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This work studies the properties of the maximum likelihood estimator (MLE) of a non-linear model with Gaussian errors and multidimensional parameter. The observations are collected in a two-stage experimental design and are dependent since…
In certain privacy-sensitive scenarios within fields such as clinical trial simulations, federated learning, and distributed learning, researchers often face the challenge of estimating correlations between variables without access to…
In this paper, we consider distributed maximum likelihood estimation (MLE) with dependent quantized data under the assumption that the structure of the joint probability density function (pdf) is known, but it contains unknown deterministic…
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…
Adaptive designs are commonly used in clinical and drug development studies for optimum utilization of available resources. In this article, we consider the problem of estimating the effect of the selected (better) treatment using a…
Optimum designs for parameter estimation in generalized regression models are standardly based on the Fisher information matrix (cf. Atkinson et al (2014) for a recent exposition). The corresponding optimality criteria are related to the…
Distributed statistical inference has recently attracted immense attention. The asymptotic efficiency of the maximum likelihood estimator (MLE), the one-step MLE, and the aggregated estimating equation estimator are established for…
Adaptive experimental designs have gained popularity in clinical trials and online experiments. Unlike traditional, fixed experimental designs, adaptive designs can dynamically adjust treatment randomization probabilities and other design…
Dose selection is critical in pharmaceutical drug development, as it directly impacts therapeutic efficacy and patient safety of a drug. The Generalized Multiple Comparison Procedures and Modeling (MCP-Mod) approach is commonly used in…
Active learning aims to efficiently build a labeled training set by strategically selecting samples to query labels from annotators. In this sequential process, each sample acquisition influences subsequent selections, causing dependencies…
Maximum likelihood estimation is a popular method in statistical inference. As a way of assessing the accuracy of the maximum likelihood estimate (MLE), the calculation of the covariance matrix of the MLE is of great interest in practice.…
Consider a setting with $N$ independent individuals, each with an unknown parameter, $p_i \in [0, 1]$ drawn from some unknown distribution $P^\star$. After observing the outcomes of $t$ independent Bernoulli trials, i.e., $X_i \sim…
Informative interim adaptations lead to random sample sizes. The random sample size becomes a component of the sufficient statistic and estimation based solely on observed samples or on the likelihood function does not use all available…
The treatment assignment mechanism in a randomized clinical trial can be optimized for statistical efficiency within a specified class of randomization mechanisms. Optimal designs of this type have been characterized in terms of the…
Distributional regression aims to find the best candidate in a given parametric family of conditional distributions to model a given dataset. As each candidate in the distribution family can be identified by the corresponding distribution…
We advocate for a practical Maximum Likelihood Estimation (MLE) approach towards designing loss functions for regression and forecasting, as an alternative to the typical approach of direct empirical risk minimization on a specific target…
This manuscript investigates unconditional and conditional-on-stopping maximum likelihood estimators (MLEs), information measures and information loss associated with conditioning in group sequential designs (GSDs). The possibility of early…
Maximum likelihood estimates and corresponding confidence regions of the estimates are commonly used in statistical inference. In practice, people often construct approximate confidence regions with the Fisher information at given sample…
Agent-based simulation with a synthetic population can help us compare different treatment conditions while keeping everything else constant within the same population (i.e., as digital twins). Such population-scale simulations require…
In fitting a mixture of linear regression models, normal assumption is traditionally used to model the error and then regression parameters are estimated by the maximum likelihood estimators (MLE). This procedure is not valid if the normal…