Theoretical properties of the log-concave maximum likelihood estimator of a multidimensional density

We present theoretical properties of the log-concave maximum likelihood estimator of a density based on an independent and identically distributed sample in $\mathbb{R}^d$. Our study covers both the case where the true underlying density is log-concave, and where this model is misspecified. We begin by showing that for a sequence of log-concave densities, convergence in distribution implies much stronger types of convergence -- in particular, it implies convergence in Hellinger distance and even in certain exponentially weighted total variation norms. In our main result, we prove the existence and uniqueness of a log-concave density that minimises the Kullback--Leibler divergence from the true density over the class all log-concave densities, and also show that the log-concave maximum likelihood estimator converges almost surely in these exponentially weighted total variation norms to this minimiser. In the case of a correctly specified model, this demonstrates a strong type of consistency for the estimator; in a misspecified model, it shows that the estimator converges to the log-concave density that is closest in the Kullback--Leibler sense to the true density.Comment: 20 pages, 0 figure

LogConcDEAD: An R Package for Maximum Likelihood Estimation of a Multivariate Log-Concave Density

In this article we introduce the R package LogConcDEAD (Log-concave density estimation in arbitrary dimensions). Its main function is to compute the nonparametric maximum likelihood estimator of a log-concave density. Functions for plotting, sampling from the density estimate and evaluating the density estimate are provided. All of the functions available in the package are illustrated using simple, reproducible examples with simulated data.

LogConcDEAD: An R package for maximum likelihood estimation of a multivariate log-concave density

In this document we introduce the R package LogConcDEAD (Log-concave density estimation in arbitrary dimensions). Its main function is to compute the nonparametric maximum likelihood estimator of a log-concave density. Functions for plotting, sampling from the density estimate and evaluating the density estimate are provided. All of the functions available in the package are illustrated using simple, reproducible examples with simulated data

Valuing EQ-5D health states: A review and analysis, CHERE Working Paper 2007/9

Objective: To identify the key methodological issues in the construction of population-level EQ-5D / Time Trade-Off (TTO) preference elicitation studies. Study Design: This study involves three components. The first was to identify existing population-level EQ-5D TTO studies. The second was to illustrate and discuss the key areas of divergence between studies, including the international comparison of tariffs. The third was to portray the relative merits of each of the approaches, and to compare the results of studies across countries. Results: While most papers report use of the protocol developed in the original UK study, we identified three key areas of divergence in the construction and analysis of surveys. These are the number of health states valued in order to determine the algorithm for estimating all health states, the approach to valuing states worse than immediate death, and the choice of algorithm. Finally, the evidence on international comparisons suggests differences between countries, although it is difficult to disentangle differences in cultural attitudes with random error and differences due to methodological divergence. Conclusion: Differences in methods are likely to obscure true differences in values between countries. However, population-specific valuation sets for countries engaging in economic evaluation would better represent societal attitudes.health state valuation, EQ5-D

Collaborative Language Planning Project: Report 07: Summer 2022

Collaborative Language Planning Project report of activities, January 2022 - July 2022

Collaborative Language Planning Project: Report 08: Winter 2023

Collaborative Language Planning Project report of activities, August 2022 - January 2023

Collaborative Language Planning Project: Report 05: Summer 2021

Collaborative Language Planning Project report of activities, January 2021 - June 2021

Collaborative Language Planning Project: Report 06: Winter 2022

Collaborative Language Planning Project report of activities, July 2021 - December 2022

La qualité relationnelle dans la famille recomposée : perspectives du parent et de l’enfant

Cette recherche porte sur les facteurs associés à la qualité relationnelle dans la famille recomposée. Elle met en relation l'âge de l'enfant, le genre de son parent biologique, le degré de contact avec le parent non gardien et la situation socio-économique familiale avec deux indicateurs de qualité relationnelle : la perception de la qualité du fonctionnement familial et la satisfaction à l'égard de ce fonctionnement. Le rendement scolaire est aussi considéré en tant que mesure du niveau d'adaptation extrafamiliale de l'enfant. L'échantillon se compose de 45 dyades enfant-parent biologique (17 pères et 28 mères) vivant dans des familles recomposées depuis en moyenne trois ans et huit mois. Aucune des hypothèses n'a trouvé d'appui dans les données issues des perceptions parentales. Deux hypothèses ont été confirmées à partir des perceptions des jeunes : a) les enfants de 9 à 11 ans perçoivent une meilleure qualité relationnelle dans leur famille recomposée que les adolescents de 14 à16 ans; et b) dans leur nouvelle famille, les enfants vivant avec leur mère biologique sont plus satisfaits des relations familiales que ceux qui vivent avec leur père biologique. Les conséquences pour la pratique et pour la recherche sont définies

Book Reviews

Reviews of the following books: Lewiston: A Textile City in Transition by James S. Leamon; Massachusetts: A Bibliography of its History edited by John D. Haskell; Bibliography of Maine, 1960-1975 compiled by Eric S. Flower; Maine in the Revolution: A Reader\u27s Guide compiled by Edwin A. Churchill and James Leamon; Maine Communities and War for Independence: A Guide for Study of Local Maine History as Related to the American Revolution compiled by Edwin A Churchill