ROBUST ADAPTIVE SCHEME FOR GAUSS MARKOV MODEL

Abstract

The Hogg’s adaptive scheme is extended to the Gauss Markov Model. The Gauss Markov model is a statistical procedure which belongs to the class of general linear model. Gauss Markov model is very sensitive to nonnormality, variance heterogeneity as well as large sample size. These assumptions may be violated as a result of departures from normality and small sample size. To overcome these problems, an Adaptive Scheme is adopted. The Adaptive Scheme is a two step procedure in which a selector statistic is used to first exam ine and classify given data based on measures of skewness and tailweight. Afterwards, a test statistic, independent of the selector statistic is chosen and a test conducted. A One way Analysis of Variance and Repeated Measures Design models were considered under uncorrelated and correlated error distributions respectively. The nine winsorised scores proposed by Hettmansperger (1984) were used because they are considered the most ap propriate rank scores for hypothesis testing. The Winsorised scores as well accommodate a wide range of distributions which are either symmetric or asymmetric with varying tail weights. In addition, the benchmarks for cut-off values for the measures of skewness and tailweights postulated by Al-Shomrani (2003) in his PhD dissertation were used. 10,000 simulations were conducted to compare the performance of the Adaptive Scheme and the Gauss Markov model from different continuous distributions under uncorrelated and correlated errors. Analyses of real datasets were as well performed to ascertain the effi ciency of the two tests. The findings favoured the Adaptive Scheme under a broad class of continuous distributions especially for non-normal distributions. The adaptive scheme is applicable to both small and large samples. It is therefore recommended that Statis ticians, Researchers and Data Analysts be encouraged to use adaptive schemes because they are applicable to a broad class of distributions.