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General log-linear models specified by non-negative integer design matrices have a potentially wide range of applications, although using models without the genuine overall effect, that is, ones which cannot be reparameterized to include a…
We consider statistical models driven by Gaussian and non-Gaussian self-similar processes with long memory and we construct maximum likelihood estimators (MLE) for the drift parameter. Our approach is based on the approximation by random…
Maximum-likelihood estimation (MLE) is arguably the most important tool for statisticians, and many methods have been developed to find the MLE. We present a new inequality involving posterior distributions of a latent variable that holds…
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…
Towards understanding the fundamental limits of estimation from data of varied quality, we study the problem of estimating a mean parameter from heteroskedastic Gaussian observations where the variances are unknown and may vary arbitrarily…
Maximum Likelihood Estimators (MLE) has many good properties. For example, the asymptotic variance of MLE solution attains equality of the asymptotic Cram{\'e}r-Rao lower bound (efficiency bound), which is the minimum possible variance for…
We consider the problem of estimating the distribution function, the density and the hazard rate of the (unobservable) event time in the current status model. A well studied and natural nonparametric estimator for the distribution function…
We study mixture of linear regression (random coefficient) models, which capture population heterogeneity by allowing the regression coefficients to follow an unknown distribution $G^*$. In contrast to common parametric methods that fix the…
This manuscript investigates unconditional and conditional-on-stopping maximum likelihood estimators (MLEs), information measures and information loss associated with conditioning in group sequential designs (GSDs). The possibility of early…
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…
The Laplace approximation (LA) has been proposed as a method for approximating the marginal likelihood of statistical models with latent variables. However, the approximate maximum likelihood estimators (MLEs) based on the LA are often…
This paper investigates the asymptotic distribution of the maximum-likelihood estimate (MLE) in multinomial logistic models in the high-dimensional regime where dimension and sample size are of the same order. While classical large-sample…
We suggest an iterative approach to computing K-step maximum likelihood estimates (MLE) of the parametric components in semiparametric models based on their profile likelihoods. The higher order convergence rate of K-step MLE mainly depends…
We revisit the classical causal inference problem of estimating the average treatment effect in the presence of fully observed confounding variables using two-stage semiparametric methods. In existing theoretical studies of methods such as…
The proportional hazards model has been extensively used in many fields such as biomedicine to estimate and perform statistical significance testing on the effects of covariates influencing the survival time of patients. The classical…
Maximum likelihood estimation of linear functionals in the inverse problem of deconvolution is considered. Given observations of a random sample from a distribution $P_0\equiv P_{F_0}$ indexed by a (potentially infinite-dimensional)…
It is well known that, under standard regularity conditions, the maximum likelihood estimator (MLE) satisfies a central limit theorem and converges in distribution to a Gaussian random variable as the sample size grows. This paper…
This paper studies parameter estimation using L-moments, an alternative to traditional moments with attractive statistical properties. The estimation of model parameters by matching sample L-moments is known to outperform maximum likelihood…
Operational risk models commonly employ maximum likelihood estimation (MLE) to fit loss data to heavy-tailed distributions. Yet several desirable properties of MLE (e.g. asymptotic normality) are generally valid only for large sample-sizes,…
This paper rigorously establishes that the existence of the maximum likelihood estimate (MLE) in high-dimensional logistic regression models with Gaussian covariates undergoes a sharp `phase transition'. We introduce an explicit boundary…