Related papers: Maximum Likelihood Estimation of Functionals of Di…
Inspired by applications to theories of coding and communication in networks of nervous tissue, we study maximum entropy distributions on weighted graphs with a given expected degree sequence. These distributions are characterized by…
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…
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,…
We study maximum likelihood estimation in log-linear models under conditional Poisson sampling schemes. We derive necessary and sufficient conditions for existence of the maximum likelihood estimator (MLE) of the model parameters and…
Distributed learning of probabilistic models from multiple data repositories with minimum communication is increasingly important. We study a simple communication-efficient learning framework that first calculates the local maximum…
We consider the problem of approximating the empirical Shannon entropy of a high-frequency data stream under the relaxed strict-turnstile model, when space limitations make exact computation infeasible. An equivalent measure of entropy is…
In this paper, we study the log-likelihood function and Maximum Likelihood Estimate (MLE) for the matrix normal model for both real and complex models. We describe the exact number of samples needed to achieve (almost surely) three…
We revisit the well-studied problem of estimating the Shannon entropy of a probability distribution, now given access to a probability-revealing conditional sampling oracle. In this model, the oracle takes as input the representation of a…
Let $ X_1, \ldots, X_n $ be independent random variables taking values in the alphabet $ \{0, 1, \ldots, r\} $, and $ S_n = \sum_{i = 1}^n X_i $. The Shepp--Olkin theorem states that, in the binary case ($ r = 1 $), the Shannon entropy of $…
We consider distributed estimation of the inverse covariance matrix, also called the concentration or precision matrix, in Gaussian graphical models. Traditional centralized estimation often requires global inference of the covariance…
In this paper, we estimate the Shannon entropy $S(f) = -\E[ \log (f(x))]$ of a one-sided linear process with probability density function $f(x)$. We employ the integral estimator $S_n(f)$, which utilizes the standard kernel density…
This paper concerns the nonparametric estimation problem of the distribution-state dependent drift vector field in an interacting $N$-particle system. Observing single-trajectory data for each particle, we derive the mean-field rate of…
In finite mixtures of location-scale distributions, if there is no constraint on the parameters then the maximum likelihood estimate does not exist. But when the ratios of the scale parameters are restricted appropriately, the maximum…
In this paper, we study the nonparametric maximum likelihood estimator (MLE) of a convex hazard function. We show that the MLE is consistent and converges at a local rate of $n^{2/5}$ at points $x_0$ where the true hazard function is…
This study focuses on the estimation of the Emax dose-response model, a widely utilized framework in clinical trials, agriculture, and environmental experiments. Existing challenges in obtaining maximum likelihood estimates (MLE) for model…
In this paper, the maximum L$q$-likelihood estimator (ML$q$E), a new parameter estimator based on nonextensive entropy [Kibernetika 3 (1967) 30--35] is introduced. The properties of the ML$q$E are studied via asymptotic analysis and…
Estimating the frequencies of multiple sinusoids in the presence of AWGN and when the data record is short is commonly accomplished by subspace-based methods such as ESPRIT, MUSIC, Min-Norm, etc. These methods do not assume that the data…
This paper develops the process of using Richardson Extrapolation to improve the Kernel Density Estimation method, resulting in a more accurate (lower Mean Squared Error) estimate of a probability density function for a distribution of data…
In the missing data literature, the Maximum Likelihood Estimator (MLE) is celebrated for its ignorability property under missing at random (MAR) data. However, its sensitivity to misspecification of the (complete) data model, even under…
Distributional regression aims to find the best candidate in a given parametric family of conditional distributions to model a given dataset. As each candidate in the distribution family can be identified by the corresponding distribution…