|
The purpose of this paper is to present some efficient techniques for recognizing from the observed data whether several response functions are identical to each other. For example, in an industrial setting the problem may be to determine whether the production coefficients established in a small-scale pilot study apply to each of several large- scale production facilities. The techniques proposed here combine sensor information from automated visual inspection of manufactured products which is carried out by means of pixel-by-pixel comparison of the sensed image of the product to be inspected with some reference pattern (or image). Let (a1, . . . , am) be p-dimensional parameters associated with m response models of the same type. This study is concerned with the simultaneous comparison of a1, . . . , am. A generalized maximum likelihood ratio (GMLR) test is derived for testing equality of these parameters, where each of the parameters represents a corresponding vector of regression coefficients. The GMLR test reduces to an equivalent test based on a statistic that has an F distribution. The main advantage of the test lies in its relative simplicity and the ease with which it can be applied. Another interesting test for the same problem is an application of Fisher's method of combining independent test statistics which can be considered as a parallel procedure to the GMLR test. The combination of independent test statistics does not appear to have been used very much in applied statistics. There does, however, seem to be potential data analytic value in techniques for combining distributional assessments in relation to statistically independent samples which are of joint experimental relevance. In addition, a new iterated test for the problem defined above is presented. A rejection of the null hypothesis by this test provides some reason why all the parameters are not equal. A numerical example is discussed in the context of the proposed procedures for hypothesis testing.
|
