Related papers: Squared Linear Models
Skew normal mixture models provide a more flexible framework than the popular normal mixtures for modelling heterogeneous data with asymmetric behaviors. Due to the unboundedness of likelihood function and the divergency of shape…
We study nonparametric maximum likelihood estimation for two classes of multivariate distributions that imply strong forms of positive dependence; namely log-supermodular (MTP$_2$) distributions and log-$L^\#$-concave (LLC) distributions.…
In many areas of applied mathematics and statistics, it is a fundamental problem to find the best representative of a model by optimizing an objective function. This can be done by determining critical points of the objective function…
Classical mathematical statistics deals with models that are parametrized by a Euclidean, i.e. finite dimensional, parameter. Quite often such models have been and still are chosen in practical situations for their mathematical simplicity…
For general data, the number of complex solutions to the likelihood equations is constant and this number is called the (maximum likelihood) ML-degree of the model. In this article, we describe the special locus of data for which the…
Random defects do not constitute the unique source of electron localization in two dimensions. Lattice quasidisorder generated from two inplane superimposed rotated, main and secondary, square lattices, namely monolayers where moir\'e…
It has been shown that for a given set of points in a plane, the least-squares regression line pivots about a fixed point when any single point in the set is repeated. We consider what happens when more than one point is repeated.…
Descriptive statistics for parametric models are currently highly sensative to departures, gross errors, and/or random errors. Here, leveraging the structures of parametric distributions and their central moment kernel distributions, a…
We investigate the statistical properties of the eigenvalues and eigenvectors in a random matrix ensemble with $H_{ij}\sim |i-j|^{-\mu}$. It is known that this model shows a localization-delocalization transition (LDT) as a function of the…
We initiate the study of the norm-squared of the momentum map as a rigorous tool in infinite dimensions. In particular, we calculate the Hessian at a critical point, show that it is positive semi-definite along the complexified orbit, and…
Likelihood profiling is an efficient and powerful frequentist approach for parameter estimation, uncertainty quantification and practical identifiablity analysis. Unfortunately, these methods cannot be easily applied for stochastic models…
The goodness of the long-term prediction in the state-space model was evaluated using the squared long-term prediction error. In order to estimate the model parameters suitable for long-term prediction, we devised a modified log-likelihood…
For a pair of coupled rectangular random matrices we consider the squared singular values of their product, which form a determinantal point process. We show that the limiting mean distribution of these squared singular values is described…
Studies of the genetic loci that contribute to variation in gene expression frequently identify loci with broad effect on gene expression: expression quantitative trait locus (eQTL) hotspots. We describe a set of exploratory graphical…
We consider the symmetric two-state 16-vertex model on the square lattice whose vertex weights are invariant under any permutation of adjacent edge states. The vertex-weight parameters are restricted to a critical manifold which is…
In spite of the recent surge of interest in quantile regression, joint estimation of linear quantile planes remains a great challenge in statistics and econometrics. We propose a novel parametrization that characterizes any collection of…
The permutation model is a classical spin system where elements of the symmetric group interact with one another. The partition function of this model is directly related to the entanglement structure of random quantum circuits and random…
Marginal models involve restrictions on the conditional and marginal association structure of a set of categorical variables. They generalize log-linear models for contingency tables, which are the fundamental tools for modelling the…
We consider marginal log-linear models for parameterizing distributions on multidimensional contingency tables. These models generalize ordinary log-linear and multivariate logistic models, besides several others. First, we obtain some…
Numerous interesting properties in nonlinear systems analysis can be written as polynomial optimization problems with nonconvex sum-of-squares problems. To solve those problems efficiently, we propose a sequential approach of local…