Related papers: Testing the fit of relational models
We propose an empirical likelihood ratio test for nonparametric model selection, where the competing models may be nested, nonnested, overlapping, misspecified, or correctly specified. It compares the squared prediction errors of models…
Mixtures of Linear Regressions (MLR) is an important mixture model with many applications. In this model, each observation is generated from one of the several unknown linear regression components, where the identity of the generated…
This article proposes omnibus portmanteau tests for contrasting adequacy of time series models. The test statistics are based on combining the autocorrelation function of the conditional residuals, the autocorrelation function of the…
Non-Gaussian outcomes are often modeled using members of the so-called exponential family. Notorious members are the Bernoulli model for binary data, leading to logistic regression, and the Poisson model for count data, leading to Poisson…
The likelihood ratio test (LRT) is widely used for comparing the relative fit of nested latent variable models. Following Wilks' theorem, the LRT is conducted by comparing the LRT statistic with its asymptotic distribution under the…
When in a full exponential family the maximum likelihood estimate (MLE) does not exist, the MLE may exist in the Barndorff-Nielsen completion of the family. We propose a practical algorithm for finding the MLE in the completion based on…
Maximum likelihood (ML) estimation is widely used in statistics. The h-likelihood has been proposed as an extension of Fisher's likelihood to statistical models including unobserved latent variables of recent interest. Its advantage is that…
We show that the mean-model parameter is always orthogonal to the error distribution in generalized linear models. Thus, the maximum likelihood estimator of the mean-model parameter will be asymptotically efficient regardless of whether the…
Particle physics experiments rely on the (generalised) likelihood ratio test (LRT) for searches and measurements, which consist of composite hypothesis tests. However, this test is not guaranteed to be optimal, as the Neyman-Pearson lemma…
Generalized linear models (GLMs) are popular for data-analysis in almost all quantitative sciences, but the choice of likelihood family and link function is often difficult. This motivates the search for likelihoods and links that minimize…
Count data take on non-negative integer values and are challenging to properly analyze using standard linear-Gaussian methods such as linear regression and principal components analysis. Generalized linear models enable direct modeling of…
Maximum likelihood fits to data can be performed using binned data and unbinned data. The likelihood fits in either case produce only the fitted quantities but not the goodness of fit. With binned data, one can obtain a measure of the…
Estimating model parameters is a crucial step in mathematical modelling and typically involves minimizing the disagreement between model predictions and experimental data. This calibration data can change throughout a study, particularly if…
Researchers are often interested in understanding the relationship between a set of covariates and a set of response variables. To achieve this goal, the use of regression analysis, either linear or generalized linear models, is largely…
A nonlinear model with response variable missing at random is studied. In order to improve the coverage accuracy, the empirical likelihood ratio (EL) method is considered. The asymptotic distribution of EL statistic and also of its…
Training modern large language models (LLMs) has become a veritable smorgasbord of algorithms and datasets designed to elicit particular behaviors, making it critical to develop techniques to understand the effects of datasets on the…
Exact MLE for generalized linear mixed models (GLMMs) is a long-standing problem unsolved until today. The proposed research solves the problem. In this problem, the main difficulty is caused by intractable integrals in the likelihood…
Databases in domains such as healthcare are routinely released to the public in aggregated form. Unfortunately, naive modeling with aggregated data may significantly diminish the accuracy of inferences at the individual level. This paper…
A connection between the General Linear Model (GLM) in combination with classical statistical inference and the machine learning (MLE)-based inference is described in this paper. Firstly, the estimation of the GLM parameters is expressed as…
We consider a problem of ecological inference, in which individual-level covariates are known, but labeled data is available only at the aggregate level. The intended application is modeling voter preferences in elections. In Rosenman and…