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Asymptotic expansions for a wide class of distribution are studied. A simple method for computation of the series coefficients is suggested. The case when regularization parameter of the distribution depends on the asymptotic parameter is…
Low rank inference on matrices is widely conducted by optimizing a cost function augmented with a penalty proportional to the nuclear norm $\Vert \cdot \Vert_*$. However, despite the assortment of computational methods for such problems,…
Implicit sampling is a weighted sampling method that is used in data assimilation, where one sequentially updates estimates of the state of a stochastic model based on a stream of noisy or incomplete data. Here we describe how to use…
A new method for analyzing high-dimensional categorical data, Linear Latent Structure (LLS) analysis, is presented. LLS models belong to the family of latent structure models, which are mixture distribution models constrained to satisfy the…
Mathematical modelling is a widely used approach to understand and interpret clinical trial data. This modelling typically involves fitting mechanistic mathematical models to data from individual trial participants. Despite the widespread…
In this paper, we consider procedures for testing hypotheses on the dimension of the linear span generated by a growing number of $p\times p$ covariance matrices from independent $q$ populations. Under a proper limiting scheme where all the…
We present a novel approach for learning an HMM whose outputs are distributed according to a parametric family. This is done by {\em decoupling} the learning task into two steps: first estimating the output parameters, and then estimating…
We introduce a new formulation of the Hidden Parameter Markov Decision Process (HiP-MDP), a framework for modeling families of related tasks using low-dimensional latent embeddings. Our new framework correctly models the joint uncertainty…
Simulations often involve the use of model parameters which are unknown or uncertain. For this reason, simulation experiments are often repeated for multiple combinations of parameter values, often iterating through parameter values lying…
This article investigates the asymptotic distribution of penalized estimators with non-differentiable penalties designed to recover low-dimensional pattern structures. Patterns play a central role in estimation, as they reveal the…
Multi-sensor state space models underpin fusion applications in networks of sensors. Estimation of latent parameters in these models has the potential to provide highly desirable capabilities such as network self-calibration. Conventional…
Parameter sharing has proven to be a parameter-efficient approach. Previous work on Transformers has focused on sharing parameters in different layers, which can improve the performance of models with limited parameters by increasing model…
This paper aims to address the issue of semiparametric efficiency for cointegration rank testing in finite-order vector autoregressive models, where the innovation distribution is considered an infinite-dimensional nuisance parameter. Our…
Models with multiple change points are used in many fields; however, the theoretical properties of maximum likelihood estimators of such models have received relatively little attention. The goal of this paper is to establish the asymptotic…
The bifactor model and its extensions are multidimensional latent variable models, under which each item measures up to one subdimension on top of the primary dimension(s). Despite their wide applications to educational and psychological…
Multiple matrix sampling is a survey methodology technique that randomly chooses a relatively small subset of items to be presented to survey respondents for the purpose of reducing respondent burden. The data produced are missing…
Nonparametric identification and maximum likelihood estimation for finite-state hidden Markov models are investigated. We obtain identification of the parameters as well as the order of the Markov chain if the transition probability…
The model of partially observed linear system depending on some unknown parameters is considered. An approximation of the unobserved component is proposed. This approximation is realized in three steps. First an estimator of the method of…
Hidden Markov models have successfully been applied as models of discrete time series in many fields. Often, when applied in practice, the parameters of these models have to be estimated. The currently predominating identification methods,…
This paper develops the inferential theory for latent factor models estimated from large dimensional panel data with missing observations. We propose an easy-to-use all-purpose estimator for a latent factor model by applying principal…