Related papers: Some results on maximum likelihood from incomplete…
Hierarchical parametric models consisting of observable and latent variables are widely used for unsupervised learning tasks. For example, a mixture model is a representative hierarchical model for clustering. From the statistical point of…
Maximum likelihood estimation in nonlinear models can exhibit substantial instability in finite samples when the data provide limited information about certain parameters. Such instability is driven by rare but extreme realizations of the…
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…
A common approach to analyzing categorical correlated time series data is to fit a generalized linear model (GLM) with past data as covariate inputs. There remain challenges to conducting inference for short time series length. By treating…
We prove two lower bounds for the complexity of non-log-concave sampling within the framework of Balasubramanian et al. (2022), who introduced the use of Fisher information (FI) bounds as a notion of approximate first-order stationarity in…
We consider a one dimensional sub-ballistic random walk evolving in a parametric i.i.d. random environment. We study the asymptotic properties of the maximum likelihood estimator (MLE) of the parameter based on a single observation of the…
In many statistical signal processing applications, the estimation of nuisance parameters and parameters of interest is strongly linked to the resulting performance. Generally, these applications deal with complex data. This paper focuses…
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 can directly sample from the conditional distribution of any log-affine model. The algorithm is a Markov chain on a bounded integer lattice, and its transition probability is the ratio of the UMVUE (uniformly minimum variance unbiased…
This paper is concerned with various Mallows ranking models. We study the statistical properties of the MLE of Mallows' $\phi$ model. We also make connections of various Mallows ranking models, encompassing recent progress in mathematics.…
This paper proposes and axiomatizes a new updating rule: Relative Maximum Likelihood (RML) for ambiguous beliefs represented by a set of priors (C). This rule takes the form of applying Bayes' rule to a subset of C. This subset is a linear…
The data of the experiment of Schiller et al., Phys. Rev. Lett. 77 (1996) 2933, are alternatively evaluated using the maximum likelihood estimation. The given data are fitted better than by the standard deterministic approach. Nevertheless,…
The James-Stein estimator's dominance over maximum likelihood in terms of mean square error (MSE) has been one of the most celebrated results in modern statistics, suggesting that biased estimators can systematically outperform unbiased…
Skew normal mixture models provide a more flexible framework than the popular normal mixtures for modelling heterogeneous data with asymmetric behaviors. Due to the unboundedness of likelihood function and the divergency of shape…
Relative error estimation has been recently used in regression analysis. A crucial issue of the existing relative error estimation procedures is that they are sensitive to outliers. To address this issue, we employ the $\gamma$-likelihood…
We provide a comprehensive overview of latent Markov (LM) models for the analysis of longitudinal categorical data. The main assumption behind these models is that the response variables are conditionally independent given a latent process…
Maximum likelihood estimation is effective for identifying dynamical systems, but applying it to large networks becomes computationally prohibitive. This paper introduces a maximum likelihood estimation method that enables identification of…
Machine Learning (ML) is an expressive framework for turning data into computer programs. Across many problem domains -- both in industry and policy settings -- the types of computer programs needed for accurate prediction or optimal…
Low-rank matrix completion concerns the problem of estimating unobserved entries in a matrix using a sparse set of observed entries. We consider the non-uniform setting where the observed entries are sampled with highly varying…
In this paper a new distribution is proposed. This new model provides more flexibility to modeling data with upside-down bathtub hazard rate function. A significant account of mathematical properties of the new distribution is presented.…