Books in the Probability and Mathematical Statistics series

The ideas of Fourier have made their way into every branch of mathematics and mathematical physics, from the theory of numbers to quantum mechanics. Fourier Series and Integrals focuses on the extraordinary power and flexibility of Fourier s basic series and integrals and on the astonishing variety

Dealing with linear models, this work examines the subject from a mean model perspective, defining rules for building mean models, regression models, mean vectors, covariance matrices and sums of squares matrices for balanced and unbalanced data sets. It includes a review of relevant linear algebra concepts.

Covers spectral analysis that is closely intertwined with the 'time domain' approach, elementary notions of Hilbert Space Theory, basic probability theory, and practical analysis of time series data.

Presents the basic notions and tools of unimodality as they relate to probability and statistics. This work also covers many applications such as the use of unimodality to obtain monotonicity properties of power functions of multivariate tests, minimum volume confidence regions, and recurrence of symmetric random walks.

Aims to fulfill the needs of academic as well as professional statisticians who want to pursue nonparametrics in their academic projects, consultation, and applied research works. This edition includes topics such as asymptotic methods, nonparametrics, convergence of probability measures, statistical inference, and others.