Formulas for estimating sample sizes are presented to provide specified levels of power for tests of significance from a longitudinal design allowing for subject attrition. These formulas are derived for a comparison of two groups in terms of single degree-of-freedom contrasts of population...

Abstract Many statistical estimation techniques for high-dimensional or functional data are based on a preliminary dimension reduction step, which consists in projecting the sample X 1 ,..., X n onto the first D eigenvectors of the Principal Component Analysis (PCA) associated with the empirical...

To overcome the curse of dimensionality, dimension reduction is important andnecessary for understanding the underlying phenomena in a variety of fields.Dimension reduction is the transformation of high-dimensional data into ameaningful representation in the low-dimensional space. It can be...

Quasi-Monte Carlo (QMC) methods are important numerical tools in the pricing and hedging of complex financial instruments. The effectiveness of QMC methods crucially depends on the discontinuity and the dimension of the problem. This paper shows how the two fundamental limitations can be...