Related papers: Essential formulae for restricted maximum likeliho…
Maximum-likelihood estimation (MLE) is arguably the most important tool for statisticians, and many methods have been developed to find the MLE. We present a new inequality involving posterior distributions of a latent variable that holds…
This work proposes a novel theoretical framework of robust limit analysis i.e. the computation of limit loads of structures in presence of uncertainties using limit analysis and robust optimization theories. We first derive generic robust…
Composite likelihoods are a class of alternatives to the full likelihood which are widely used in many situations in which the likelihood itself is intractable. A composite likelihood may be computed without the need to specify the full…
The maximum likelihood degree of a statistical model refers to the number of solutions, where the derivative of the log-likelihood function is zero, over the complex field. This paper examines the maximum likelihood degree of the parameter…
We characterize the existence of the maximum likelihood estimator for discrete exponential families. Our criterion is simple to apply as we show in various settings, most notably for exponential models of random graphs. As an application,…
We present an approximated maximum likelihood method for the multifractal random walk processes of [E. Bacry et al., Phys. Rev. E 64, 026103 (2001)]. The likelihood is computed using a Laplace approximation and a truncation in the…
Implicit probabilistic models are models defined naturally in terms of a sampling procedure and often induces a likelihood function that cannot be expressed explicitly. We develop a simple method for estimating parameters in implicit models…
Let X_1, ..., X_n be independent and identically distributed random vectors with a log-concave (Lebesgue) density f. We first prove that, with probability one, there exists a unique maximum likelihood estimator of f. The use of this…
Variational methods are employed in situations where exact Bayesian inference becomes intractable due to the difficulty in performing certain integrals. Typically, variational methods postulate a tractable posterior and formulate a lower…
For a single equation in a system of linear equations, estimation by instrumental variables is the standard approach. In practice, however, it is often difficult to find valid instruments. This paper proposes a maximum likelihood method…
Non-parametric methods avoid the problem of having to specify a particular data generating mechanism, but can be computationally intensive, reducing their accessibility for large data problems. Empirical likelihood, a non-parametric…
One of the most common anticipated difficulties in applying mainstream maximum likelihood inference upon extreme values is articulated on the scarcity of extreme observations for bringing the extreme value theorem to hold across a series of…
In this paper, we develop statistical inference techniques for the unknown coefficient functions and single-index parameters in single-index varying-coefficient models. We first estimate the nonparametric component via the local linear…
We develop a non-negative polynomial minimum-norm likelihood ratio (PLR) of two distributions of which only moments are known. The sample PLR converges to the unknown population PLR under mild conditions. The methodology allows for…
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…
The likelihood function of a finite mixture model is a non-convex function with multiple local maxima and commonly used iterative algorithms such as EM will converge to different solutions depending on initial conditions. In this paper we…
Composite likelihood estimation has an important role in the analysis of multivariate data for which the full likelihood function is intractable. An important issue in composite likelihood inference is the choice of the weights associated…
Large crossed data sets, described by generalized linear mixed models, have become increasingly common and provide challenges for statistical analysis. At very large sizes it becomes desirable to have the computational costs of estimation,…
The restricted maximum likelihood (REML) estimator of the dispersion matrix for random coefficient models is rewritten in terms of the sufficient statistics of the individual regressions.
We propose an efficient algorithm for approximate computation of the profile maximum likelihood (PML), a variant of maximum likelihood maximizing the probability of observing a sufficient statistic rather than the empirical sample. The PML…