Related papers: Asymptotic Properties for Cumulative Probability M…
Continuous response variables often need to be transformed to meet regression modeling assumptions; however, finding the optimal transformation is challenging and results may vary with the choice of transformation. When a continuous…
Ordinal cumulative probability models (CPMs) -- also known as cumulative link models -- such as the proportional odds regression model are typically used for discrete ordered outcomes, but can accommodate both continuous and mixed…
Cumulative probability models (CPMs) are a robust alternative to linear models for continuous outcomes. However, they are not feasible for very large datasets due to elevated running time and memory usage, which depend on the sample size,…
Detection limits (DLs), where a variable is unable to be measured outside of a certain range, are common in research. Most approaches to handle DLs in the response variable implicitly make parametric assumptions on the distribution of data…
Continuous monitoring is becoming more popular due to its significant benefits, including reducing sample sizes and reaching earlier conclusions. In general, it involves monitoring nuisance parameters (e.g., the variance of outcomes) until…
Randomized experiments have become important tools in empirical research. In a completely randomized treatment-control experiment, the simple difference in means of the outcome is unbiased for the average treatment effect, and covariate…
Approximate Bayesian computation allows for statistical analysis in models with intractable likelihoods. In this paper we consider the asymptotic behaviour of the posterior distribution obtained by this method. We give general results on…
Regression problems with bounded continuous outcomes frequently arise in real-world statistical and machine learning applications, such as the analysis of rates and proportions. A central challenge in this setting is predicting a response…
As language models (LMs) become more capable, it is increasingly important to align them with human preferences. However, the dominant paradigm for training Preference Models (PMs) for that purpose suffers from fundamental limitations, such…
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…
We consider a linear mixed-effects model with a clustered structure, where the parameters are estimated using maximum likelihood (ML) based on possibly unbalanced data. Inference with this model is typically done based on asymptotic theory,…
We study asymptotic behaviour of stochastic approximation procedures with three main characteristics: truncations with random moving bounds, a matrix valued random step-size sequence, and a dynamically changing random regression function.…
Interval-censored multi-state data arise in many studies of chronic diseases, where the health status of a subject can be characterized by a finite number of disease states and the transition between any two states is only known to occur…
Diffusion probabilistic models (DPMs) have emerged as a promising technique in generative modeling. The success of DPMs relies on two ingredients: time reversal of diffusion processes and score matching. In view of possibly unguaranteed…
Tuning parameters are parameters involved in an estimating procedure for the purpose of reducing the risk of some other estimator. Examples include the degree of penalization in penalized regression and likelihood problems, as well as the…
Difference-in-differences (DID) approaches are widely used for estimating causal effects with observational data before and after an intervention. DID traditionally estimates the average treatment effect among the treated after making a…
Interval censoring arises frequently in clinical, epidemiological, financial, and sociological studies, where the event or failure of interest is known only to occur within an interval induced by periodic monitoring. We formulate the…
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,…
Recent developments in statistical regression methodology shift away from pure mean regression towards distributional regression models. One important strand thereof is that of conditional transformation models (CTMs). CTMs infer the entire…
We develop asymptotic approximations that can be applied to sequential estimation and inference problems, adaptive randomized controlled trials, and related settings. In batched adaptive settings where the decision at one stage can affect…