Asymptotic Properties of QML Estimators for VARMA Models with Time‐dependent Coefficients

This paper is about vector autoregressive‐moving average models with time‐dependent coefficients to represent non‐stationary time series. Contrary to other papers in the univariate case, the coefficients depend on time but not on the series' length n. Under appropriate assumptions, it is shown that a Gaussian quasi‐maximum likelihood estimator is almost surely consistent and asymptotically normal. The theoretical results are illustrated by means of two examples of bivariate processes. It is shown that the assumptions underlying the theoretical results apply. In the second example, the innovations are marginally heteroscedastic with a correlation ranging from ?0.8 to 0.8. In the two examples, the asymptotic information matrix is obtained in the Gaussian case. Finally, the finite‐sample behaviour is checked via a Monte Carlo simulation study for n from 25 to 400. The results confirm the validity of the asymptotic properties even for short series and the asymptotic information matrix deduced from the theory.     

On the pointwise mean squared error of a multidimensional term-by-term thresholding wavelet estimator

In this paper we provide a theoretical contribution to the pointwise mean squared error of an adaptive multidimensional term-by-term thresholding wavelet estimator. A general result exhibiting fast rates of convergence under mild assumptions on the model is proved. It can be applied for a wide range of non parametric models including possible dependent observations. We give applications of this result for the non parametric regression function estimation problem (with random design) and the conditional density estimation problem.     

Aging and well-being in French older adults regularly practicing physical activity: a self-determination perspective

The purpose of this study was to identify the motivational profiles of physically active older adults and to achieve a better understanding of their perceived motives to explain their regular physical activity behavior in relation to self-determination theory (SDT). To address these aims, this study used quantitative and qualitative approaches. Older adults (n = 92; M = 74.95, SD = 4.6) completed the French version of the Sport Motivational Scale. A cluster analysis showed two motivational profiles with differential motivational patterns. The first was named the high combined profile, with high scores on intrinsic motivation and introjected regulation and low levels of external regulation. The second profile was the low to moderate motivational profile, with low scores on intrinsic motivation and moderate scores on introjected regulation. The qualitative study's results demonstrate the usefulness of SDT in explaining the relationship between these motivational profiles and the intertwining of the three basic psychological needs.     

Mapping the diversity of gender preferences and sex imbalances in Indonesia in 2010

Indonesia is usually viewed as a country free of the acute forms of gender discrimination observed elsewhere in East or South Asia, a situation often ascribed to Indonesia's bilateral kinship system. I re-examine this hypothesis by focusing on ethnic and regional variations in sex differentials. New indicators of marriage practices and gender bias derived from 2010 census microdata highlight the presence of patrilocal patterns as well as a distinct presence of son preference in fertility behaviour in many parts of the archipelago. I also present evidence for excessive child sex ratios and excess mortality of females in some areas that appear to be related to son preference and patrilocal residence systems. The findings confirm the association between son preference, sex differentials in mortality, prenatal sex selection, and kinship systems. I conclude with a more regional perspective on demographic vulnerability of females, distinguishing bilateral South East Asia from more patrilineal Melanesia.     

Inferring multiple graphical structures

Gaussian Graphical Models provide a convenient framework for representing dependencies between variables. Recently, this tool has received a high interest for the discovery of biological networks. The literature focuses on the case where a single network is inferred from a set of measurements. But, as wetlab data is typically scarce, several assays, where the experimental conditions affect interactions, are usually merged to infer a single network. In this paper, we propose two approaches for estimating multiple related graphs, by rendering the closeness assumption into an empirical prior or group penalties. We provide quantitative results demonstrating the benefits of the proposed approaches. The methods presented in this paper are embeded in the R package simone from version 1.0-0 and later.     

A new class of skew distributions with climate data analysis

In this paper, we develop a new general class of skew distributions with flexibility properties on the tails. Moreover, such class can provide heavy and light tails. Some of its mathematical properties are studied, including the quantile function, the moments, the moment generating function and the mean of deviations. New skew distributions are derived and used to construct new models capturing asymmetry inherent to data. The estimation of the class parameters is investigated by the method of maximum likelihood and the performance of the estimators is assessed by a simulation study. Applications of the proposed distribution are explored for two climate data sets. The first data set concerns the annual heat wave index and the second data set involves temperature and precipitation measures from the meteorological station located at Schiphol, Netherlands. Data fitting results show that our models perform better than the competitors.     

Modelling functional additive quantile regression using support vector machines approach

This work deals with conditional quantiles estimation when several functional covariates are involved, via a support vector machines nonparametric methodology. We establish weak consistency of this estimator. To fit the additive components, we use an ordinary backfitting procedure combined with an iterative reweighted least-squares procedure to solve the penalised minimisation problem. This procedure makes it possible to derive a split sample method for choosing the hyper-parameters of the model. The performances of the proposed technique, in terms of forecast accuracy, are evaluated through simulation and a real dataset study.     

Le Cam theorem on interval division by randomly chosen points: Pedagogical explanations and application to temporal cluster detection

The aim of this paper is to propose a pedagogical explanation of the Le Cam theorem and to illustrate its use, through a practical application, for temporal cluster detection. This theorem focusses on the interval division by randomly chosen points. The aim of the theorem is to characterize the asymptotic behavior of a certain category of sums of functions applied to the length of successive intervals between points. It is not very intuitive and its understanding needs some deepening. After enouncing the theorem, its different aspects are explained and detailed in a way as pedagogical as possible. Theoretical applications are proposed through the proof of two propositions. Then a very concrete application of this theorem for temporal cluster detection is presented, tested by a power study, and compared with other global cluster detection tests. Finally, this approach is applied to the well-known Knox temporal data set.     

Adaptive wavelet estimation of a function from an m-dependent process with possibly unbounded m

The estimation of a multivariate function from a stationary m-dependent process is investigated, with a special focus on the case where m is large or unbounded. We develop an adaptive estimator based on wavelet methods. Under flexible assumptions on the nonparametric model, we prove the good performances of our estimator by determining sharp rates of convergence under two kinds of errors: the pointwise mean squared error and the mean integrated squared error. We illustrate our theoretical result by considering the multivariate density estimation problem, the derivatives density estimation problem, the density estimation problem in a GARCH-type model and the multivariate regression function estimation problem. The performance of proposed estimator has been shown by a numerical study for a simulated and real data sets.