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If the log likelihood is approximately quadratic with constant Hessian, then the maximum likelihood estimator (MLE) is approximately normally distributed. No other assumptions are required. We do not need independent and identically…
This paper introduces a Monte Carlo method for maximum likelihood inference in the context of discretely observed diffusion processes. The method gives unbiased and a.s.\@ continuous estimators of the likelihood function for a family of…
We consider a one-dimensional recurrent random walk in random environment (RWRE) when the environment is i.i.d. with a parametric, finitely supported distribution. Based on a single observation of the path, we provide a maximum likelihood…
Causal mediation analysis with random interventions has become an area of significant interest for understanding time-varying effects with longitudinal and survival outcomes. To tackle causal and statistical challenges due to the complex…
The Grenander estimator is a well-studied procedure for univariate nonparametric density estimation. It is usually defined as the Maximum Likelihood Estimator (MLE) over the class of all non-increasing densities on the positive real line.…
State-space models have been used in many applications, including econometrics, engineering, medical research, etc. The maximum likelihood estimation (MLE) of the static parameter of general state-space models is not straightforward because…
Dose selection is critical in pharmaceutical drug development, as it directly impacts therapeutic efficacy and patient safety of a drug. The Generalized Multiple Comparison Procedures and Modeling (MCP-Mod) approach is commonly used in…
This paper considers maximum likelihood (ML) estimation in a large class of models with hidden Markov regimes. We investigate consistency of the ML estimator and local asymptotic normality for the models under general conditions which allow…
Monte Carlo maximum likelihood (MCML) provides an elegant approach to find maximum likelihood estimators (MLEs) for latent variable models. However, MCML algorithms are computationally expensive when the latent variables are…
The log-concave maximum likelihood estimator (MLE) problem answers: for a set of points $X_1,...X_n \in \mathbb R^d$, which log-concave density maximizes their likelihood? We present a characterization of the log-concave MLE that leads to…
Auto-regressive sequence generative models trained by Maximum Likelihood Estimation suffer the exposure bias problem in practical finite sample scenarios. The crux is that the number of training samples for Maximum Likelihood Estimation is…
Every student in statistics or data science learns early on that when the sample size largely exceeds the number of variables, fitting a logistic model produces estimates that are approximately unbiased. Every student also learns that there…
Modeling sparse data such as microbiome and transcriptomics (RNA-seq) data is very challenging due to the exceeded number of zeros and skewness of the distribution. Many probabilistic models have been used for modeling sparse data,…
Numerous statistical methods have been developed to explore genomic imprinting and maternal effects, which are causes of parent-of-origin patterns in complex human diseases. However, most of them either only model one of these two…
A major line of contemporary research on complex networks is based on the development of statistical models that specify the local motifs associated with macro-structural properties observed in actual networks. This statistical approach…
Lately, a New Transmuted Logistic-exponential (NTLE) distribution was introduced and studied as an extension of the Logistic-Exponential Distribution (LED) with wider applicability in lifetime modelling. However, the maximum likelihood…
Anomaly estimation, or the problem of finding a subset of a dataset that differs from the rest of the dataset, is a classic problem in machine learning and data mining. In both theoretical work and in applications, the anomaly is assumed to…
We compare an autoencoder convolutional neural network (AE-CNN) with a conventional maximum-likelihood estimator (MLE) for inferring cluster virial masses, $M_v$, directly from the galaxy distribution around clusters, without identifying…
Markov regime switching models have been widely used in numerous empirical applications in economics and finance. However, the asymptotic distribution of the maximum likelihood estimator (MLE) has not been proven for some empirically…
We introduce a general covariate-assisted statistical ranking model within the Plackett--Luce framework. Unlike previous studies focusing on individual effects with fixed covariates, our model allows covariates to vary across comparisons.…