Related papers: Squared Linear Models
Latent space models are powerful statistical tools for modeling and understanding network data. While the importance of accounting for uncertainty in network analysis has been well recognized, the current literature predominantly focuses on…
The smooth piecewise-linear models cover a wide range of applications nowadays. Basically, there are two classes of them: models are transitional or hyperbolic according to their behaviour at the phase-transition zones. This study explored…
We study linear pencils of curves on normal surface singularities. Using the minimal good resolution of the pencil, we describe the topological type of generic elements of the pencil and characterize the behaviour of special elements. Then…
The critical properties of the stochastic susceptible-exposed-infected model on a square lattice is studied by numerical simulations and by the use of scaling relations. In the presence of an infected individual, a susceptible becomes…
Spatial-temporal linear model and the corresponding likelihood-based statistical inference are important tools for the analysis of spatial-temporal lattice data. In this paper, we study the asymptotic properties of maximum likelihood…
The Plackett--Luce model has been extensively used for rank aggregation in social choice theory. A central statistical question in this model concerns estimating the utility vector that governs the model's likelihood. In this paper, we…
By analogy with Carleson's observation on Cardy's formula describing crossing probabilities for the scaling limit of critical percolation, we exhibit ``privileged geometries'' for Stochastic Loewner Evolutions with various parameters, for…
Maximum likelihood estimation (MLE) is a fundamental problem in statistics. Characteristics of the MLE problem for discrete algebraic statistical models are reflected in the geometry of the $\textit{likelihood correspondence}$, a variety…
Often the goal of model selection is to choose a model for future prediction, and it is natural to measure the accuracy of a future prediction by squared error loss. Under the Bayesian approach, it is commonly perceived that the optimal…
Motivated by studying asymptotic properties of the maximum likelihood estimator (MLE) in stochastic volatility (SV) models, in this paper we investigate likelihood estimation in state space models. We first prove, under some regularity…
We study a linear observation model with an unknown permutation called \textit{permuted/shuffled linear regression}, where responses and covariates are mismatched and the permutation forms a discrete, factorial-size parameter. The…
This paper considers the maximum likelihood estimation of factor models of high dimension, where the number of variables (N) is comparable with or even greater than the number of observations (T). An inferential theory is developed. We…
We study maximum likelihood estimation for the statistical model for undirected random graphs, known as the $\beta$-model, in which the degree sequences are minimal sufficient statistics. We derive necessary and sufficient conditions, based…
We study vectors chosen at random from a compact convex polytope in $\mathbb{R}^n$ given by a finite number of linear constraints. We determine which projections of these random vectors are asymptotically normal as $n\to\infty$. Marginal…
Loop models have been widely studied in physics and mathematics, in problems ranging from polymers to topological quantum computation to Schramm-Loewner evolution. I present new loop models which have critical points described by conformal…
In this letter, the 6-vertex model on dynamical random lattices is defined via a matrix model and rewritten (following I. Kostov) as a deformation of the O(2) model. In the large N planar limit, an exact solution is found at criticality.…
We initiate the study of positive-tropical generators as positive analogues of the concept of tropical bases. Applying this to the tropicalization of determinantal varieties, we develop criteria for characterizing their positive part. We…
In the last few decades both the volume of high-quality observing data on variable stars and common access to them have boomed; however the standard used methods of data processing and interpretation have lagged behind this progress. The…
We classify the two-way independence quasi-independence models (or independence models with structural zeros) that have rational maximum likelihood estimators, or MLEs. We give a necessary and sufficient condition on the bipartite graph…
The uniform probability measure on a convex polytope induces piecewise polynomial densities on its projections. For a fixed combinatorial type of simplicial polytopes, the moments of these measures are rational functions in the vertex…