Having Power Functions Independent of $\sigma$ , 1940 .

[20]  G. Doetsch,et al.  Die Zweidimensionale Laplace-Transformation , 1950 .

[21]  D. Burkholder Sufficiency in the Undominated Case , 1961 .

[22]  A. Berger On Uniformly Consistent Tests , 1951 .