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Chiara Tommasi

Publications and source records attributed to Chiara Tommasi.

6 recordsLinked to original sources
arXiv2024

Maximum Likelihood Estimation under the Emax Model: Existence, Geometry and Efficiency

This study focuses on the estimation of the Emax dose-response model, a widely utilized framework in clinical trials, agriculture, and environmental experiments. Existing challenges in obtaining maximum likelihood estimates (MLE) for model parameters are often ascribed to computational issues but, in reality, stem from the absence of a MLE. Our contribution provides a new understanding and control of all the experimental situations that practitioners might face, guiding them in the estimation process. We derive the exact MLE for a three-point experimental design and we identify the two scenarios where the MLE fails. To address these challenges, we propose utilizing Firth's modified score, providing its analytical expression as a function of the experimental design. Through a simulation study, we demonstrate that, in one of the problematic cases, the Firth modification yields a finite estimate. For the remaining case, we introduce a design-augmentation strategy akin to a hypothesis test.

stat.ME↗
arXiv2022

Designing to detect heteroscedasticity in a regression model

We consider the problem of designing experiments to detect the presence of a specified heteroscedastity in a non-linear Gaussian regression model. In this framework, we focus on the ${\rm D}_s$- and KL-criteria and study their relationship with the noncentrality parameter of the asymptotic chi-squared distribution of a likelihood-based test, for local alternatives. Specifically, we found that when the variance function depends just on one parameter, the two criteria coincide asymptotically and in particular, the ${\rm D}_1$-criterion is proportional to the noncentrality parameter. Differently, if the variance function depends on a vector of parameters, then the KL-optimum design converges to the design that maximizes the noncentrality parameter. Furthermore, we confirm our theoretical findings through a simulation study concerning the computation of asymptotic and exact powers of the log-likelihood ratio statistic.

math.ST↗
arXiv2019

The Effects of Adaptation on Inference for Non-Linear Regression Models with Normal Errors

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 the second stage design is determined by the observations at the first stage; the MLE maximizes the total likelihood. Differently from the most of the literature, the first stage sample size is small, and hence asymptotic approximation is used only in the second stage. It is proved that the MLE is consistent and that its asymptotic distribution is a specific Gaussian mixture, via stable convergence. Finally, a simulation study is provided in the case of a dose-response Emax model.

math.ST↗
arXiv2016

Best estimation of functional linear models

Observations which are realizations from some continuous process are frequent in sciences, engineering, economics, and other fields. We consider linear models, with possible random effects, where the responses are random functions in a suitable Sobolev space. The processes cannot be observed directly. With smoothing procedures from the original data, both the response curves and their derivatives can be reconstructed, even separately. From both these samples of functions, just one sample of representatives is obtained to estimate the vector of functional parameters. A simulation study shows the benefits of this approach over the common method of using information either on curves or derivatives. The main theoretical result is a strong functional version of the Gauss-Markov theorem. This ensures that the proposed functional estimator is more efficient than the best linear unbiased estimator based only on curves or derivatives.

math.ST↗
arXiv2014

KL-optimum designs: theoretical properties and practical computation

In this paper some new properties and computational tools for finding KL-optimum designs are provided. KL-optimality is a general criterion useful to select the best experimental conditions to discriminate between statistical models. A KL-optimum design is obtained from a minimax optimization problem, which is defined on a infinite-dimensional space. In particular, continuity of the KL-optimality criterion is proved under mild conditions; as a consequence, the first-order algorithm converges to the set of KL-optimum designs for a large class of models. It is also shown that KL-optimum designs are invariant to any scale-position transformation. Some examples are given and discussed, together with some practical implications for numerical computation purposes.

stat.ME↗