Related papers: Minimum penalized Hellinger distance for model sel…
Popular statistical software provides Bayesian information criterion (BIC) for multilevel models or linear mixed models. However, it has been observed that the combination of statistical literature and software documentation has led to…
The fundamental task of classification given a limited number of training data samples is considered for physical systems with known parametric statistical models. The standalone learning-based and statistical model-based classifiers face…
This work introduces a new, explicit bound on the Hellinger distance between a continuous random variable and a Gaussian with matching mean and variance. As example applications, we derive a quantitative Hellinger central limit theorem and…
Using predictive adaptive arithmetic coding and the Minimum Description Length principle, we derive an efficient tool for model selection problems : the RIC information criterion. We then present an extension of these coding techniques to…
Selecting the number of regimes in Hidden Markov models is an important problem. There are many criteria that are used to select this number, such as Akaike information criterion (AIC), Bayesian information criterion (BIC), integrated…
The first investigation is made of designs for screening experiments where the response variable is approximated by a generalised linear model. A Bayesian information capacity criterion is defined for the selection of designs that are…
Model selection criteria are one of the most important tools in statistics. Proofs showing a model selection criterion is asymptotically optimal are tailored to the type of model (linear regression, quantile regression, penalized…
In this article, we develop a modern perspective on Akaike's Information Criterion and Mallows' Cp for model selection. Despite the diff erences in their respective motivation, they are equivalent in the special case of Gaussian linear…
The question of selecting the "best" amongst different choices is a common problem in statistics. In drug development, our motivating setting, the question becomes, for example: what is the dose that gives me a pre-specified risk of…
Model selection based on classical information criteria, such as BIC, is generally computationally demanding, but its properties are well studied. On the other hand, model selection based on parameter shrinkage by $\ell_1$-type penalties is…
Structural equation modeling (SEM) is a statistical method used to investigate relationships among latent variables. In SEM, the model must be specified in advance. However, in practice, statisticians often have several candidate models and…
We provide a means of computing and estimating the asymptotic distributions of statistics based on an outer minimization of an inner maximization. Such test statistics, which arise frequently in moment models, are of special interest in…
Estimating the number of sources impinging on an array of sensors is a well known and well investigated problem. A common approach for solving this problem is to use an information theoretic criterion, such as Minimum Description Length…
Model selection aims to find the best model in terms of accuracy, interpretability or simplicity, preferably all at once. In this work, we focus on evaluating model performance of Gaussian process models, i.e. finding a metric that provides…
We consider approximate Bayesian model choice for model selection problems that involve models whose Fisher-information matrices may fail to be invertible along other competing submodels. Such singular models do not obey the regularity…
A new method is proposed for variable screening, variable selection and prediction in linear regression problems where the number of predictors can be much larger than the number of observations. The method involves minimizing a penalized…
Adequacy for estimation between an inferential method and a model can be de{\ldots}ned through two main requirements: {\ldots}rstly the inferential tool should de{\ldots}ne a well posed problem when applied to the model; secondly the…
The uncertainty-penalized information criterion (UBIC) has been proposed as a new model-selection criterion for data-driven partial differential equation (PDE) discovery. In this paper, we show that using the UBIC is equivalent to employing…
Traditional probabilistic methods for the simulation of advection-diffusion equations (ADEs) often overlook the entropic contribution of the discretization, e.g., the number of particles, within associated numerical methods. Many times, the…
Estimator selection has become a crucial issue in non parametric estimation. Two widely used methods are penalized empirical risk minimization (such as penalized log-likelihood estimation) or pairwise comparison (such as Lepski's method).…