Optimal Testing for Serial Correlation in a Large Number of Small Samples

Abstract

In recent years, there has been an increased awareness of the potential one-sided nature of many testing problems in applied sciences. Usually, these testing problems can be reduced, either by conditioning on suflicient statistics or by invariant techniques. Cox and SOLOMON (1988) considered testing the serial correlation coeflicient of a stationary first order autoregressive process and concentrated on four independent samples, with each of size three. We outline a general method for testing the serial correlation coeflicient, using locally best invariant, point optimal invariant and locally most mean powerful invariant test procedures. The first procedure optimizes power near the null hypothesis, the second optimizes it at a pre-determined point away from the null while the third optimizes the average curvature of the power hypersurface in the neighbourhood of the null hypothesis.

Point optimal testing: A survey of the post 1987 literature

“…Since 1987, point optimal invariant tests have been proposed for a wide range of testing problems involving the covariance matrix in the linear regression model. These include (i) testing for autocorrelation in the presence of missing observations (Shively, 1993), (ii) testing for first order autoregressive (AR 1)disturbances when the data is made up of the aggregate of a large number of small samples (Bhatti, 1992), (iii) testing for spatial autocorrelation in the disturbances (Martellosio, 2010(Martellosio, , 2012, (iv) testing for block effects caused by random coefficients (Bhatti and Barry, 1995), (v) testing for quarter-dependent simple fourth-order autoregressive (AR(4)) disturbances (Wu and King, 1996), (vi) testing for joint AR(1)-AR(4) disturbances against joint MA(1)-MA 4disturbances (Silvapulle and King, 1993) and (vii) testing for the presence of a particular error component (El- Bassiouni and Charif, 2004). Hwang and Schmidt (1996) extended the work of Dufour and King (1991) Dufour and King's (1991) tests, the main difference being the treatment of the initial observation.…”

Environmetric analysis in complex surveys

“…He notes that SSMN distributions arise naturally from multivariate models in which means and variances of individual variables are known, thus allowing these variables to be standardized. Such standardizations are always made and play important roles in the techniques for reduction of dimensionality, e.g., in canonical variables by Anderson (1984) and generalized canonical variables analysis by SenGupta (1981SenGupta ( , 1983), Bhatti (1992), and, more recently, Thalib et al (1999).…”

Testing regression models based on sample survey data

“…In part III of the thesis we consider Cox and Solomon's model (see [4,5]) and construct a locally best invariant test, POI test and LMMPI test (see [3]). Throughout this thesis we have used the principle of invariance to eliminate the nuisance parameters where possible thus reducing the dimension of the testing problem.…”