The effect of skewness and kurtosis on the Kenward-Roger approximation when group distributions differ

This study examined the independent effect of skewness and kurtosis on the robustness of the linear mixed model (LMM), with the Kenward-Roger (KR) procedure, when group distributions are different, sample sizes are small, and sphericity cannot be assumed. Methods: A Monte Carlo simulation study considering a split-plot design involving three groups and four repeated measures was performed. Results: The results showed that when group distributions are different, the effect of skewness on KR robustness is greater than that of kurtosis for the corresponding values. Furthermore, the pairings of skewness and kurtosis with group size were found to be relevant variables when applying this procedure. Conclusions: With sample sizes of 45 and 60, KR is a suitable option for analyzing data when the distributions are: (a) mesokurtic and not highly or extremely skewed, and (b) symmetric with different degrees of kurtosis. With total sample sizes of 30, it is adequate when group sizes are equal and the distributions are: (a) mesokurtic and slightly or moderately skewed, and sphericity is assumed; and (b) symmetric with a moderate or high/extreme violation of kurtosis. Alternative analyses should be considered when the distributions are highly or extremely skewed and samples sizes are small.

A proposal for a new specification for a conditionally heteroskedastic variance model: the Quadratic Moving-Average Conditional Heteroskedasticity and an application to the D. Mark-U.S. dollar Exchange Rate

Ever since the appearance of the ARCH model [Engle(1982a)], an impressive array of variance specifications belonging to the same class of models has emerged [i.e. Bollerslev's (1986) GARCH; Nelson's (1990) EGARCH]. This recent domain has achieved very successful developments. Nevertheless, several empirical studies seem to show that the performance of such models is not always appropriate [Boulier(1992)]. In this paper we propose a new specification: the Quadratic Moving Average Conditional heteroskedasticity model. Its statistical properties, such as the kurtosis and the symmetry, as well as two estimators (Method of Moments and Maximum Likelihood) are studied. Two statistical tests are presented, the first one tests for homoskedasticity and the second one, discriminates between ARCH and QMACH specification. A Monte Carlo study is presented in order to illustrate some of the theoretical results. An empirical study is undertaken for the DM-US exchange rate.

Motion estimation using higher-order statistics

The objective of this paper is to introduce a fourth-order cost function of the displaced frame difference (DFD) capable of estimatingmotion even for small regions or blocks. Using higher than second-orderstatistics is appropriate in case the image sequence is severely corruptedby additive Gaussian noise. Some results are presented and compared to those obtained from the mean kurtosis and the mean square error of the DFD.

ICA Cleaning procedure for EEG signals analysis: application to Alzheimer's disease detection

To develop systems in order to detect Alzheimer’s disease we want to use EEG signals. Available database is raw, so the first step must be to clean signals properly. We propose a new way of ICA cleaning on a database recorded from patients with Alzheimer's disease (mildAD, early stage). Two researchers visually inspected all the signals (EEG channels), and each recording's least corrupted (artefact-clean) continuous 20 sec interval were chosen for the analysis. Each trial was then decomposed using ICA. Sources were ordered using a kurtosis measure, and the researchers cleared up to seven sources per trial corresponding to artefacts (eye movements, EMG corruption, EKG, etc), using three criteria: (i) Isolated source on the scalp (only a few electrodes contribute to the source), (ii) Abnormal wave shape (drifts, eye blinks, sharp waves, etc.), (iii) Source of abnormally high amplitude ( �100 �V). We then evaluated the outcome of this cleaning by means of the classification of patients using multilayer perceptron neural networks. Results are very satisfactory and performance is increased from 50.9% to 73.1% correctly classified data using ICA cleaning procedure.