Adaptive Methods for use in t-Tests

Jurek Malarecki

This project sought to develop robust statistical methods that adaptively detect and remove outliers in small to moderately sized samples. In particular, there was a focus on the technique published in Clarke (2000) that selectively trims a proportion of observat ions, a = g/ n, where g is the number of observations removed and n is the sample size, such that it minimises an objective function (Clarke 2008). This procedure was in the form of the adaptive trimmed likelihood algorithm (ATLA) that successfully identifies any number of outliers, which may account for as much as half of the data, but is quite computationally intensive. Modification of the objective function was intended to enhance this procedure in identifying and removing outliers. Furthermore, the work of Clarke (1994) concerning the one sample problem was extended to the two sample problem by modification of ATLA to incorporate two-sample data. The presence of inliers was shown to have little effect on the coverage and length of the confidence intervals, thereby enabling the development of a more efficient method of identification and trimming of outliers for two-sample data to produce adaptive confidence intervals. This led to a general technique to adaptively trim three or four sample data that utilises oneway analysis of variance (ANOVA). Finally, simulations with the Rand MATLAB packages helped to demonstrate the robustness of these procedures.

Adaptive Methods for use in t-Tests

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