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Parameter estimation via unbinned maximum likelihood fits is central for many analyses performed in high energy physics. Unbinned maximum likelihood fits using event weights, for example to statistically subtract background contributions…
For the tree topology, previous studies show the maximum likelihood estimate (MLE) of a link/path takes a polynomial form with a degree that is one less than the number of descendants connected to the link/path. Since then, the main concern…
Every student in statistics or data science learns early on that when the sample size largely exceeds the number of variables, fitting a logistic model produces estimates that are approximately unbiased. Every student also learns that there…
Probabilities of causation provide principled ways to assess causal relationships but face computational challenges due to partial identifiability and latent confounding. This paper introduces both algorithmic simplifications, significantly…
Composite likelihood inference has gained much popularity thanks to its computational manageability and its theoretical properties. Unfortunately, performing composite likelihood ratio tests is inconvenient because of their awkward…
We revisit the problem of the existence of the maximum likelihood estimate for multi-class logistic regression. We show that one method of ensuring its existence is by assigning positive probability to every class in the sample dataset. The…
Feynman integral computations in theoretical high energy particle physics frequently involve square roots in the kinematic variables. Physicists often want to solve Feynman integrals in terms of multiple polylogarithms. One way to obtain a…
We study the inference of network archaeology in growing random geometric graphs. We consider the root finding problem for a random nearest neighbor tree in dimension $d \in \mathbb{N}$, generated by sequentially embedding vertices…
Misclassification of binary responses, if ignored, may severely bias the maximum likelihood estimators (MLE) of regression parameters. For such data, a binary regression model incorporating misclassification probabilities is extensively…
Multiple imputation (MI) inference handles missing data by imputing the missing values $m$ times, and then combining the results from the $m$ complete-data analyses. However, the existing method for combining likelihood ratio tests (LRTs)…
In algebraic statistics, the maximum likelihood degree of a statistical model is the number of complex critical points of its log-likelihood function. A priori knowledge of this number is useful for applying techniques of numerical…
We study probability density functions that are log-concave. Despite the space of all such densities being infinite-dimensional, the maximum likelihood estimate is the exponential of a piecewise linear function determined by finitely many…
Estimating a constrained relation is a fundamental problem in machine learning. Special cases are classification (the problem of estimating a map from a set of to-be-classified elements to a set of labels), clustering (the problem of…
Relative error approaches are more of concern compared to absolute error ones such as the least square and least absolute deviation, when it needs scale invariant of output variable, for example with analyzing stock and survival data. An…
AIMS. The maximum-likelihood method is the standard approach to obtain model fits to observational data and the corresponding confidence regions. We investigate possible sources of bias in the log-likelihood function and its subsequent…
A chief problem in phylogenetics and database theory is the computation of a maximum consistent tree from a set of rooted or unrooted trees. A standard input are triplets, rooted binary trees on three leaves, or quartets, unrooted binary…
In many complex statistical models maximum likelihood estimators cannot be calculated. In the paper we solve this problem using Markov chain Monte Carlo approximation of the true likelihood. In the main result we prove asymptotic normality…
We present new results for consistency of maximum likelihood estimators with a focus on multivariate mixed models. Our theory builds on the idea of using subsets of the full data to establish consistency of estimators based on the full…
The method of extended maximum likelihood is a well known concept of parameter estimation. One can implement external knowledge on the unknown parameters by multiplying the likelihood by constraint terms. In this note, we emphasize that…
In this article we discuss estimation of the common variance of several normal populations with tree order restricted means. We discuss the asymptotic properties of the maximum likelihood estimator of the variance as the number of…