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In this paper, testing the equality of two mean vectors is considered when each dataset has a monotone pattern of missing observations. A simplified Hotelling's T2-type test statistic in a two-sample problem under monotone missing data is given. Transformed test statistics of this simplified T2 statistic based on Bartlett adjustment to improve the chi-squared approximation are derived. Furthermore, the accuracy of the approximations is investigated using a Monte Carlo simulation. Finally, the numerical power of the proposed test is presented. [ABSTRACT FROM AUTHOR]

One of the basic statistical methods of dimensionality reduction is analysis of discriminant coordinates given by Fisher (1936) and Rao (1948). The space of discriminant coordinates is a space convenient for presenting multidimensional data originating from multiple groups and for the use of various classification methods (methods of discriminant analysis). In the present paper, we adapt the classical discriminant coordinates analysis to multivariate functional data. The theory has been applied to analysis of textural properties of apples of six varieties, measured over a period of 180 days, stored in two types of refrigeration chamber. [ABSTRACT FROM AUTHOR]

Multivariate skewness and kurtosis were defined by Mardia. However, the distribution of multivariate normality test statistics based on skewness and kurtosis is only obtainable for large samples. In this paper, we propose a normalizing transformation statistic for Mardia's multivariate kurtosis. The accuracy of the normal approximation of this statistic, i.e. its expectation, variance, skewness, kurtosis, sample error Type I, and power for chosen alternative distributions, was investigated by Monte Carlo simulations for given sizes and dimensions. [ABSTRACT FROM AUTHOR]

In this study, the distribution of the simplified Hotelling's statistic for testing the mean vector when a data matrix has a monotone missing pattern is considered. The test statistic is decomposed, and an asymptotic expansion of the null distribution of each term is derived. Using the result, approximations to the upper percentiles of this statistic are derived. Furthermore, transformed test statistics based on the Bartlett adjustment are proposed. Finally, using a Monte Carlo simulation it is shown that the transformed statistics usually perform better than the original statistic with respect to the speed of convergence to the chi-squared limiting distribution. [ABSTRACT FROM AUTHOR]

In the paper, tests for multivariate normality (MVN) of Jarque-Bera type, based on skewness and kurtosis, have been considered. Tests proposed by Mardia and Srivastava, and the combined tests based on skewness and kurtosis defined by Jarque and Bera have been taken into account. In the Monte Carlo simulations, for each combination of p = 2, 3, 4, 5 number of traits and n = 10(5)50(10)100 sample sizes 10,000 runs have been done to calculate empirical Type I errors of tests under consideration, and empirical power against different alternative distributions. Simulation results have been compared to the Henze-Zirkler’s test. It should be stressed that no test yet proposed is uniformly better than all the others in every combination of conditions examined. [ABSTRACT FROM AUTHOR]