Optimal testing for equicorrelated linear regression models

Environmetric analysis in complex surveys

“…Part of the growing literature on the subject is based on the traditional sampling framework such as, for example, the works of Konijn (1962) and Kish and Frankel (1974). Others such as Scott and Holt (1982), Deaton and Irish (1983), King and Evans (1986), Christensen (1984Christensen ( , 1986Christensen ( , 1987a, Moulton (1986Moulton ( , 1990), Dorfman (1993), Rao et al (1993), and more recently, Bhatti (1995Bhatti ( , 1996Bhatti ( , 1997Bhatti ( , 1999 have focused on the model-based approach.…”

“…Let it be assumed that there is interest in testing H 0 : = 0, based on y, which has been defined earlier as an nx1 random vector whose distribution has probability density function f(y|), where is a px1 vector of unknown parameters. When p = 1, the LB test of H 0 : = 0 against H a + : > 0 is that with critical regions of the form Ѩlnf ͑y|͒ Ѩ =0 > c 1 (12) where c 1 in (12) is a suitably chosen constant; (see Ferguson, 1967, p. 235) and King and Hillier (1985). King and Hillier (1985) noted that this test is equivalent to the LM1 test based on the square root of the standard LM test statistic.…”

“…In Wu and Bhatti (1994), Bhatti (1995), and Bhatti (2000) various PO tests related to complex data are considered that optimize power at a predetermined point away from the null hypothesis. The main findings of these tests were in the context of SSMN and SMN distributions, the point optimal tests are BO and UMP invariant (UMPI), respectively.…”

“…4. The structure of the variance-covariance matrix of the observed vector, y, is identical to that of the residuals in panel and survey data, [see Balestra and Nerlove (1966) and Bhatti (1995), respectively]. 5.…”

“…Recently, there has been an increasing use of regression techniques based on survey data in environmental, social, physical, and biological sciences. Examples of these awareness may be found in Wu et al (1988), Bhatti (1993), Rao et al (1993), Ghosh and Rao (1994), Wu and Bhatti (1994), and series of articles by Bhatti (1995Bhatti ( , 1996Bhatti ( , 1997Bhatti ( , 1999Bhatti ( , 2000, and Stukel and Rao (1997), among aothers. Often the data arising from these areas are naturally in blocks.…”