Related papers: Nonparametric (smoothed) likelihood and integral e…

We derive a maximum a posteriori estimator for the linear observation model, where the signal and noise covariance matrices are both uncertain. The uncertainties are treated probabilistically by modeling the covariance matrices with prior…

We study nonparametric estimation of the sub-distribution functions for current status data with competing risks. Our main interest is in the nonparametric maximum likelihood estimator (MLE), and for comparison we also consider a simpler…

In this paper we address smoothing-that is, optimisation-based-estimation techniques for localisation problems in the case where motion sensors are very accurate. Our mathematical analysis focuses on the difficult limit case where motion…

Skew normal mixture models provide a more flexible framework than the popular normal mixtures for modelling heterogeneous data with asymmetric behaviors. Due to the unboundedness of likelihood function and the divergency of shape…

Consider an $(L,1)$ random walk in an i.i.d. random environment, whose environment involves certain parameter. We get the maximum likelihood estimator(MLE) of the environment parameter which can be written as functionals of a multitype…

The problem of accurate nonparametric estimation of distributional functionals (integral functionals of one or more probability distributions) has received recent interest due to their wide applicability in signal processing, information…

We study mixed models with a single grouping factor, where inference about unknown parameters requires optimizing a marginal likelihood defined by an intractable integral. Low-dimensional numerical integration techniques are regularly used…

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…

We derive bilateral asymptotic as well as non-asymptotic estimates for the multivariate Laplace integrals. Possible applications: Tauberian theorems for random vectors.

This paper continues our earlier investigations into the inversion of random functions in a general (abstract) setting. In Section 2 we investigate a concept of invertibility and the invertibility of the composition of random functions. In…

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,…

Determinantal point processes (DPPs) have wide-ranging applications in machine learning, where they are used to enforce the notion of diversity in subset selection problems. Many estimators have been proposed, but surprisingly the basic…

We apply the techniques of stochastic integration with respect to fractional Brownian motion and the theory of regularity and supremum estimation for stochastic processes to study the maximum likelihood estimator (MLE) for the drift…

In the context of a species sampling problem we discuss a non-parametric maximum likelihood estimator for the underlying probability mass function. The estimator is known in the computer science literature as the high profile estimator. We…

We discuss the problem of parameter estimation in nonlinear stochastic differential equations based on sampled time series. A central message from the theory of integrating stochastic differential equations is that there exists in general…

We propose and study properties of maximum likelihood estimators in the class of conditional transformation models. Based on a suitable explicit parameterisation of the unconditional or conditional transformation function, we establish a…

Machine Learning models incorporating multiple layered learning networks have been seen to provide effective models for various classification problems. The resulting optimization problem to solve for the optimal vector minimizing the…

Latent variable models have been widely applied in different fields of research in which the constructs of interest are not directly observable, so that one or more latent variables are required to reduce the complexity of the data. In…

We initiate the study of smoothed analysis for the sequential probability assignment problem with contexts. We study information-theoretically optimal minmax rates as well as a framework for algorithmic reduction involving the maximum…

The zero-shot capability of Large Language Models (LLMs) has enabled highly flexible, reference-free metrics for various tasks, making LLM evaluators common tools in NLP. However, the robustness of these LLM evaluators remains relatively…