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Max-stable distributions and processes are important models for extreme events and the assessment of tail risks. The full, multivariate likelihood of a parametric max-stable distribution is complicated and only recent advances enable its…
We study optimal estimation when the likelihood may be misspecified. Building on tools from the theory of decision-making under uncertainty, we analyze a class of axiomatically grounded optimality criteria which nests several existing…
We consider a one-dimensional recurrent random walk in random environment (RWRE) when the environment is i.i.d. with a parametric, finitely supported distribution. Based on a single observation of the path, we provide a maximum likelihood…
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…
Conditional copula models allow dependence structures to vary with observed covariates while preserving a separation between marginal behavior and association. We study the uniform asymptotic behavior of kernel-weighted local likelihood…
Pairwise comparisons of large language models using total variation distance mutual information (TVD-MI) produce binary critic decisions per pair. We show that averaging TVD-MI's binary trials yields centered-probability scores with…
In most machine learning applications, classification accuracy is not the primary metric of interest. Binary classifiers which face class imbalance are often evaluated by the $F_\beta$ score, area under the precision-recall curve, Precision…
Likelihood-free methods are useful for parameter estimation of complex models with intractable likelihood functions for which it is easy to simulate data. Such models are prevalent in many disciplines including genetics, biology, ecology…
In some estimation problems, especially in applications dealing with information theory, signal processing and biology, theory provides us with additional information allowing us to restrict the parameter space to a finite number of points.…
Bradley-Terry-Luce (BTL) model estimation is a well-established strategy to rank a collection of items given a dataset of pairwise comparisons. Although the theoretical performance of BTL estimation methods, such as spectral and maximum…
Positive and unlabelled learning is an important problem which arises naturally in many applications. The significant limitation of almost all existing methods lies in assuming that the propensity score function is constant (SCAR…
Ranking a vector of alternatives on the basis of a series of paired comparisons is a relevant topic in many instances. A popular example is ranking contestants in sport tournaments. To this purpose, paired comparison models such as the…
We consider hidden Markov models indexed by a binary tree where the hidden state space is a general metric space. We study the maximum likelihood estimator (MLE) of the model parameters based only on the observed variables. In both…
We study asymptotic behavior of one-step weighted $M$-estimators based on samples from arrays of not necessarily identically distributed random variables and representing explicit approximations to the corresponding consistent weighted…
A parameter estimation problem is considered, in which dispersed sensors transmit to the statistician partial information regarding their observations. The sensors observe the paths of continuous semimartingales, whose drifts are linear…
We study asymptotic behavior of one-step $M$-estimators based on samples from arrays of not necessarily identically distributed random variables and representing explicit approximations to the corresponding consistent $M$-estimators. These…
Tuning parameters are parameters involved in an estimating procedure for the purpose of reducing the risk of some other estimator. Examples include the degree of penalization in penalized regression and likelihood problems, as well as the…
Many statistical applications involve models for which it is difficult to evaluate the likelihood, but from which it is relatively easy to sample. Approximate Bayesian computation is a likelihood-free method for implementing Bayesian…
We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size…
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…