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This article studies the conditional dependency between random variables, conditionally upon a covariate (vector). The conditional copula fully characterizes this conditional dependency. A way to summarize this dependence structure taking into account the impact of the covariate is via the average conditional copula, which under fairly general conditions coincides with the partial copula. A mean is just one way to summarize this conditional dependence behaviour. In this article, we introduce the notions of median conditional copula and more generally quantile conditional copula. We investigate the existence of these concepts and establish explicit expressions for calculating them. Examples are given to illustrate the concepts, and the practical use of them is demonstrated in real data examples.

When the interest is in studying conditional dependencies, and more precisely the strength of conditional dependencies, some kind of averaging over the conditioning random vector may be needed. Examples of average measures that can serve in this context are the average conditional Kendall’s tau and partial Kendall’s tau. It is known that these measures differ in general. Some statistical tests are based on these average measures, and a better knowledge of them is of importance. The aim of this paper is to provide a quantitative study of the possible differences of these two average measures, and to establish su˚cient conditions under which they coincide. Both measures are studied in two fairly general settings. In each setting theoretical results are established as well as several illustrative examples given.

The empirical likelihood cannot be used directly sometimes when an infinite dimensional parameter of interest is involved. To overcome this difficulty, the sieve empirical likelihoods are introduced in this paper. Based on the sieve empirical likelihoods, a unified procedure is developed for estimation of constrained parametric or non–parametric regression models with unspecified error distributions. It shows some interesting connections with certain extensions of the generalized least squares approach. A general asymptotic theory is provided. In the parametric regression setting it is shown that under certain regularity conditions the proposed estimators are asymptotically efficient even if the restriction functions are discontinuous. In the non–parametric regression setting the convergence rate of the maximum estimator based on the sieve empirical likelihood is given. In both settings, it is shown that the estimator is adaptive for the inhomogeneity of conditional error distributions with respect to predictor, especially for heteroscedasticity. [ABSTRACT FROM AUTHOR]

Local maximum likelihood estimation is a nonparametric counterpart of the widely used parametric maximum likelihood technique. It extends the scope of the parametric maximum likelihood method to a much wider class of parametric spaces. Associated with this nonparametric estimation scheme is the issue of bandwidth selection and bias and variance assessment. This paper provides a unified approach to selecting a bandwidth and constructing confidence intervals in local maximum likelihood estimation. The approach is then applied to least squares nonparametric regression and to nonparametric logistic regression. Our experiences in these two settings show that the general idea outlined here is powerful and encouraging. [ABSTRACT FROM AUTHOR]

Nowadays, Predictive Maintenance is a mandatory tool to reduce the cost of production in the semiconductor industry. This paper considers as a case study a critical part of the electrochemical deposition system, namely, the four Pins that hold a wafer inside a chamber. The aim of the study is to replace the schedule of replacement of Pins presently based on fixed timing (Preventive Maintenance) with a Hardware/Software system that monitors the conditions of the Pins and signals possible conditions of failure (Predictive Maintenance). The system is composed of optical sensors endowed with an image processing methodology. The prototype built for this study includes one optical camera that simultaneously takes images of the four Pins on a roughly daily basis. Image processing includes a pre-processing phase where images taken by the camera at different times are coregistered and equalized to reduce variations in time due to movements of the system and to different lighting conditions. Then, some indicators are introduced based on statistical arguments that detect outlier conditions of each Pin. Such indicators are pixel-wise to identify small artifacts. Finally, criteria are indicated to distinguish artifacts due to normal operations in the chamber from issues prone to a failure of the Pin. An application (PINapp) with a user friendly interface has been developed that guides industry experts in monitoring the system and alerting in case of potential issues. The system has been validated on a plant at STMicroelctronics in Catania (Italy). The study allowed for understanding the mechanism that gives rise to the rupture of the Pins and to increase the time of replacement of the Pins by a factor at least 2, thus reducing downtime.

Multivariate tail coefficients are an important tool when investigating dependencies between extreme events for different components of a random vector. Although bivariate tail coefficients are well-studied, this is, to a lesser extent, the case for multivariate tail coefficients. This paper contributes to this research area by (i) providing a thorough study of properties of existing multivariate tail coefficients in the light of a set of desirable properties; (ii) proposing some new multivariate tail measurements; (iii) dealing with estimation of the discussed coefficients and establishing asymptotic consistency; and, (iv) studying the behavior of tail measurements with increasing dimension of the random vector. A set of illustrative examples is given, and practical use of the tail measurements is demonstrated in a data analysis with a focus on dependencies between stocks that are part of the EURO STOXX 50 market index.