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Originally introduced as a neural network for ensemble learning, mixture of experts (MoE) has recently become a fundamental building block of highly successful modern deep neural networks for heterogeneous data analysis in several…
In this paper, we develop a novel efficient and robust nonparametric regression estimator under a framework of feedforward neural network. There are several interesting characteristics for the proposed estimator. First, the loss function is…
This paper derives the nonparametric maximum likelihood estimator (NPMLE) of a distribution function from observations which are subject to both bias and censoring. The NPMLE is obtained by a simple EM algorithm which is an extension of the…
This paper introduces a high-dimensional binary variate model that accommodates nonstationary covariates and factors, and studies their asymptotic theory. This framework encompasses scenarios where single indices are nonstationary or…
In many signal detection and classification problems, we have knowledge of the distribution under each hypothesis, but not the prior probabilities. This paper is aimed at providing theory to quantify the performance of detection via…
In nonlinear deterministic parameter estimation, the maximum likelihood estimator (MLE) is unable to attain the Cramer-Rao lower bound at low and medium signal-to-noise ratios (SNR) due the threshold and ambiguity phenomena. In order to…
It is well known that under general regularity conditions the distribution of the maximum likelihood estimator (MLE) is asymptotically normal. Very recently, bounds of the optimal order $O(1/\sqrt n)$ on the closeness of the distribution of…
We employ a parameter-free distribution estimation framework where estimators are random distributions and utilize the Kullback-Leibler (KL) divergence as a loss function. Wu and Vos [J. Statist. Plann. Inference 142 (2012) 1525-1536] show…
Training the parameters of statistical models to describe a given data set is a central task in the field of data mining and machine learning. A very popular and powerful way of parameter estimation is the method of maximum likelihood…
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.…
Orthogonal group synchronization aims to recover orthogonal group elements from their noisy pairwise measurements. It has found numerous applications including computer vision, imaging science, and community detection. Due to the orthogonal…
In this article, we present the maximum weighted likelihood estimator (MWLE) for robust estimations of heavy-tail finite mixture models (FMM). This is motivated by the complex distributional phenomena of insurance claim severity data, where…
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…
This paper develops a unified estimation framework, the Maximum Ideal Likelihood Estimation (MILE), for general parametric models with latent variables. Unlike traditional approaches relying on the marginal likelihood of the observed data,…
The H\"usler-Reiss distribution describes the limit of the pointwise maxima of a bivariate normal distribution. This distribution is defined by a single parameter, $\lambda$. We provide asymptotic theory for maximum likelihood estimation of…
Maximum likelihood estimation of a location parameter fails when the density have unbounded mode. An alternative approach is considered by leaving out a data point to avoid the unbounded density in the full likelihood. This modification…
We present a new algorithm to generate a random (unclustered) version of an magnitude limited observational galaxy redshift catalogue. It takes into account both galaxy evolution and the perturbing effects of large scale structure. The key…
A number of problems in quantum state and system identification are addressed. Specifically, it is shown that the maximum likelihood estimation (MLE) approach, already known to apply to quantum state tomography, is also applicable to…
We develop a multi-level restricted Gaussian maximum likelihood method for estimating the covariance function parameters and computing the best unbiased predictor. Our approach produces a new set of multi-level contrasts where the…
In this work, we explore the theoretical properties of conditional deep generative models under the statistical framework of distribution regression where the response variable lies in a high-dimensional ambient space but concentrates…