The behavior of locally most powerful tests

On locally optimal tests for the mean direction of the Langevin distribution

Hayakawa (1990) has very recently studied the behavior of the power for several large sample tests for the mean direction vector of the Langevin distribution. These tests are not known to possess any non-trivial optimal property. Here we derive some multiparameter locally optimal tests, e.g., best first and second directional derivative tests and locally most mean powerful tests. For the case w...

Locally Most Powerful Tests Based on Sequential Ranks

Sequential ranks of data X1, X2, . . . observed sequentially in time are defined as ranks computed from the data observed so far, denoting Rii the rank of Xi among the values X1, X2, . . . , Xi for any i. This paper studies tests of various hypotheses based on sequential ranks and derives such tests, which are locally most powerful among all tests based on sequential ranks. Such locally most po...

Some Locally Most Powerful Rank Tests For Correlation

OPTIMAL STATISTICAL TESTS BASED ON FUZZY RANDOM VARIABLES

A novel approach is proposed for the problem of testing statistical hypotheses about the fuzzy mean of a fuzzy random variable.The concept of the (uniformly) most powerful test is extended to the (uniformly) most powerful fuzzy-valued test in which the test function is a fuzzy set representing the degrees of rejection and acceptance of the hypothesis of interest.For this purpose, the concepts o...

Durbin-watson Tests for Serial Correlation in Regressions with Missing Observations*

We study two Durbin-Watson type tests for serial correlation of errors in regression models when observations are missing. We derive them by applying standard methods used in time series and linear models to deal with missing observations. The first test may be viewed as a regular Durbin-Watson test in the context of an extended model. We discuss appropriate adjustments that allow one to use al...