In this talk we will first remind the robust procedures existing to estimate the regression parameter and the regression function under a generalized partial linear model. Based on them, we will describe how to construct a Wald type statistic to test hypothesis on the regression parameter and a robust test to decide if the regression function is linear. The asymptotic behavior of the test statistics and derived and results from a Monte Carlo study will be presented.

The presentation focus on the ongoing and future work on the performance analysis of joint control schemes for the process mean (vector) and (co)variance (matrix), when the usual assumptions of independence and normality are no longer valid. We shall give special attention to two performance measures: the probability of a misleading signal (PMS) and the run length to a misleading signal (RLMS). We use stochastic ordering to analyze their monotonicity properties in terms of shifts in the parameters being monitored, and of changes in the autocorrelation parameter.

We consider the numerical inversion of three classes of generating functions (GFs): classes of probability generating functions (PGFs) that are given in rational and non-rational forms, and a class of GFs that are not PGFs. Particular emphasis is on those PGFs that are not explicitly given but contain a number of unknowns. We show that the desired sequence can be obtained to any given accuracy, so long as enough numerical precision is used.

With the increase in the number of models induced from data that are used by organizations for decision support, the problem of algorithm (and parameter) selection is becoming increasingly important. Two approaches to obtain empirical knowledge that is useful for that purpose are empirical studies and metalearning. However, most empirical (meta)knowledge is obtained from a relatively small set of datasets. In this paper, we propose a method to obtain a large number of datasets which is based on a simple transformation of existing datasets, referred to as datasetoids. We test our approach on the problem of using metalearning to predict when to prune decision trees. The results show significant improvement when using datasetoids. Additionally, we identify a number of potential anomalies in the generated datasetoids and propose methods to solve them.

In the paper, we derive a non-linear cokriging predictor for spatial interpolating of multivariate environmental process. The suggested predictor is based on the locally weighted scatterplot smoothing method of Cleveland (1979) applied simultaneously to several processes. This approach is more flexible as the linear cokriging predictor usually applied in mulivariate environmental statistics and extends the LOESS predictor of Bodnar and Schmid (2009) to multivariate data. In an empirical study, we apply the suggested approach for interpolating the most significant air pollutants in the Berlin/Brandenburg region.

Most of the statistical methods in nonparametric regression are designed for complete data sets and problems arise when missing observations are present which is a common situation in biomedical or socioeconomic studies, for example. Classic examples are found in the field of social sciences with the problem of non-response in sample surveys, in Physics, in Genetics (Meng, 2000), among others. We will consider inference with an incomplete data set where the responses satisfy a semiparametric partly linear regression model. We will introduce a family of robust procedures to estimate the regression parameter as well as the marginal location of the responses, when there are missing observations in the response variable, but the covariates are totally observed. In this context, it is necessary to require some conditions regarding the loss of an observation. We model the aforementioned loss assuming that the data are missing at random, i.e, the probability of observing a missing data is independent of the response variable, and it only depends on the covariate. Our proposal is based on a robust profile likelihood approach adapted to the presence of missing data. The asymptotic behavior of the robust estimators for the regression parameter is derived. Several proposals for the marginal location are considered. A Monte Carlo study is carried out to compare the performance of the robust proposed estimators among them and also with the classical ones, in normal and contaminated samples, under different missing data models.

There exists a vast range of applications of Stochastic Dominance (SD) rules in different areas of knowledge, such as: Mathematics, Statistic, Biology, Sociology, Economy, etc. Currently, the main areas of application of SD in Economics and Finance are: efficient portfolio selection, asset valuation, risk, insurance, etc. In this talk we will show the utility of SD in Economics.For that, we will start by explaining the classic concepts of SD and their economic interpretation, as well as other definitions used in this context (likelihood ratio order, hazard rate order, Lorenz’s order level crossing order, etc). One of the main topics we will treat is optimal portfolio selection and its relation with associated weighted random variables and utility functions. In particular, we will establish relations between the utilities of the weighted random variables, given the stochastic relations of the original random variables from which we obtained the weighted random variables. Another context in which SD rules are applied is the ruin and risk problems; we will show a generalization of the classic ruin mode and some SD relations between ruin times of two (stochastic) risk processes. Also SD rules can be used in asset valuation context; we will treat, as an example, the Cox and Rubinstein’s model. Others applications of SD rules will also be commented, including: Black Scholes’ model, integral stochastic calculus, inventory theory, chains, etc.

When dealing with multivariate data, like classical PCA, robust PCA searches for directions with maximal dispersion of the data projected on it. Instead of using the variance as a measure of dispersion, a robust scale estimator s_n may be used in the maximization problem. This approach was first in Li and Chen (1985) while a maximization algorithm was proposed in Croux and Ruiz-Gazen (1996) and their influence function was derived by Croux and Ruiz-Gazen (2005). Recently, their asymptotic distribution was studied in Cui et al. (2003).

Let $X(t)$ be a stochastic process with continuous trajectories and finite second moment, defined on a finite interval. We will denote by $\Gamma (t,s)=cov(X(t),X(s))$ its covariance function and by ${\varphi }_j$ and ${\lambda }_j$ the eigenfunctions and the eigenvalues of the covariance operator with ${\lambda }_j$ in the decreasing order. Dauxois et al. (1982) derived the asymptotic properties of non-smooth principal components of functional data obtained by considering the eigenfunctions of the sample covariance operator. On the other hand, Silverman (1996) and Ramsay and Silverman (1997), introduced smooth principal components for functional data, based on roughness penalty methods while Boente and Fraiman (2000) considered a kernel-based approach. More recent work, dealing with estimation of the principal components of the covariance function, includes Gervini (2006), Hall and Hosseini-Nasab (2006), Hall et al. (2006) and Yao and Lee (2006). Up to our knowledge, the first attempt to provide estimators of the principal components less sensitive to anomalous observations was done by Locantore et al. (1999) who considered the coefficients of a basis expansion. Besides, Gervini (2008) studied a fully functional approach to robust estimation of the principal components by considering a functional version of the spherical principal components defined in Locantore et al. (1999). On the other hand, Hyndman and Ullah (2007) provide a method combining a robust projection-pursuit approach and a smoothing and weighting step to forecast age-specific mortality and fertility rates observed over time.

In this talk, we introduce robust estimators of the principal components and we obtain their consistency under mild conditions. Our approach combines robust projection-pursuit with different smoothing methods.

Volatility is a central concept when dealing with financial applications. It is usually equated with the risk and plays a central role in the pricing of derivative securities. It is also widely acknowledged nowadays that volatility is both time-varying and predictable, and stochastic volatility models are commonplace. The approach based on autoregressive conditional heteroscedasticity (ARCH) introduced by Engle, and later generalized to GARCH by Bollerslev, was the first attempt to take into account the changes in volatility over time. The class of stochastic volatility (SV) models is now recognized as a powerful alternative to the traditional and widely used ARCH/GARCH approach. We focus on the maximum likelihood estimation of the class of stochastic volatility models. The main technique is based on the Kalman filter (KF), which is known to be numerically unstable. Using the advanced array square-root form of the KF, we construct a new square-root algorithm for the log-likelihood gradient (score) evaluation. This avoids the use of the conventional KF with its inherent numerical instabilities and improves the robustness of computations against roundoff errors. The proposed square-root adaptive KF scheme is ideal for simultaneous parameter estimation and extraction of the latent volatility series.

We consider the problem of validating computer models that produce multivariate output, particularly when the model is computationally demanding. Our strategy builds on Gaussian process-based response-surface approximations to the output of the computer model independently constructed for each of its components. These are then combined in a statistical model involving field observations to produce a predictor of the multivariate output at untested input vectors. We illustrate the methodology in a situation where the output consists of a two-dimensional output of very irregular functions.

We will consider the problem of estimating highly oscillatory signals from noisy measurements. These signals are often referred to as chirps in the literature; they are found everywhere in nature, and frequently arise in scientific and engineering problems. Mathematically, they can be written in the general form A(t) exp(ilambda varphi(t)), where lambda is a large constant base frequency, the phase varphi(t) is time-varying, and the envelope A(t) is slowly varying. Given a sequence of noisy measurements, we study the problem of estimating this chirp from the data.

We introduce novel, flexible and practical strategies for addressing these important nonparametric statistical problems. The main idea is to calculate correlations of the data with a rich family of local templates in a first step, the multiscale chirplets, and in a second step, search for meaningful aggregations or chains of chirplets which provide a good global fit to the data. From a physical viewpoint, these chains correspond to realistic signals since they model arbitrary chirps. From an algorithmic viewpoint, these chains are identified as paths in a convenient graph. The key point is that this important underlying graph structure allows to unleash very effective algorithms such as network flow algorithms for finding those chains which optimize a near optimal trade-off between goodness of fit and complexity.

Our estimation procedures provide provably near optimal performance over a wide range of chirps and numerical experiments show that our estimation procedures perform exceptionally well over a broad class of chirps.

The purpose of this communication is to present the methodology adopted in the last exercise of resident population projections in Portugal, carried out by the Statistics Portugal.

These population projections are based on the concept of resident population and adopt the cohort-component method, where the initial population is grouped into cohorts defined by age and sex, and continuously updated, according to the assumptions of future development set for each of the components of population change - fertility, mortality and migration - that is, by adding the natural balance and net migration, in addition to the natural aging process. This method, widely used in the elaboration of population projections at national level, allows the development of different scenarios of demographic evolution based on different combinations of likely developments of the components.

The results are conditioned, on the one hand by the structure and composition of the initial population, and on the other, by the different behaviour patterns of fertility, mortality and migration in each set of assumptions about the evolution over the projection period, so it should be emphasize the conditional nature of the results, since it is a method of scenarios of "if ... then ..." in that each combines differently the assumptions outlined for the components.

Given the importance of the projections of individual components to the outcome of the exercise, we proceed to the presentation of the methodologies used in the projection of each of these. The projection of components is carried out using a set of statistical methods, adequate to the background information and the proposed target. Thus in the case of fertility we have modelled the fertility rates using the method proposed by Schmertmann (2003), for mortality we have used the Poisson-Lee-Carter with limit life table proposed by Bravo (2007) and for migration, given the increased fragility of the data and consequently the difficulties regarding the practical application of methods for statistical modelling, was adopted as a initial reference the average of the estimated flows in the last 15 years. Finally, we will present the main results of this exercise, both in regard to components and to the future population.

In the spirit of a forthcoming research project within CEMAT this talk aims at introducing a probabilistic approach to PDE. This probabilistic interpretation for systems of second order quasilinear parabolic PDE is obtained by establishing a kind of backward stochastic differential equation. We look at several aspects of this link.