Related papers: Adaptive exponential power distribution with movin…
The paper offers a unified approach to the study of three locally adaptive estimation methods in the context of univariate time series from both theoretical and empirical points of view. A general procedure for the computation of critical…
We introduce Exponential Family Discriminant Analysis (EFDA), a unified generative framework that extends classical Linear Discriminant Analysis (LDA) beyond the Gaussian setting to any member of the exponential family. Under the assumption…
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…
The exponential family is well known in machine learning and statistical physics as the maximum entropy distribution subject to a set of observed constraints, while the geometric mixture path is common in MCMC methods such as annealed…
Trajectory estimation of maneuvering objects is applied in numerous tasks like navigation, path planning and visual tracking. Many previous works get impressive results in the strictly controlled condition with accurate prior statistics and…
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…
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…
The {\lambda}-exponential family has recently been proposed to generalize the exponential family. While the exponential family is well-understood and widely used, this it not the case of the {\lambda}-exponential family. However, many…
In this article, we proposed a new probability distribution named as power Maxwell distribution (PMaD). It is another extension of Maxwell distribution (MaD) which would lead more flexibility to analyze the data with non-monotone failure…
We introduce a new generalization of the Pseudo-Lindley distribution by applying alpha power transformation. The obtained distribution is referred as the Pseudo-Lindley alpha power transformed distribution (\textit{PL-APT}). Some tractable…
We consider the problem of approximating the stationary distribution of an ergodic Markov chain given a set of sampled transitions. Classical simulation-based approaches assume access to the underlying process so that trajectories of…
We introduce a class of adaptive timestepping strategies for stochastic differential equations with non-Lipschitz drift coefficients. These strategies work by controlling potential unbounded growth in solutions of a numerical scheme due to…
In this article we propose a locally adaptive strategy for estimating a function from its Exponential Radon Transform (ERT) data, without prior knowledge of the smoothness of functions that are to be estimated. We build a non-parametric…
Estimating function inference is indispensable for many common point process models where the joint intensities are tractable while the likelihood function is not. In this paper we establish asymptotic normality of estimating function…
While it is a common knowledge that AC coefficients of Fourier-related transforms, like DCT-II of JPEG image compression, are from Laplace distribution, there was tested more general EPD (exponential power distribution) $\rho\sim…
Targeted maximum likelihood estimation (TMLE) is a general method for estimating parameters in semiparametric and nonparametric models. Each iteration of TMLE involves fitting a parametric submodel that targets the parameter of interest. We…
The $p$-tensor Ising model is a one-parameter discrete exponential family for modeling dependent binary data, where the sufficient statistic is a multi-linear form of degree $p \geq 2$. This is a natural generalization of the matrix Ising…
Heavy-tailed distributions are infamously difficult to estimate because their moments tend to infinity as the shape of the tail decay increases. Nevertheless, this study shows the utilization of a modified group of moments for estimating a…
Much of the theory of estimation for exponential family models, which include exponential-family random graph models (ERGMs) as a special case, is well-established and maximum likelihood estimates in particular enjoy many desirable…
We analyze the \textit{Large Deviation Probability (LDP)} of linear factor models generated from non-identically distributed components with \textit{regularly-varying} tails, a large subclass of heavy tailed distributions. An efficient…