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During the past few decades, missing-data problems have been studied extensively, with a focus on the ignorable missing case, where the missing probability depends only on observable quantities. By contrast, research into non-ignorable…
The asymptotic variance of the maximum likelihood estimate is proved to decrease when the maximization is restricted to a subspace that contains the true parameter value. Maximum likelihood estimation allows a systematic fitting of…
Numerically estimating the integral of functions in high dimensional spaces is a non-trivial task. A oft-encountered example is the calculation of the marginal likelihood in Bayesian inference, in a context where a sampling algorithm such…
In fitting a mixture of linear regression models, normal assumption is traditionally used to model the error and then regression parameters are estimated by the maximum likelihood estimators (MLE). This procedure is not valid if the normal…
We obtain an asymptotic normality result that reveals the precise asymptotic behavior of the maximum likelihood estimators of parameters for a very general class of linear mixed models containing cross random effects. In achieving the…
Adaptive experiments are becoming increasingly popular in real-world applications for effectively maximizing in-sample welfare and efficiency by data-driven sampling. Despite their growing prevalence, however, the statistical foundations…
Multivariate normal mixtures provide a flexible model for high-dimensional data. They are widely used in statistical genetics, statistical finance, and other disciplines. Due to the unboundedness of the likelihood function, classical…
We consider tests of hypotheses when the parameters are not identifiable under the null in semiparametric models, where regularity conditions for profile likelihood theory fail. Exponential average tests based on integrated profile…
Generalized linear mixed models are useful in studying hierarchical data with possibly non-Gaussian responses. However, the intractability of likelihood functions poses challenges for estimation. We develop a new method suitable for this…
Problems of probabilistic inference and decision making under uncertainty commonly involve continuous random variables. Often these are discretized to a few points, to simplify assessments and computations. An alternative approximation is…
Joint models are well suited to modelling linked data from laboratories and health registers. However, there are few examples of joint models that allow for (a) multiple markers, (b) multiple survival outcomes (including terminal events,…
Data augmentation is often used to incorporate inductive biases into models. Traditionally, these are hand-crafted and tuned with cross validation. The Bayesian paradigm for model selection provides a path towards end-to-end learning of…
Generalized Linear Mixed Models (GLMMs) are widely used for analysing clustered data. One well-established method of overcoming the integral in the marginal likelihood function for GLMMs is penalized quasi-likelihood (PQL) estimation,…
We consider Monte Carlo approximations to the maximum likelihood estimator in models with intractable norming constants. This paper deals with adaptive Monte Carlo algorithms, which adjust control parameters in the course of simulation. We…
A recent article on generalised linear mixed model asymptotics, Jiang et al. (2022), derived the rates of convergence for the asymptotic variances of maximum likelihood estimators. If $m$ denotes the number of groups and $n$ is the average…
We study behavior of the restricted maximum likelihood (REML) estimator under a misspecified linear mixed model (LMM) that has received much attention in recent gnome-wide association studies. The asymptotic analysis establishes consistency…
A procedure for asymptotic bias reduction of maximum likelihood estimates of generic estimands is developed. The estimator is realized as a plug-in estimator, where the parameter maximizes the penalized likelihood with a penalty function…
We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size…
This paper develops asymptotic theory for estimation of parameters in regression models for binomial response time series where serial dependence is present through a latent process. Use of generalized linear model (GLM) estimating…
The change-plane Cox model is a popular tool for the subgroup analysis of survival data. Despite the rich literature on this model, there has been limited investigation into the asymptotic properties of the estimators of the…