Related papers: A Coefficient of Determination (R2) for Linear Mix…

We propose a new and rather stringent criterion for testing the goodness of fit between a theory and experiment. It is motivated by the paradox that the criterion on \chi^2 for testing a theory is much weaker than the criterion for finding…

This paper proposes the asymmetric linear double autoregression, which jointly models the conditional mean and conditional heteroscedasticity characterized by asymmetric effects. A sufficient condition is established for the existence of a…

This paper introduces a general framework for estimating variance components in the linear mixed models via general unbiased estimating equations, which include some well-used estimators such as the restricted maximum likelihood estimator.…

A lot of studies on the summary measures of predictive strength of categorical response models consider the likelihood ratio index (LRI), also known as the McFadden-$R^2$, a better option than many other measures. We propose a simple…

Measurement error arises through a variety of mechanisms. A rich literature exists on the bias introduced by covariate measurement error and on methods of analysis to address this bias. By comparison, less attention has been given to errors…

Functional data analysis is proved to be useful in many scientific applications. The physical process is observed as curves and often there are several curves observed due to multiple subjects, providing the replicates in statistical sense.…

We consider here estimation of an unknown probability density s belonging to L2(mu) where mu is a probability measure. We have at hand n i.i.d. observations with density s and use the squared L2-norm as our loss function. The purpose of…

Deciding whether a model provides a good description of data is often based on a goodness-of-fit criterion summarized by a p-value. Although there is considerable confusion concerning the meaning of p-values, leading to their misuse, they…

Two commonly used methods for improving precision and power in clinical trials are stratified randomization and covariate adjustment. However, many trials do not fully capitalize on the combined precision gains from these two methods, which…

We reexamine the classical linear regression model when the model is subject to two types of uncertainty: (i) some of covariates are either missing or completely inaccessible, and (ii) the variance of the measurement error is undetermined…

Many methods of estimating causal models do not provide estimates of confidence in the resulting model. In this work, a metric is proposed for validating the output of a causal model fit; the robustness of the model structure with resampled…

We propose a new model selection criterion for mixed effects regression models that is computable when the model is fitted with a two-step method, even when the structure and the distribution of the random effects are unknown. The criterion…

Analyses of randomised trials are often based on regression models which adjust for baseline covariates, in addition to randomised group. Based on such models, one can obtain estimates of the marginal mean outcome for the population under…

The standard Cox model in survival analysis assumes that the covariate effect is constant across the entire covariate domain. However, in many applications, there is interest in considering the possibility that the covariate of main…

A common problem in health research is that we have a large database with many variables measured on a large number of individuals. We are interested in measuring additional variables on a subsample; these measurements may be newly…

The generalised linear model (GLM) is a very important tool for analysing real data in biology, sociology, agriculture, engineering and many other application domain where the relationship between the response and explanatory variables may…

Semicontinuous outcomes commonly arise in a wide variety of fields, such as insurance claims, healthcare expenditures, rainfall amounts, and alcohol consumption. Regression models, including Tobit, Tweedie, and two-part models, are widely…

Many applications of machine learning methods involve an iterative protocol in which data are collected, a model is trained, and then outputs of that model are used to choose what data to consider next. For example, one data-driven approach…

In causal inference, interference occurs when the treatment of one unit may affect the outcomes of other units. The goal of this work is to serve as a guide to the use of linear outcome modeling for estimating causal effects in settings…

Uncertainty quantification is a critical aspect of machine learning models, providing important insights into the reliability of predictions and aiding the decision-making process in real-world applications. This paper proposes a novel way…