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Estimating model parameters is a crucial step in mathematical modelling and typically involves minimizing the disagreement between model predictions and experimental data. This calibration data can change throughout a study, particularly if…
Probabilistic regression models the entire predictive distribution of a response variable, offering richer insights than classical point estimates and directly allowing for uncertainty quantification. While diffusion-based generative models…
The primary objective of this scholarly work is to develop two estimation procedures - maximum likelihood estimator (MLE) and method of trimmed moments (MTM) - for the mean and variance of lognormal insurance payment severity data sets…
The paper studies asymptotic properties of estimators of multidimensional stochastic differential equations driven by Brownian motions from high-frequency discrete data. Consistency and central limit properties of a class of estimators of…
In this paper we present a novel method for estimating the parameters of a parametric diffusion processes. Our approach is based on a closed-form Maximum Likelihood estimator for an approximating Continuous Time Markov Chain (CTMC) of the…
In this article, we consider diffusion approximations for a general class of stochastic recursions. Such recursions arise as models for population growth, genetics, financial securities, multiplicative time series, numerical schemes and…
This paper deals with nonlinear mechanics of an elevator brake system subjected to uncertainties. A deterministic model that relates the braking force with uncertain parameters is deduced from mechanical equilibrium conditions. In order to…
We consider the problem of the estimation of the invariant distribution function of an ergodic diffusion process when the drift coefficient is unknown. The empirical distribution function is a natural estimator which is unbiased, uniformly…
This paper explores Maximum Likelihood in parametric models in the context of Sanov type Large Deviation Probabilities. MLE in parametric models under weighted sampling is shown to be associated with the minimization of a specific…
Markov regime switching models have been widely used in numerous empirical applications in economics and finance. However, the asymptotic distribution of the maximum likelihood estimator (MLE) has not been proven for some empirically…
In this paper, we study networks of positive linear systems subject to time-invariant and random uncertainties. We present linear matrix inequalities for checking the stability of the whole network around the origin with prescribed…
We introduce several new models whose common feature is to take into account effects from topological vorticity. The macroscopic unknown is driven by a dissipative anomalous diffusion (of SQG-type) and is coupled with the orientation of the…
Maximum likelihood estimation is a common method of estimating the parameters of the probability distribution from a given sample. This paper aims to introduce the maximum likelihood estimation in the framework of sublinear expectation. We…
We study maximum-likelihood-type estimation for diffusion processes when the coefficients are nonrandom and observation occurs in nonsynchronous manner. The problem of nonsynchronous observations is important when we consider the analysis…
A theorem of McCann shows that for any two absolutely continuous probability measures on R^d there exists a monotone transformation sending one probability measure to the other. A consequence of this theorem, relevant to statistics, is that…
Machine-Learned Likelihoods (MLL) combines machine-learning classification techniques with likelihood-based inference tests to estimate the experimental sensitivity of high-dimensional data sets. We extend the MLL method by including Kernel…
Generalized linear models (GLMs) are fundamental tools for statistical modeling, with maximum likelihood estimation (MLE) serving as the classical approach for parameter inference. While MLE performs well for canonical GLMs, it can become…
We consider the problem of estimating the joint distribution function of the event time and a continuous mark variable based on censored data. More specifically, the event time is subject to current status censoring and the continuous mark…
In this paper we study the properties of the Lasso estimator of the drift component in the diffusion setting. More specifically, we consider a multivariate parametric diffusion model $X$ observed continuously over the interval $[0,T]$ and…
Consider the nonparametric logistic regression problem. In the logistic regression, we usually consider the maximum likelihood estimator, and the excess risk is the expectation of the Kullback-Leibler (KL) divergence between the true and…