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We use the delta method and Stein's method to derive, under regularity conditions, explicit upper bounds for the distributional distance between the distribution of the maximum likelihood estimator (MLE) of a $d$-dimensional parameter and…

Statistics Theory · Mathematics 2020-02-04 Andreas Anastasiou , Robert E. Gaunt

The behavior of maximum likelihood estimates (MLEs) and the likelihood ratio statistic in a family of problems involving pointwise nonparametric estimation of a monotone function is studied. This class of problems differs radically from the…

Statistics Theory · Mathematics 2009-09-29 Moulinath Banerjee

We prove the asymptotic properties of the maximum likelihood estimator (MLE) in time-varying transition probability (TVTP) regime-switching models. This class of models extends the constant regime transition probability in Markov-switching…

Econometrics · Economics 2021-12-06 Chaojun Li , Yan Liu

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…

Methodology · Statistics 2022-07-21 Jeongseop Han , Youngjo Lee

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…

Representation Theory · Mathematics 2020-07-21 Harm Derksen , Visu Makam

This paper considers the maximum likelihood estimation of factor models of high dimension, where the number of variables (N) is comparable with or even greater than the number of observations (T). An inferential theory is developed. We…

Statistics Theory · Mathematics 2012-05-31 Jushan Bai , Kunpeng Li

The saddlepoint approximation gives an approximation to the density of a random variable in terms of its moment generating function. When the underlying random variable is itself the sum of $n$ unobserved i.i.d. terms, the basic classical…

Statistics Theory · Mathematics 2022-01-25 Jesse Goodman

This paper establishes asymptotic results for the maximum likelihood and restricted maximum likelihood (REML) estimators of the parameters in the nested error regression model for clustered data when both of the number of independent…

Statistics Theory · Mathematics 2021-01-25 Ziyang Lyu , A. H. Welsh

We study nonparametric maximum likelihood estimation of a log-concave density function $f_0$ which is known to satisfy further constraints, where either (a) the mode $m$ of $f_0$ is known, or (b) $f_0$ is known to be symmetric about a fixed…

Statistics Theory · Mathematics 2019-05-15 Charles R. Doss , Jon A. Wellner

Strong consistency and asymptotic normality of the Quasi-Maximum Likelihood Estimator (QMLE) are given for a general class of multidimensional causal processes. For particular cases already studied in the literature (for instance univariate…

Statistics Theory · Mathematics 2009-01-09 Jean-Marc Bardet , Olivier Wintenberger

In the context of a large system of $N$ neurons interacting through spike events in a mean-field regime as $N\rightarrow \infty$, we characterize the estimation of a multidimensional parameter in the spiking rate, when the neural states are…

Statistics Theory · Mathematics 2026-05-06 Aline Duarte , Dasha Loukianova , Aurélien Velleret

We study the distribution of the maximum likelihood estimate (MLE) in high-dimensional logistic models, extending the recent results from Sur (2019) to the case where the Gaussian covariates may have an arbitrary covariance structure. We…

Statistics Theory · Mathematics 2023-01-05 Qian Zhao , Pragya Sur , Emmanuel J. Candès

We study and compare three estimators of a discrete monotone distribution: (a) the (raw) empirical estimator; (b) the "method of rearrangements" estimator; and (c) the maximum likelihood estimator. We show that the maximum likelihood…

Statistics Theory · Mathematics 2009-10-20 Hanna K. Jankowski , Jon A. Wellner

In a regular full exponential family, the maximum likelihood estimator (MLE) need not exist in the traditional sense. However, the MLE may exist in the completion of the exponential family. Existing algorithms for finding the MLE in the…

Statistics Theory · Mathematics 2020-11-30 Daniel J. Eck , Charles J. Geyer

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…

Methodology · Statistics 2023-01-02 Anna Klimova , Matthias Kuhn

Empirical economic research frequently applies maximum likelihood estimation in cases where the likelihood function is analytically intractable. Most of the theoretical literature focuses on maximum simulated likelihood (MSL) estimators,…

Econometrics · Economics 2019-08-13 Michael Griebel , Florian Heiss , Jens Oettershagen , Constantin Weiser

Consider a parametrized family of general hidden Markov models, where both the observed and unobserved components take values in a complete separable metric space. We prove that the maximum likelihood estimator (MLE) of the parameter is…

Statistics Theory · Mathematics 2011-03-10 Randal Douc , Eric Moulines , Jimmy Olsson , Ramon van Handel

Two new test statistics are introduced to test the null hypotheses that the sampling distribution has an increasing hazard rate on a specified interval [0,a]. These statistics are empirical L_1-type distances between the isotonic estimates,…

Statistics Theory · Mathematics 2015-03-17 Piet Groeneboom , Geurt Jongbloed

We describe Monte Carlo approximation to the maximum likelihood estimator in models with intractable norming constants and explanatory variables. We consider both sources of randomness (due to the initial sample and to Monte Carlo…

Methodology · Statistics 2016-12-08 Blazej Miasojedow , Wojciech Niemiro , Jan Palczewski , Wojciech Rejchel

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…

Statistics Theory · Mathematics 2009-12-19 Karine Bertin , Soledad Torres , Ciprian Tudor