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This research deals with the estimation and imputation of missing data in longitudinal models with a Poisson response variable inflated with zeros. A methodology is proposed that is based on the use of maximum likelihood, assuming that data…
Consider a setting with $N$ independent individuals, each with an unknown parameter, $p_i \in [0, 1]$ drawn from some unknown distribution $P^\star$. After observing the outcomes of $t$ independent Bernoulli trials, i.e., $X_i \sim…
An efficient monotone data augmentation (MDA) algorithm is proposed for missing data imputation for incomplete multivariate nonnormal data that may contain variables of different types, and are modeled by a sequence of regression models…
Data imputation is a cornerstone technique for handling missing values in real-world datasets, which are often plagued by missingness. Despite recent progress, prior studies on Large Language Models-based imputation remain limited by…
We revisit the classical problem of deriving convergence rates for the maximum likelihood estimator (MLE) in finite mixture models. The Wasserstein distance has become a standard loss function for the analysis of parameter estimation in…
The parameter estimation of unnormalized models is a challenging problem. The maximum likelihood estimation (MLE) is computationally infeasible for these models since normalizing constants are not explicitly calculated. Although some…
Widely used methods for analyzing missing data can be biased in small samples. To understand these biases, we evaluate in detail the situation where a small univariate normal sample, with values missing at random, is analyzed using either…
The asymptotic normality of the maximum likelihood estimator (MLE) under regularity conditions is a cornerstone of statistical theory. In this paper, we give explicit upper bounds on the distributional distance between the distribution of…
Detecting changes is of fundamental importance when analyzing data streams and has many applications, e.g., in predictive maintenance, fraud detection, or medicine. A principled approach to detect changes is to compare the distributions of…
Simulation-based inference techniques are indispensable for parameter estimation of mechanistic and simulable models with intractable likelihoods. While traditional statistical approaches like approximate Bayesian computation and Bayesian…
Finite mixture models are widely used in econometric analyses to capture unobserved heterogeneity. This paper shows that maximum likelihood estimation of finite mixtures of parametric densities can suffer from substantial finite-sample bias…
Balancing weights have been widely applied to single or monotone missingness due to empirical advantages over likelihood-based methods and inverse probability weighting approaches. This paper considers non-monotone missing data under the…
Linear mixed models (LMMs) are used as an important tool in the data analysis of repeated measures and longitudinal studies. The most common form of LMMs utilize a normal distribution to model the random effects. Such assumptions can often…
Histogram-based empirical Bayes methods developed for analyzing data for large numbers of genes, SNPs, or other biological features tend to have large biases when applied to data with a smaller number of features such as genes with…
Estimating population quantities such as mean outcomes from user feedback is fundamental to platform evaluation and social science, yet feedback is often missing not at random (MNAR): users with stronger opinions are more likely to respond,…
This paper develops several interesting, significant, and interconnected approaches to nonparametric or semi-parametric statistical inferences. The overwhelmingly favoured maximum likelihood estimator (MLE) under parametric model is…
Missing data are ubiquitous in empirical databases, yet statistical analyses typically require complete data matrices. Multiple imputation offers a principled solution for filling these gaps. This study evaluates the performance of several…
Mixture models have attracted significant attention due to practical effectiveness and comprehensive theoretical foundations. A persisting challenge is model misspecification, which occurs when the model to be fitted has more mixture…
This paper proposes a novel exact maximum likelihood (ML) estimation method for general Gaussian processes, where all parameters are estimated jointly. The exact ML estimator (MLE) is consistent and asymptotically normally distributed. We…
When outcomes are missing for reasons beyond an investigator's control, there are two different ways to adjust a parameter estimate for covariates that may be related both to the outcome and to missingness. One approach is to model the…