Related papers: Anova of Balanced Variance Component Models

Generalized linear models are a popular tool in applied statistics, with their maximum likelihood estimators enjoying asymptotic Gaussianity and efficiency. As all models are wrong, it is desirable to understand these estimators' behaviours…

We derive the asymptotic theory of Bai (2009)'s interactive fixed effects estimator for unbalanced panels in which the source of attrition is conditionally random. For inference, we propose a method of alternating projections algorithm…

The beta distribution is a basic distribution serving several purposes. It is used to model data, and also, as a more flexible version of the uniform distribution, it serves as a prior distribution for a binomial probability. The bivariate…

In this article we recover the distribution function (and possible density) of an arbitrary random variable that is subject to an additive measurement error. This problem is also known as deconvolution and has a long tradition in…

In many applications, for example when computing statistics of fast subsystems in a multiscale setting, we wish to find the stationary distributions of systems of continuous time Markov chains. Here we present a class of models that appears…

We propose a novel method to directly learn a stochastic transition operator whose repeated application provides generated samples. Traditional undirected graphical models approach this problem indirectly by learning a Markov chain model…

Fixed effects models are very flexible because they do not make assumptions on the distribution of effects and can also be used if the heterogeneity component is correlated with explanatory variables. A disadvantage is the large number of…

Factor models are widely used for dimension reduction in the analysis of multivariate data. This is achieved through decomposition of a p x p covariance matrix into the sum of two components. Through a latent factor representation, they can…

Unsupervised learning aims at the discovery of hidden structure that drives the observations in the real world. It is essential for success in modern machine learning. Latent variable models are versatile in unsupervised learning and have…

In this paper, we consider the usual linear regression model in the case where the error process is assumed strictly stationary. We use a result from Hannan (1973), who proved a Central Limit Theorem for the usual least square estimator…

In a clustered observational study, a treatment is assigned to groups and all units within the group are exposed to the treatment. We develop a new method for statistical adjustment in clustered observational studies using approximate…

We analytically determine the number and distribution of fixed points in a canonical model of a chaotic neural network. This distribution reveals that fixed points and dynamics are confined to separate shells in phase space. Furthermore,…

Linear mixed models are widely used to analyze non-independent data, but inference for fixed effects can be unreliable under misspecification of the random-effects distribution, inaccurate Fisher information estimation, or convergence…

These notes build an introduction to Convolution Quadrature techniques applied to linear convolutions and convolution equations with a bias to problems related to wave propagation. The notes are self-contained and emphasize algorithmic…

Training large-scale recommendation models under a single global objective implicitly assumes homogeneity across user populations. However, real-world data are composites of heterogeneous cohorts with distinct conditional distributions. As…

Recently, there as been an increasing interest in the use of heavily restricted randomization designs which enforces balance on observed covariates in randomized controlled trials. However, when restrictions are strict, there is a risk that…

Many structural econometric models include latent variables on whose probability distributions one may wish to place minimal restrictions. Leading examples in panel data models are individual-specific variables sometimes treated as "fixed…

I present here a pedagogical introduction to the works by Rashel Tublin and Yan V. Fyodorov on random linear systems with quadratic constraints, using tools from Random Matrix Theory and replicas. These notes illustrate and complement the…

Nested error regression models are useful tools for analysis of grouped data, especially in the case of small area estimation. This paper suggests a nested error regression model using uncertain random effects in which the random effect in…

Distributed principal component analysis (PCA) produces node-level estimates of both a mean vector and a principal subspace. Robustly aggregating these heterogeneous objects requires a relative scale between mean error and subspace error.…