Data-driven stochastic inversion via functional quantization

In this paper, we propose a new methodology for solving stochastic inversion problems through computer experiments, the stochasticity being driven by a functional random variables. This study is motivated by an automotive application. In this context, the simulator code takes a double set of simulation inputs: deterministic control variables and functional uncertain variables. This framework is characterized by two features. The first one is the high computational cost of simulations. The second is that the probability distribution of the functional input is only known through a finite set of realizations. In our context, the inversion problem is formulated by considering the expectation over the functional random variable. We aim at solving this problem by evaluating the model on a design, whose adaptive construction combines the so-called stepwise uncertainty reduction methodology with a strategy for an efficient expectation estimation. Two greedy strategies are introduced to sequentially estimate the expectation over the functional uncertain variable by adaptively selecting curves from the initial set of realizations. Both of these strategies consider functional principal component analysis as a dimensionality reduction technique assuming that the realizations of the functional input are independent realizations of the same continuous stochastic process. The first strategy is based on a greedy approach for functional data-driven quantization, while the second one is linked to the notion of space-filling design. Functional PCA is used as an intermediate step. For each point of the design built in the reduced space, we select the corresponding curve from the sample of available curves, thus guaranteeing the robustness of the procedure to dimension reduction. The whole methodology is illustrated and calibrated on an analytical example. It is then applied on the automotive industrial test case where we aim at identifying the set of control parameters leading to meet the pollutant emission standards of a vehicle.     

On conditional risk estimation considering model risk

Usually, parametric procedures used for conditional variance modelling are associated with model risk. Model risk may affect the volatility and conditional value at risk estimation process either due to estimation or misspecification risks. Hence, non-parametric artificial intelligence models can be considered as alternative models given that they do not rely on an explicit form of the volatility. In this paper, we consider the least-squares support vector regression (LS-SVR), weighted LS-SVR and Fixed size LS-SVR models in order to handle the problem of conditional risk estimation taking into account issues of model risk. A simulation study and a real application show the performance of proposed volatility and VaR models.     

A new generalized two-sided class of distributions with an emphasis on two-sided generalized normal distribution

The ordinary-G class of distributions is defined to have the cumulative distribution function (cdf) as the value of the cdf of the ordinary distribution F whose range is the unit interval at G, that is, F(G), and it generalizes the ordinary distribution. In this work, we consider the standard two-sided power distribution to define other classes like the beta-G and the Kumaraswamy-G classes. We extend the idea of two-sidedness to other ordinary distributions like normal. After studying the basic properties of the new class in general setting, we consider the two-sided generalized normal distribution with maximum likelihood estimation procedure.     

Merging data from multiple sources: pretest and shrinkage perspectives

In this article, we have developed asymptotic theory for the simultaneous estimation of the k means of arbitrary populations under the common mean hypothesis and further assuming that corresponding population variances are unknown and unequal. The unrestricted estimator, the Graybill-Deal-type restricted estimator, the preliminary test, and the Stein-type shrinkage estimators are suggested. A large sample test statistic is also proposed as a pretest for testing the common mean hypothesis. Under the sequence of local alternatives and squared error loss, we have compared the asymptotic properties of the estimators by means of asymptotic distributional quadratic bias and risk. Comprehensive Monte-Carlo simulation experiments were conducted to study the relative risk performance of the estimators with reference to the unrestricted estimator in finite samples. Two real-data examples are also furnished to illustrate the application of the suggested estimation strategies.     

Periodic integer-valued bilinear time series model

This paper deals with the study of some probabilistic and statistical properties of a periodic integer-valued diagonal bilinear model. The existence of a periodically strict stationary integer-valued process is shown. Sufficient conditions for the periodically stationary, both in the first and second orders, are established. The closed-forms of the mean and the second moment are obtained. The closed-form of the periodic autocovariance function is established. The Yule–Walker estimations of the underlying parameters are obtained. A simulation study is provided.     

Selective Maintenance in System Reliability with Random Costs of Repairing and Replacing the Components

In this paper we consider the problem of determining the optimum number of repairable and replaceable components to maximize a system's reliability when both, the cost of repairing the components and the cost of replacement of components by new ones, are random. We formulate it as a problem of non-linear stochastic programming. The solution is obtained through Chance Constrained programming. We also consider the problem of finding the optimal maintenance cost for a given reliability requirement of the system. The solution is then obtained by using Modified E-model. A numerical example is solved for both the formulations.     

The local geographies of welfare in Tunisia: Does neighbourhood matter?*

Amara M, Ayadi M. The local geographies of welfare in Tunisia: Does neighbourhood matter? The aim of this article is to show that spatial analysis techniques outperform non‐spatial statistical counterparts for understanding the geographic determinants of welfare and poverty in Tunisia. First, an Exploratory Spatial Data Analysis, based on a Geographical Information System, was conducted to visualise the local spatial structure of welfare. Second, a spatial autoregressive (SAR) model and a geographically weighted regression (GWR) model, respectively, were used to deal with both spatial autocorrelations and unobserved spatial heterogeneity of households' behaviours. Spatial and non‐spatial models were compared according to their predictive performances. Results of this case study confirm that SAR and GWR spatial models are preferable to the traditional non‐spatial regression model and that they give a better approximation of the Tunisian poverty map.     

Patterns and severity of menopausal symptoms among Jordanian women

We examined 359 women aged 45–65 years who visited Jordan University Hospital between February and November 2014. The menopausal symptoms were assessed using a validated Arabic version of the menopause rating scale. The mean age at menopause was 49.4 years. Women aged 50–55 years more frequently exhibited hot flushes and vaginal dryness. Although premenopausal women were 1.5 times more likely to experience irritability, perimenopausal women were more likely to experience hot flushes, physical and mental irritability, sexual problems, vaginal dryness, and joint and muscular discomfort. Hence, health care providers should focus on women at all stages of life.     

Sparse conformal predictors

Conformal predictors, introduced by Vovk et al. (Algorithmic Learning in a Random World, Springer, New York, 2005), serve to build prediction intervals by exploiting a notion of conformity of the new data point with previously observed data. We propose a novel method for constructing prediction intervals for the response variable in multivariate linear models. The main emphasis is on sparse linear models, where only few of the covariates have significant influence on the response variable even if the total number of covariates is very large. Our approach is based on combining the principle of conformal prediction with the ℓ ₁ penalized least squares estimator (LASSO). The resulting confidence set depends on a parameter ε>0 and has a coverage probability larger than or equal to 1−ε. The numerical experiments reported in the paper show that the length of the confidence set is small. Furthermore, as a by-product of the proposed approach, we provide a data-driven procedure for choosing the LASSO penalty. The selection power of the method is illustrated on simulated and real data.     

Distribution of linear combination of exponential variates

The exact distribution of a linear combination of n independent negative exponential random variables, when the coefficients of the linear combination are distinct and positive quantities, is well-known. This paper extends the above result to the general case, namely when the coefficients are arbitrary real numbers, positive or negative, distinct or coincident.