Related papers: Finiteness of small factor analysis models
We report results of two investigations of the double-scaling equations for the unitary matrix models. First, the fixed area partition functions have all positive coefficients only for the first four critical points. This implies that the…
Let $\mathbb{F}$ be a field. Denote by $t_n(\mathbb{F})$ the greatest possible dimension for a vector space of $n$-by-$n$ matrices over $\mathbb{F}$ in which every element is triangularizable over $\mathbb{F}$. It was recently proved that…
This paper studies the covariance matrix estimation for high-dimensional time series within a new framework that combines low-rank factor and latent variable-specific cluster structures. The popular methods based on assuming the sparse…
The majority-voter model is studied by Monte Carlo simulations on hypercubic lattices of dimension $d=2$ to 7 with periodic boundary conditions. The critical exponents associated to the Finite-Size Scaling of the magnetic susceptibility are…
Unidimensional factor models justify some of the most consequential summaries in science -- single scores, single ranks, and single leaderboards -- yet unidimensionality is usually assessed indirectly by fitting and evaluating models on…
Modeling and forecasting covariance matrices of asset returns play a crucial role in finance. The availability of high frequency intraday data enables the modeling of the realized covariance matrix directly. However, most models in the…
A matrix is said to have factor width at most $k$ if it can be written as a sum of positive semidefinite matrices that are non-zero only in a single $k \times k$ principal submatrix. We explore the ``factor-width-$k$ rank'' of a matrix,…
Finite quandles with n elements can be represented as n-by-n matrices. We show how to use these matrices to distinguish all isomorphism classes of finite quandles for a given cardinality n, as well as how to compute the automorphism group…
We prove that, in any field of characteristic not two and not three except the five-element field, each element decomposes into a product of four factors whose sum vanishes. We also find all $k,n,q$ such that every $n\times n$ matrix over…
The model implied by factor score predictors does not reproduce the non-diagonal elements of the observed covariance matrix as well as the factor loadings. It is therefore investigated whether it is possible to estimate factor loadings for…
We show global uniqueness of the solution to a class of constrained variational problems, using scaling properties. This is used to establish the essential uniqueness of solutions of a large deviations problem in multiple dimensions. The…
Finite elements, which are well-known and studied in the framework of vector lattices, are investigated in $\ell$-algebras, preferably in $f$-algebras, and in product algebras. The additional structure of an associative multiplication leads…
The covariance matrix is formulated in the framework of a linear multivariate ARCH process with long memory, where the natural cross product structure of the covariance is generalized by adding two linear terms with their respective…
We provide a family of group measure space II_1 factors for which all finite index subfactors can be explicitly listed. In particular, the set of all indices of irreducible subfactors can be computed. Concrete examples show that this index…
The calculation of common factor means in structured means analysis (SMM) is considered. The SMM equations imply that the unique factors are defined as having zero means. It was shown within the one factor solution that this definition…
My dissertation revolves around Bayesian approaches towards constrained statistical inference in the factor analysis (FA) model. Two interconnected types of restricted-model selection are considered. These types have a natural connection to…
Shrunk sample covariance matrix is a factor model of a special form combining some (typically, style) risk factor(s) and principal components with a (block-)diagonal factor covariance matrix. As such, shrinkage, which essentially inherits…
Identification of multinomial choice models is often established by using special covariates that have full support. This paper shows how these identification results can be extended to a large class of multinomial choice models when all…
A decision problem is called parameterized if its input is a pair of strings. One of these strings is referred to as a parameter. The problem: given a propositional logic program P and a non-negative integer k, decide whether P has a stable…
In this thesis we investigate finite size effects in 1+1 dimensional integrable QFT. In particular we consider matrix elements of local operators (finite volume form factors) and vacuum expectation values and correlation functions at finite…