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We revisit the classical problem of deriving convergence rates for the maximum likelihood estimator (MLE) in finite mixture models. The Wasserstein distance has become a standard loss function for the analysis of parameter estimation in…

Statistics Theory · Mathematics 2022-06-22 Tudor Manole , Nhat Ho

Consider a setting with $N$ independent individuals, each with an unknown parameter, $p_i \in [0, 1]$ drawn from some unknown distribution $P^\star$. After observing the outcomes of $t$ independent Bernoulli trials, i.e., $X_i \sim…

Statistics Theory · Mathematics 2019-02-13 Ramya Korlakai Vinayak , Weihao Kong , Gregory Valiant , Sham M. Kakade

We consider 1-dimensional location estimation, where we estimate a parameter $\lambda$ from $n$ samples $\lambda + \eta_i$, with each $\eta_i$ drawn i.i.d. from a known distribution $f$. For fixed $f$ the maximum-likelihood estimate (MLE)…

Statistics Theory · Mathematics 2022-07-20 Shivam Gupta , Jasper C. H. Lee , Eric Price , Paul Valiant

\cite{bickel2009nonparametric} developed a general framework to establish consistency of community detection in stochastic block model (SBM). In most applications of this framework, the community label is discrete. For example, in…

Methodology · Statistics 2017-10-17 Lu Liu , Lili Wang , Qingsong Xu

The Expectation-Maximization (EM) algorithm is an iterative method to maximize the log-likelihood function for parameter estimation. Previous works on the convergence analysis of the EM algorithm have established results on the asymptotic…

Statistics Theory · Mathematics 2017-05-31 Chong Wu , Can Yang , Hongyu Zhao , Ji Zhu

We study statistical inference for small-noise-perturbed multiscale dynamical systems. We prove consistency, asymptotic normality, and convergence of all scaled moments of an appropriately-constructed maximum likelihood estimator (MLE) for…

Probability · Mathematics 2016-06-16 Siragan Gailus , Konstantinos Spiliopoulos

We study asymptotic properties of maximum likelihood estimators of drift parameters for a jump-type Heston model based on continuous time observations, where the jump process can be any purely non-Gaussian L\'evy process of not necessarily…

Statistics Theory · Mathematics 2018-06-08 Matyas Barczy , Mohamed Ben Alaya , Ahmed Kebaier , Gyula Pap

We solve the problem of estimating the distribution of presumed i.i.d. observations for the total variation loss. Our approach is based on density models and is versatile enough to cope with many different ones, including some density…

Statistics Theory · Mathematics 2024-01-05 Y. Baraud , H. Halconruy , G. Maillard

Models with multiple change points are used in many fields; however, the theoretical properties of maximum likelihood estimators of such models have received relatively little attention. The goal of this paper is to establish the asymptotic…

Statistics Theory · Mathematics 2011-02-28 Heping He , Thomas A. Severini

In this article, we study the limit distribution of the least square estimator, properly normalized, from a regression model in which observations are assumed to be finite ($\alpha N$) and sampled under two different random times. Based on…

Statistics Theory · Mathematics 2020-12-17 Tania Roa , Soledad Torres , Ciprian tudor

Distributed statistical inference has recently attracted immense attention. The asymptotic efficiency of the maximum likelihood estimator (MLE), the one-step MLE, and the aggregated estimating equation estimator are established for…

Methodology · Statistics 2020-08-14 Ping Zhou , Zhen Yu , Jingyi Ma , Maozai Tian , Ye Fan

The problem of estimating an unknown deterministic parameter vector from sign measurements with a perturbed sensing matrix is studied in this paper. We analyze the best achievable mean square error (MSE) performance by exploring the…

Information Theory · Computer Science 2015-06-18 Jiang Zhu , Xiaohan Wang , Yuantao Gu

In this paper, we study the asymptotic behaviors of the extreme of mixed skew-t distribution. We considered limits on distribution and density of maximum of mixed skew-t distribution under linear and power normalization, and further derived…

Statistics Theory · Mathematics 2016-06-13 Jingyao Hou , Xin Liao , Zuoxiang Peng

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

In order to learn the complex features of large spatio-temporal data, models with large parameter sets are often required. However, estimating a large number of parameters is often infeasible due to the computational and memory costs of…

Computation · Statistics 2018-07-02 Matthew Edwards , Stefano Castruccio , Dorit Hammerling

This short note is to point the reader to notice that the proof of high dimensional asymptotic normality of MLE estimator for logistic regression under the regime $p_n=o(n)$ given in paper: "Maximum likelihood estimation in logistic…

Statistics Theory · Mathematics 2018-01-29 Huiming Zhang

The convergence of variable-step L1 scheme is studied for the time-fractional molecular beam epitaxy (MBE) model with slope selection.A novel asymptotically compatible $L^2$ norm error estimate of the variable-step L1 scheme is established…

Numerical Analysis · Mathematics 2023-01-31 Yin Yang , Jindi Wang , Yanping Chen , Hong-lin Liao

Maximum marginal likelihood estimation (MMLE) can be formulated as the optimization of a free energy functional. From this viewpoint, the Expectation-Maximisation (EM) algorithm admits a natural interpretation as a coordinate descent method…

Machine Learning · Statistics 2026-03-10 Adam Rozzio , Rafael Athanasiades , O. Deniz Akyildiz

We consider estimation of a one-dimensional location parameter by means of M-estimators S_n with monotone influence curve psi. For growing sample size n, on suitably thinned out convex contamination ball BQ_n of shrinking radius r/sqrt(n)…

Statistics Theory · Mathematics 2010-06-02 Peter Ruckdeschel

Let $\{X_i,i=1,2,...\}$ be i.i.d. standard gaussian variables. Let $S_n=X_1+...+X_n$ be the sequence of partial sums and $$ L_n=\max_{0\leq i<j\leq n}\frac{S_j-S_i}{\sqrt{j-i}}. $$ We show that the distribution of $L_n$, appropriately…

Probability · Mathematics 2008-06-06 Zakhar Kabluchko