Consider a semiparametric partly linear model, with response variable $y$ and covariates $x_1,\dots, x_p$ and $t$. This model can be a suitable choice when one suspects that the response depends linearly on $x$, but that it is nonlinearly related to $t$. Least square estimators have been studied by several authors. All these estimators, as nonparametric estimators, depend on a smoothing parameter that should be chosen by the practitioner. As it is well known, large bandwidths produce estimators with small variance but high bias, while small values produce more wiggly curves. This trade-off between bias and variance lead to several proposals to select the smoothing parameter, such as cross-validation procedures and plug-in methods. It is well known that, both in linear regression and in nonparametric regression, least squares estimators can be seriously affected by anomalous data. The same statement holds for partly linear models. To avoid that problem, Bianco and Boente (2003) considered a three-step robust estimate for the regression parameter and the regression function. In this talk, we will introduce a robust plug-in selector for the bandwidth, under a partly linear model with fixed design which converges to the optimal one and leads to robust data-driven estimates of the regression function and the regression parameter. Our plug-in proposal is based on nonparametric robust estimates of the $j$-th derivatives, which extends the proposals given when $j=2$. We define an empirical influence measure for data-driven bandwidth selectors and, through it, we study the sensitivity of the plug-in selector. We use a Monte Carlo study to compare the performance of the classical approach and of the resistant selectors under normality and contamination. It appears that the robust selector compares favourably to its competitor, despite the need to select a pilot bandwidth. When combined with the three-step procedure proposed by Bianco and Boente (2003), it leads to robust data-driven estimates both of the regression function and the regression parameter.

O tráfego na Internet apresenta hoje em dia uma grande complexidade estatística devido, por um lado, à multiplicidade de aplicações suportadas e, por outro, à sofisticação dos mecanismos de geração e controle de tráfego que, no seu conjunto, influenciam a rede numa gama alargada de escalas temporais. Nos últimos anos foram identificados diversos comportamentos peculiares no tráfego da Internet, como por exemplo a autosimilaridade, a dependência de longo prazo e a multifractalidade, cuja propriedade comum é a invariância das estatísticas quanto à escala temporal. Estes comportamentos têm um impacto significativo na qualidade de serviço oferecida pela rede e necessitam portanto de ser devidamente modelados. Nesta apresentação faremos inicialmente uma descrição dos mecanismos de geração e controle de tráfego mais importantes e das principais metodologias de análise de desempenho usadas na Internet, como forma de motivar a importância de uma adequada caracterização estatística do tráfego. Seguidamente analisaremos os comportamentos peculiares do tráfego, avançando uma possível explicação física para a sua origem. Passaremos então a abordar a problemática específica da caracterização estatística do tráfego, abrangendo os seus dois ramos, a estatística descritiva e a modelação estocástica, e dando uma visão integrada dos aspectos relativos às diferentes escalas temporais. No decorrer da exposição daremos exemplos de caracterização em escalas temporais pequenas e grandes. A modelação estocástica será alvo de um destaque especial devido ao detalhe com que permite efectuar a caracterização do tráfego. Faremos uma tipificação dos modelos mais importantes e serão descritos alguns procedimentos de inferência de parâmetros que usam diferentes estratégias para incorporar a noção de escala temporal. Por fim apresentaremos a nossa visão sobre os desafios que se colocam nesta importante área da caracterização estatística de tráfego, tendo em vista a sua aplicabilidade na gestão de tráfego da Internet.

Em muitas situações reais, além de se estar perante fenómenos com saltos em instantes aleatórios, as observações que constituem a série poderão apresentar um grande enviesamento, serem estritamente positivas com valores muito pequenos, próximos de zero. Um processo que poderá modelar este tipo de situações, e que se irá considerar neste trabalho, é o modelo bilinear $BL(1,0,1,1)$ com erros exponenciais. Em particular, obtêm-se as condições sob as quais o modelo é estritamente estacionário e apresentam-se algumas propriedades da distribuição estacionária, em termos dos seus momentos. Sugerem-se duas metodologias para a estimação de parâmetros, no domínio temporal e no domínio da frequência, respectivamente a abordagem bayesiana e o critério de Whittle. Os procedimentos propostos são ilustrados e comparados através de um estudo de simulação. Finalmente, faz-se ainda uma breve análise de predição, usando a metodologia Bayesiana para fazer a previsão da observação futura.

A new approach to measuring skewness of univariate distributions is developed. A corresponding notion of kurtosis follows naturally. Further developments are briefly indicated.

Voice over IP (VoIP) uses TCP/IP as the transport network for voice conversations, taking advantage of its statistical multiplexion and allowing the usage of 'free' transport networks as the Internet. The main shortcoming of VoIP are: possibility of data losses and increase of transport delay. These impairments can severely affect the perceived conversation's quality and must be carefully avoided by the appropriate use of queueing analysis, connection admission control algorithms and dimensioning methods. In all these cases, an accurate VoIP traffic modeling is needed. This seminar is aimed to introduce the modeling of VoIP traffic, taking into account the effect of the modern codec used in VoIP: the Voice Activity Detection and the Confort Noise Generation. The one voice source case is first introduced. After that, the multiplexion of several sources is addressed, and the main well known models (Fluid Model and Markov modulated Poisson process) are adapted to the VoIP scenario. Finally a comparative study of the adequacy of the existing models concludes the seminar.

The Markowitz theory of portfolio selection is a classical part of asset allocation. Under the assumption of Gaussian asset returns and investor’s preferences given by the quadratic utility function, we can present the optimal portfolio weights as a function of the first two moments of asset returns. The true moments are unknown to the investor and should be estimated from a sample. Because of this practical applications often suffer from very large or negative portfolio weights. The aim of this project is to assess the distributional properties of estimated portfolio weights and to develop improved estimation procedures. Okhrin and Schmid (2005a) consider the maximum-likelihood estimation of the moments of asset returns. They provide expression for the mean and variance of the estimated portfolio weights of four different types. It appears that the estimated weights are heavily biased in small samples and have very large variance. This explains the empirical evidence from practical applications. It is also shown that the estimated global minimum variance portfolio weights follow multivariate t-distribution, what is of special interest in testing problems. For the portfolio weights that maximize the Sharpe ratio it appears that the moments of order equal or greater than one do not exist. This questions the usefulness of such estimator and makes the results untractable. A classical approach to decrease the volatility of an estimator is shrinkage technique. Using the result of Stein, Jorion (1986) first applied the shrinkage estimation of the expected asset returns to portfolio selection. Recently Ledoit and Wolf (2003, 2004) constructed a shrinkage estimator of the covariance matrix, which is robust against the singularity of sample covariance matrix. Okhrin and Schmid (2005b) applied the shrinkage methodology directly to the optimal portfolio weights by shrinking the classical portfolio weights to the weights obtained from a linear factor model. The optimal shrinkage intensity is derived to minimize the mean-square error. It appears, that the shrinkage estimator is also very successful in the reduction of the variance of portfolio return. Additionally, a new estimator is constructed by using predictive moments from a Bayesian framework with zero-mean prior distribution for the slopes of the factor model.

We consider a general model for a continuous time Markov chain in random environment. We study certain form of interaction between the process of interest and the environmental process, under which the stationary joint distribution is tractable. More specifically we obtain necessary and sufficient conditions for a generalized product-form stationary distribution. When these conditions fail we propose an alternative technique that transform the original system of the balance equations to an equivalent system. Applications in queueing and population growth models illustrate the scope and the efficiency of the methods.

The computer program system R already offers extremely many powerful data analysis tools. The development of a general graphical user interface is still at the beginning (Fox, 2004). We discuss the historical entrance of an older data analysis system (DAS) with many ``new'' and powerful features in an R-package. This is designed for graphically oriented analysis with special emphasis on geochemical data. Practical examples from the Kola project are illustrated.