The photography industry underwent a disruptive change in technology during the 1990s when the traditional film was replaced by digital photography (see e.g. The Economist January 14th 2012). In particular Kodak was largely affected : by 1976 Kodak accounted for 90% of film and 85% of camera sales in America. Hence it was a near-monopoly in America. Kodak′s revenues were nearly 16 billion in 1996 but the prediction is that it will decrease to 6.2 billion in 2011. Kodak tried to get (squeeze) as much money out of the film business as possible and it prepared for the switch to digital film. The result was that Kodak did eventually build a profitable business out of digital cameras but it lasted only a few years before camera phones overtook it.

According to Mr Komori, the former CEO of Fujifilm of 2000-2003, Kodak aimed to be a digital company, but that is a small business and not enough to support a big company. For Kodak it was like seeing a tsunami coming and there′s nothing you can do about it, according to Mr. Christensen in The Economist (January 14th 2012).

In this paper we study the problem of a firm that produces with a current technology for which it faces a declining sales volume. It has two options: it can either exit this industry or invest in a new technology with which it can produce an innovative product. We distinguish between two scenarios in the sense that the resulting new market can be booming or ends up to be smaller than the old market used to be.

We derive the optimal strategy of a firm for each scenario and specify the probabilities with which a firm would decide to innovate or to exit. Furthermore, we assume that the firm can additionally choose to suspend production for some time in case demand is too low, instead of immediately taking the irreversible decision to exit the market. We derive conditions under which such an suspension area exists and show how long a firm is expected to remain in this suspension area before resuming production, investing in new technology or exiting the market.

Forecasting The Temperature Data:

This paper aims at describing the intraday temperature variations which is a challenging task in modern econometrics and environmetrics. Having a high-frequency data, we separate the dynamics within a day and over days. Three main models have been considered in our study. As the benchmark we employ a simple truncated Fourier series with autocorrelated residuals. The second model uses the functional data analysis, and is called the shape invariant model (SIM). The third one is the dynamic semiparametric factor model (DSFM). In this work we discuss rises and pitfalls of all the methods and compare their in- and out-of-sample performances.

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Localising Temperature Risk:

On the temperature derivative market, modelling temperature volatility is an important issue for pricing and hedging. In order to apply the pricing tools of financial mathematics, one needs to isolate a Gaussian risk factor. A conventional model for temperature dynamics is a stochastic model with seasonality and intertemporal autocorrelation. Empirical work based on seasonality and autocorrelation correction reveals that the obtained residuals are heteroscedastic with a periodic pattern. The object of this research is to estimate this heteroscedastic function so that, after scale normalisation, a pure standardised Gaussian variable appears. Earlier works investigated temperature risk in different locations and showed that neither parametric component functions nor a local linear smoother with constant smoothing parameter are flexible enough to generally describe the variance process well. Therefore, we consider a local adaptive modelling approach to find, at each time point, an optimal smoothing parameter to locally estimate the seasonality and volatility. Our approach provides a more flexible and accurate fitting procedure for localised temperature risk by achieving nearly normal risk factors. We also employ our model to forecast the temperature in different cities and compare it to a model developed in Campbell and Deibol (2005).

Symbolic Data, introduced by E. Diday in the late eighties of the last century, is concerned with analysing data presenting intrinsic variability, which is to be explicitly taken into account. In classical Statistics and Multivariate Data Analysis, the elements under analysis are generally individual entities for which a single value is recorded for each variable - e.g., individuals, described by their age, salary, education level, marital status, etc.; cars each described by its weight, length, power, engine displacement, etc.; students for each of which the marks at different subjects were recorded. But when the elements of interest are classes or groups of some kind - the citizens living in given towns; teams, consisting of individual players; car models, rather than specific vehicles; classes and not individual students - then there is variability inherent to the data. To reduce this variability by taking central tendency measures - mean values, medians or modes - obviously leads to a too important loss of information.

Symbolic Data Analysis provides a framework allowing representing data with variability, using new variable types. Also, methods have been developed which suitably take data variability into account. Symbolic data may be represented using the usual matrix-form data arrays, where each entity is represented in a row and each column corresponds to a different variable - but now the elements of each cell are generally not single real values or categories, as in the classical case, but rather finite sets of values, intervals or, more generally, distributions.

In this talk we shall introduce and motivate the field of Symbolic Data Analysis, present into some detail the new variable types that have been introduced to represent variability, illustrating with some examples. We shall furthermore discuss some issues that arise when analysing data that does not follow the usual classical model, and present data representation models for some variable types.

Diagnostic tests are helpful tools for decision-making in a biomedical context. In order to determine the clinical relevance and practical utility of each test, it is critical to assess its ability to correctly distinguish diseased from non-diseased individuals. Statistical analysis has an essential role in the evaluation of diagnostic tests, since it is used to estimate performance measures of the tests, such as sensitivity and specificity. Ideally, these measures are determined by comparison with a gold standard, i.e., a reference test with perfect sensitivity and specificity.

When no gold standard is available, admitting the supposedly best available test as a reference may cause misclassifications leading to biased estimates. Alternatively, Latent Class Models (LCM) may be used to estimate diagnostic tests performance measures as well as the disease prevalence, in the absence of a gold standard. The most common LCM estimation approaches are the maximum likelihood estimation using the Expectation-Maximization algorithm and the Bayesian inference using Markov Chain Monte Carlo methods, via Gibbs sampling.

This talk illustrates the use of Bayesian Latent Class Models (BLCM) in the context of malaria and canine dirofilariosis. In each case, multiple diagnostic tests were applied to distinct subpopulations. To analyze the subpopulations simultaneously, a product multinomial distribution was considered, since the subpopulations were independent. By introducing constraints, it was possible to explore differences and similarities between subpopulations in terms of prevalence, sensitivities and specificities.

We also discuss statistical issues such as the assumption of conditional independence, model identifiability, sampling strategies and prior distribution elicitation.

Part I: Univariate and multivariate models based on thinning

Part II: Modelling and forecasting time series of counts

Time series of counts arise when the interest lies on the number of certain events occurring during a specified time interval. Many of these data sets are characterized by low counts, asymmetric distributions, excess zeros, over dispersion, etc, ruling out normal approximations. Thus, during the last decades there has been considerable interest in models for integer-valued time series and a large volume of work is now available in specialized monographs. Among the most successful models for integer-valued time series are the INteger- valued AutoRegressive Moving Average, INARMA, models based on the thinning operation. These models are attractive since they are linear-like models for discrete time series which exhibit recognizable correlation structures. Furthermore, in many situations the collected time series are multivariate in the sense that there are counts of several events observed over time and the counts at each time point are correlated. The first talk introduces univariate and multivariate models for time series of counts based on the thinning operator and discusses their statistical and probabilistic properties. The second talk addresses estimation and diagnostic issues and illustrates the inference procedures with simulated and observed data.

Linear models are one of the most popular models in Statistics. However, in many situations the nature of the phenomenon is intrinsically nonlinear and so, linear approximations are not valid and the data must be fitted using a nonlinear model. Besides, in some occasions the responses are incomplete and some of them are missing at random.

It is well known that, in this setting, the classical estimator of the regression parameter based on least squares is very sensitive to outliers. A family of general M-estimators is proposed to estimate the regression parameter in a nonlinear model. We give a unified approach to treat full data or data with missing responses. Under mild conditions, the proposed estimators are Fisher-consistent, consistent and asymptotically normal. To study local robustness, their influence function is also derived.

A family of robust tests based on a Wald-type statistic is introduced in order to check hypotheses that involve the regression parameter. Monte Carlo simulations illustrate the finite sample behaviour of the proposed procedures in different settings in contaminated and uncontaminated samples.

Most of the literature concerned with the design of control charts relies on perfect knowledge of the distribution for at least the good (so-called in-control) process. Some papers treated the handling of EWMA charts monitoring normal mean in case of unknown parameters - refer to Jones, Champ and Rigdon (2001) for a good introduction. In Jensen, Jones-Farmer, Champ, and Woodall (2006): “Effects of Parameter Estimation on Control Chart Properties: A Literature Review” a nice overview was given. Additionally, it was mentioned that it would be interesting and useful to evaluate and take into account these effects also for variance control charts. Here, we consider EWMA charts for monitoring the normal variance. Given a sequence of batches of size $n$, $\{X_{i j}\}$, $i=1,2,\ldots$ and $j=1,2,\ldots,n$ utilize the following EWMA control chart: \begin{align*} Z_0 & = z_0 = \sigma_0^2 = 1 \,, \\ Z_i & = (1-\lambda) Z_{i-1} + \lambda S_i^2 \,,\; i = 1,2,\ldots \,,\\ & \qquad\qquad S_i^2 = \frac{1}{n-1} \sum_{i=1}^n (X_{ij} - \bar X_i)^2 \,,\; \bar X_i = \frac{1}{n} \sum_{i=1}^n X_{ij} \,, \\ L & = \inf \left\{ i \in I\!\!N: Z_i > c_u \sigma_0^2 \right\} \,. \end{align*} The parameters $\lambda \in (0,1]$ and $c_u \gt 0$ are chosen to enable a certain useful detection performance (not too much false alarms and quick detection of changes). The most popular performance measure is the so-called Average Run Length (ARL), that is $E_{\sigma}(L)$ for the true standard deviation $\sigma$. If $\sigma_0$ has to be estimated by sampling data during a pre-run phase, then this uncertain parameter effects, of course, the behavior of the applied control chart. Typically the ARL is increased. Most of the papers about characterizing the uncertainty impact deal with the changed ARL patterns and possible adjustments. Here, a different way of designing the chart is treated: Setup the chart through specifying a certain false alarm probability such as $P_{\sigma_0}(L\le 1000) \le \alpha$. This results in a specific $c_u$. Here we describe a feasible way to determine this value $c_u$ also in case of unknown parameters for a pre-run series of given size (and structure). A two-sided version of the introduced EWMA scheme is analyzed as well.

Standard practice in statistical process control is to run two individual charts, one for the process mean and another one for the process variance. The resulting scheme is known as a simultaneous scheme and it provides a way to satisfy Shewhart's dictum that proper process control implies monitoring both location and dispersion.

When we use a simultaneous scheme, the quality characteristic is deemed to be out-of-control whenever a signal is triggered by either individual chart. As a consequence, the misidentification of the parameter that has changed can occur, meaning that a shift in the process mean can be misinterpreted as a shift in the process variance and vice-versa. These two events are known as misleading signals (MS) and can occur quite frequently.

We discuss (necessary and) sufficient conditions to achieve values of PMS smaller than or equal to \(0.5\), explore, for instance, alternative simultaneous Shewhart-type schemes and check if they lead to PMS which are smaller than the ones of the popular \((\bar{X}, S^2)\) simultaneous scheme.

Localização de acidentes rodoviários, local da ignição de incêndios florestais, a distribuição de corais no mar das Caraíbas são exemplos de acontecimentos que ocorrem tipicamente em localizações aleatórias. Se o nosso interesse é sobre esta caraterística dos dados, os processos pontuais espaciais são os modelos estatísticos mais adequados. Num problema desta natureza, principia-se o estudo tentando estabelecer se as localizações observadas satisfazem a hipótese de aleatoriedade completa, correspondendo a uma situação de uniformidade da distribuição das localizações (regularidade), ou se pelo contrário o padrão espacial observado pode ser considerado como agregado. No primeiro caso recorre-se a uma modelação baseada em processos de Poisson de taxa proporcional à area em estudo e, no segundo caso, tem de se modelar o padrão espacial agregado através de modelos que levem em conta a dependência espacial evidenciada por esses padrões. A abordagem que se faz no contexto dos processos pontuais espaciais é tradicionalmente não paramétrica, com o recurso a estatísticas resumo, tendo mais recentemente evoluído para a utilização de modelos paramétricos flexíveis, com eventual inclusão de covariáveis, sendo a inferência feita através do método da máxima verosimilhança assistido por métodos numéricos. Neste seminário faz-se uma breve descrição dos modelos mais usuais neste tipo de modelação e para este tipo de dados, numa perspectiva essencialmente aplicada a um conjunto de dados de acidentes rodoviários com vítimas na cidade de Lisboa (projecto SACRA, PTDC/TRA/66161/2006), e recorrendo ao pacote estatístico spatstat do R-project.

Este trabalho teve como motivação principal a análise de um conjunto de dados de medicina. Esses dados resultaram de um estudo observacional destinado a identificar os factores que influenciam o resultado de um determinado método de tratamento cirúrgico da escoliose (curvatura lateral anormal da coluna vertebral). O número de observações do conujnto de dados é 392 mas algumas dessas observações são relativas ao mesmo doente (curvas duplas). O modelo de regressão linear múltipla surge à partida como uma possibilidade para analisar estes dados mas, dado que as curvas duplas não devem ser ignoradas, a suposição de erros não correlacionados é claramente violada, o que foi de facto confirmado no diagnóstico dos resíduos do modelo usual (teste de Durbin-Watson e teste “runs”). Um modelo mais apropriado obtém-se mantendo a estrutura linear mas admitindo a existência de correlações não nulas entre os erros relativos ao mesmo doente. Para este modelo consideram-se dois métodos de estimação: mínimos quadrados generalizados com parâmetros de correlação estimados iterativamente (o que pode ser visto como uma adaptação do método de Cochrane-Orcutt para erros auto-correlacionados) e estimação de todos os parâmetros por máxima verosimilhança. Finalmente apresentam-se versões robustas destes dois métodos assim como do teste de Durbin-Watson e que foram as que permitiram analisar de forma mais satisfatória os dados referidos.