We study the Latent Dirichlet Allocation model, a popular Bayesian algorithm for text analysis. We show that the model's parameters are not identified, which suggests that the choice of prior matters. We characterize the range of values that the posterior mean of a given functional of the...

A novel factorization for the sum of two single-pair matrices is established as product of lower-triangular, tridiagonal, and upper-triangular matrices, leading to semi-closed-form formulas for tridiagonal matrix inversion. Subsequent factorizations are established, leading to semi-closed-form...

Matrix algebra was covered in the linear regression, multiple regression section and simultaneous equations models. I use simple EViews 6 and matrix algebra examples to facilitate your learning experience and increase your enjoyment. Econometrics is basically related to economic measurement. It...

Topological relation between geographical objects is one of the key components of the Geographical Information System (GIS). Considering the objects to be exact with sharp boundaries, four intersection, and nine intersection matrices initiated the study of calculating the topological relations....

In the context of some multi-criteria decision-making methods, such as the Analytic Hierarchy Process, an expert is required to compare entities, e.g. alternatives and criteria. However, often, for various reasons, the expert cannot provide judgments on all pairs of entities. For these cases,...

In this work we present a new method for Quickest Change Detection (QCD) and Quickest Hub Discovery (QHD) in correlation structures that geometrically represents solutions from asymptotic Random Matrix theory (RMT) consistently, and allows to incorporate new distance metrics for both tests. We...

We develop estimation methods for Bayesian models where the covariance matrix has a block structure. A block covariance matrix partitions the data into groups or blocks; variances and covariances are equal within blocks while covariances are equal across blocks. We derive the posterior and...

We investigate the performance of non-linear return prediction models in the high complexity regime, i.e., when the number of model parameters exceeds the number of observations. We document a "virtue of complexity" in all asset classes that we study (US equities, international equities, bonds,...

The generalized asymmetric Laplace (GAL) distribution, also known as the variance/mean-gamma model, is a popular flexible class of distributions that can account for peakedness, skewness, and heavier than normal tails, often observed in financial or other empirical data. We consider extensions...

There is considerable literature on matrix-variate gamma distributions, also known as Wishart distributions, which are driven by a shape parameter with values in the (Gindikin) set {i/2, i = 1, . . . , k−1}∪((k−1)/2, ∞). We provide an extension of this class to the case where the shape...

Maximise student engagement and understanding of matrix methods in data-driven applications with this modern teaching package. Students are introduced to matrices in two preliminary chapters, before progressing to advanced topics such as the nuclear norm, proximal operators and convex...

We introduce a novel covariance estimator that exploits the heteroskedastic nature of financial time series by employing exponential weighted moving averages and shrinking the in-sample eigenvalues through cross-validation. Our estimator is model-agnostic in that we make no assumptions on the...

Cross-sectional asset pricing tests with GMM can generate spuriously high explanatory power for factor models when the moment conditions are specified such that they allow the estimated factor means to substantially deviate from the observed sample averages. In fact, by shifting the weights on...

Under rotation-equivariant decision theory, sample covariance matrix eigenvalues can be optimally shrunk by recombining sample eigenvectors with a (potentially nonlinear) function of the unobservable population covariance matrix. The optimal shape of this function reflects the loss/risk that is...

The idiosyncratic (microscopic) and systemic (macroscopic) components of market structure have been shown to be responsible for the departure of the optimal mean-variance allocation from the heuristic 'equally-weighted' portfolio. In this paper, we exploit clustering techniques derived from...

We introduce the new F-Riesz distribution to model tail-heterogeneity in fat-tailed covariance matrix observations. In contrast to the typical matrix-valued distributions from the econometric literature, the F-Riesz distribution allows for di↵erent tail behavior across all variables in the...

Linear algebra is without a doubt a fundamental tool to deal with empirical economic problems. The goal of this paper is to use some of these techniques to treat business cycles. To do that, we present the classic ordinary least square approach to estime the coefficients of a detrended time...

We study the rank of the instantaneous or spot covariance matrix Σ(t) of a multidimensional continuous semi-martingale X(t). Given highfrequency observations X(i=n), i = 0; : : : ;n, we test the null hypothesis rank (Σ(t)) ≤ r for all t against local alternatives where the average (r + 1)st...

The rank of the Hankel matrix, corresponding to a system transfer function, is equal to the order of its minimal state space realization. The computation of the rank of the Hankel matrix is complicated by the fact that its block elements are rarely given exactly but are estimated instead. In...