An empirical Ω
We hope to arrive at powerful tests using test statistics of the quadratic ratio type (2.1) with significance points that can be tabulated. For this purpose, we developed the BLUF estimator w of J′u; see (3.2). The estimator depends on the following matrices: the n × p matrix J, the p × p matrix Q, the p × p matrix Ω = KK ′, the n × n matrix Г, the n × k matrix X, and the n-element vector y. Both X and y are specified by observation and it is assumed that y ~n(Xβ, σ2 Г), where Г = Г 0 under the null hypothesis ℋ 0 . Hence, Г in (3.2) is specified by ℋ 0 . One is free to choose J and Q. The only practical specifications we know are J = I(n) or J is an n × (n−k) submatrix of I(n), like J in the BLUS vectors, and Q = I or Q = Г−1. In this chapter we take J = I, so that p = n. Because most current tests have Г = I as the null hypothesis, the most important specifications for practical application would seem to be Г= Q = J = I(n).
KeywordsScalar Multiplication Cipal Component Selection Device Economic Time Series Regression Space
Unable to display preview. Download preview PDF.