Applied directional statistics : modern methods and case studies / edited by Christophe Ley and Thomas Verdebout.

A unified framework -- Empirical and limiting spectral distribution -- Moment method -- A metric for probability measures -- Patterned matrices: a unified approach -- Scaling -- Reduction to bounded case -- Trace formula and circuits -- Words -- Vertices -- Pair-matched word -- Sub-sequential limit -- Exercises -- Common symmetric patterned matrices -- Wigner matrix -- Semi-circle law, non-crossing partitions, Catalan words -- LSD -- Toeplitz and Hankel matrices -- Toeplitz matrix -- Hankel matrix -- Reverse circulant matrix -- Symmetric circulant and related matrices -- Additional properties of the LSD -- Moments of Toeplitz and Hankel LSD -- Contribution of words and comparison of LSD -- Unbounded support of Toeplitz and Hankel LSD -- Non-unimodality of Hankel LSD -- Density of Toeplitz LSD -- Pyramidal multiplicativity -- Exercises -- Patterned XX matrices -- A unified set up -- Aspect ratio y = -- Preliminaries -- Sample variance-covariance matrix -- Catalan words and Marcenko-Pastur law -- LSD -- Other XX matrices -- Aspect ratio y = -- Sample variance-covariance matrix -- Other XX matrices -- Exercises -- k-circulant matrices -- Normal approximation -- Circulant matrix -- k-circulant matrices -- Eigenvalues -- Eigenvalue partition -- Lower order elements -- Degenerate limit -- Non-degenerate limit -- Exercises -- Wigner type matrices -- Wigner-type matrix -- Exercises -- Balanced Toeplitz and Hankel matrices -- Main results -- Exercises -- Patterned band matrices -- LSD for band matrices -- Proof -- Reduction to uniformly bounded input -- Trace formula, circuits, words and matches -- Negligibility of higher order edges -- (M) condition -- Exercises -- Triangular matrices -- General pattern -- Triangular Wigner matrix -- LSD -- Contribution of Catalan words -- Exercises -- Joint convergence of iid patterned matrices -- Non-commutative probability space -- Joint convergence -- Nature of the limit -- Exercises -- Joint convergence of independent patterned matrices -- Definitions and notation -- Joint convergence -- Freeness -- Sum of independent patterned matrices -- Proofs -- Exercises -- Autocovariance matrix -- Preliminaries -- Main results -- Proofs -- Exercises.

"This book describes new data-driven methodologies and case studies. The primary targeted audience is researchers in statistics, as well as those in fundamental roles such as earth sciences, environmetrics, astrophysics, machine learning, image analysis and bioinformatics"--