Recent Studies on Risk Analysis and Statistical Modeling

This study examines the effects of reduced radioactive dosage data collection on positron emission tomography reconstruction reliability and investigates the efficiency of various reconstruction methods. Also, it investigates properties of the reconstructed images under these circumstances and the limitations of the currently used algorithms. The methods are based on maximum likelihood and maximum a posteriori estimation, but no explicit solutions exist and hence iterative schemes are obtained using the expectation-maximisation and one-step-late methods, while greater efficiency is obtained by using an ordered-subset approach. Ten replicate real datasets, from the Hoffman brain phantom collected using a Siemens Biograph mMR scanner, are considered using standard deviation, bias and mean-squared error as quantitative output measures. The variability is very high when low prior parameter values are used but reduces substantially for higher values. However, in contrast, the bias is low for low parameter values and high for high parameter values. For individual reconstructions, low parameter values lead to detail being lost in the noise whereas high values produce unacceptable artefacts at the boundaries between different anatomical regions. Considering the mean-squared error, a balance between bias and variability, still identifies high prior parameter values as giving the best results, but this is in contradiction to visual inspection. These findings demonstrate that when it comes to low counts, variability and bias become significant and are visible in the images, but that improved reconstruction can be achieved by a careful choice of the prior parameter.

Here we consider retroperitoneal tumors in childhood as examples from oncology generating difficult multicriterial decision problems. Inter-patient heterogeneity causes multifractal behavior of images for mammary cancer. Here we fit mixture models to box-counting fractal dimensions in order to better understand this variability. In this context the effect of chemotherapy is studied. The approach of Shape Analysis, proposed already in the work of Giebel (Bull Soc Sci Med Grand Duche Luxemb 1:121–130, 2008; Zur Anwendung der Formanalyse. Application of shape analysis. University of Luxembourg, Luxembourg, 2011), is used. This approach has considered a small number of cases and the test according to Ziezold (Biom J 3:491–510, 1994) is distribution free. Our method here is parametric.

The author presents results of the research conducted for hedge funds for the period of 1990–2014. They were divided into ten investment strategies and net asset values calculated for indexes created for them were used. Chosen alternative risk-return ratios (Calmar, Sterling and Burke ratio) were calculated and their values were compared with the Sharpe ratio for the same period of time. The main conclusion is that these alternative measures give different results from the traditional Sharpe ratio, that is hedge fund rankings made with these two kinds of measures are not the same. This in turn indicates that arguments of opponents of using traditional efficiency ratios in the hedge fund analysis may not be exaggerated.

Tail dependence is an important issue to evaluate risk. The multivariate extreme values theory is the most suitable to deal with the extremal dependence. The extremal coefficient measures the degree of dependence between the marginals of max-stable distributions, a natural class of models in this framework. The estimation of the extremal coefficient is addressed and a new estimator is compared through simulation with existing methods. An illustration with real data is presented.

In this work, we present a methodology based on a Chilean business confidence index, which allows us to describe aspects of the market at a global level, as well as at industrial and sector levels of Chilean great brands. We introduce some issues related to business intelligence, customer surveys, market variables, and the confidence index mentioned. In addition, we carry out analytics of real-world data using this index, whose results show the competitiveness of some Chilean great brands.

Banks and financial institutions are exposed with credit risk, liquidity risk, market risk, operational risk, and others. Credit risk often comes from undue concentration of loan portfolios. Among the diversity of tools available in literature for risk measurement, in our study the Coefficient of Variation (CV) was chosen taking into account that it reveals a very useful characteristic when loan portfolios comparison is desired: CV is unitless—it is independent of the unit of measure associated with the data. We obtain the lower and upper bounds for sample CV and the possibility of using it for measuring the risk concentration in a loan portfolio is investigated. The capital adequacy and the single borrower limit are considered and some theoretical results are obtained. Finally, we implement and illustrate this approach using a real data set.

In various manufacturing industries it is important to investigate the presence of some chemical or harmful substances in lots of raw material or final products, in order to evaluate if they are in conformity to requirements. In this work we highlight the adequacy of the inflated Pareto distribution to model measurements obtained by chromatography, and we define and evaluate acceptance-sampling plans under this distributional setup for lots of large dimension. Some technical results associated with the construction and evaluation of such sampling plans are provided as well as an algorithm for an easy implementation of the sampling plan that exhibits the best performance.

The impact of environmental extreme events, ranging from disturbances in ecosystems to economic impacts on society and losses of life, motivated the study of extremes of random fields.

In this paper the main question of interest is about risk: if occurs one exceedance of a high level in a given location, \(\mathbf {x}\in {\mathbb {R}}^2\), and the maximum over a neighborhood of x does not exceed the level then, what will be the probability that an exceedance occurs in another location? We define a coefficient as a measure of this probability which allows us to evaluate the risk of return levels. This coefficient is independent of the univariate marginal distribution of the random field and can be related to well-known dependence coefficients, which will provide immediate estimators. The performance of the proposed estimator is analyzed with a max-stable maxima of moving maxima random field. We illustrate the results with an application to annual maxima temperatures over Texas.

The soluble silica content in the demineralized water is a continuous variable measured and controlled in the Chemical Laboratory of a Portuguese thermoelectric central, in order to keep the equipment operating under the best conditions, allowing, in particular, to extend its useful life. In this case study, this variable could be considered approximately normal distributed and because we just have one measure, for each group of the sample, an individual control chart to monitor the silica content is obtained based on average moving range. Once the available sample size is small and it is hard to fit a model, robust control limits using a nonparametric method based on empirical quantiles (which according to some simulations studies perform also well under the normality of the observations) are also estimated with the bootstrap procedure. The comparison of the control limits obtained with different approaches and with(out) outliers is very important for technicians since the value of silica should be as small as possible. The process capability study, also developed, shows that the process does not stay within the engineering specification limits, although it seems stable.

The extreme value index characterizes the tail behaviour of a distribution, and indicates the size and frequency of certain extreme events under a given probability model. In this work, we are interested in improvements attained through the reduction of bias of the extreme value index estimators related to Lehmer’s mean of the log-excesses. A comparison with other reduced bias estimators, namely the corrected-Hill estimator, in Caeiro et al. (Revstat 3(2):111–136, 2005), is also performed.

The target of this paper is to discuss a generalized form of the well-known Law of Frequency Error. This particular Law of Frequency of Errors is what is known as “Gaussian” or “Normal” distribution and appeared to have an aesthetic appeal to all the branches of Science. The Generalized Normal Distribution is presented as a basis to our study. We derive also the corresponding hazard function as well as the future lifetime of the Generalized Normal Distribution (GND), while new results are also presented. Moreover, due to some of the important distribution the GND family includes, specific results can also be extracted for some other distributions.

The presence of outliers or discrepant observations has a negative impact in time series modelling. This paper considers the problem of detecting outliers, additive or innovational, single, multiple or in patches, in count time series modelled by first-order Poisson integer-valued autoregressive, PoINAR(1), models. To address this problem, two wavelet-based approaches that allow the identification of the time points of outlier occurrence are proposed. The effectiveness of the proposed methods is illustrated with synthetic as well as with an observed dataset.

The analysis of low integer-valued time series is an area of growing interest as time series of counts arising from many different areas have become available in the last three decades. Statistical quality control, computer science, economics and finance, medicine and epidemiology and environmental sciences are just some of the fields that we can mention to point out the wide variety of contexts from which discrete time series have emerged.

In many of these areas it is not just the statistical modelling of count data that matters. For instance, in environmental sciences or epidemiology, surveillance and risk analysis are critical and timely intervention is mandatory in order to ensure safety and public health. Actually, a major issue in the analysis of a large variety of random phenomena relates to the ability to detect and warn the occurrence of a catastrophe or some other event connected with an alarm system.

In this work, the principles for the construction of optimal alarm systems are discussed and their implementation is described. As there is no unifying approach to the modelling of all integer-valued time series, we will focus our attention in the class of observation-driven models. The implementation of the optimal alarm system will be described in detail for a particular non-linear model in this class, the INteger-valued Asymmetric Power ARCH, or, in short, INAPARCH(p, q).

This paper introduces and studies a non-negative integer-valued process referred to as Ψ-INARMA(1,1), an extension of the geometric ARMA(1,1) process, introduced by McKenzie (Adv Appl Probab 18:679–705, 1986). The Ψ-INARMA(1,1) process is obtained by replacing the binomial thinning operator, proposed in Steutel and van Harn (Ann. Probab. 7:893–899, 1979), by a generalized thinning operator, introduced in Aly and Bouzar (REVSTAT Stat J 6:101–121, 2005). We prove its strictly stationarity and specify its asymptotic independence and local dependence behaviour. As a consequence, we conclude that the sequence of maxima converges in distribution to a discrete Gumbel distribution, when the sequence of innovations belongs to Anderson’s class (J Appl Probab 7:99–113, 1970).

In this work we revisit the statistical properties of the Bartels randomness test. The exact distribution of the statistic, under the randomization hypothesis, can only be obtained when the sample size (n) is small, since it requires the full set of permutations of the first n positive integers. Here, we present the exact null distribution without ties, for samples of size 10 ≤ n ≤ 17, extending the results available in the literature. Since the null distribution is asymptotically normally distributed, but at a slow rate, Bartels concluded that the null distribution is well approximated by a Beta distribution, for samples of size 10 ≤ n ≤ 100. We present a new approximation, based on the Edgeworth series, for the null distribution of the Bartels randomness statistic. The precision of this new approximation is also discussed.

In this work it is shown that using well-known series expansions it is possible to represent a single gamma distribution and also the logarithm of a single beta distribution, as an infinite mixture of gamma distributions. Then, using these representations, it is possible to derive simple gamma-series representations for the distribution of the sum of independent gamma random variables and for the sum of independent logbeta random variables, which by simple transformation may be used to represent also the distribution of the product of independent beta random variables. These representations may be used to develop accurate asymptotic approximations for corresponding distributions.

While the likelihood ratio test for the equality of mean vectors, when the covariance matrices are assumed to be only positive-definite, is a common test in multivariate analysis, similar likelihood ratio tests are not available in the literature when the covariance matrices are assumed to have some common given structure. In this compact paper the author deals with the problem of developing likelihood ratio tests for the equality of mean vectors when the covariance matrices are assumed to have a circular or circulant structure. The likelihood ratio statistic is obtained and its exact distribution is expressed in terms of products of independent Beta random variables. Then, it is shown how for some particular cases it is possible to obtain very manageable finite form expressions for the probability density and cumulative distribution functions of this distribution, while for the other cases, given the intractability of the expressions for these functions, very sharp near-exact distributions are developed. Numerical studies show the extreme closeness of these near-exact distributions to the exact distributions.

Mixed models whose variance–covariance matrices are the positive definite linear combinations of pairwise orthogonal orthogonal projection matrices have orthogonal block structure. Here, we will obtain uniformly minimum-variance unbiased estimators for the relevant parameters when normality is assumed and we show that those for estimable vectors are, in general, uniformly best linear unbiased estimators. This is, they are best linear unbiased estimators whatever the variance components.

We describe a method to construct some non-compact Klein surfaces without boundary from 3-regular oriented graphs with a bicoloration of edges. These Klein surfaces are in fact Belyi Klein surfaces where we pinch the preimages of branched points. We can complete such surfaces to compact ones and these surfaces are the random Klein surfaces (without boundary). The consideration of random 3-regular graphs with orientation and a bicoloration of edges give us a method for computing the probability of satisfying a given geometrical property for random Klein surfaces. The relation between random Klein surfaces and random Riemann surfaces allows to claim new properties for random Klein surfaces.

In emerging economies the easiest way to ensure the geodetic support still is the static relative positioning (SRP) using a single reference station. This technique provides surveyors the ability to determine the 3D coordinates of a new point with centimeter-level accuracy. The objective of this work is to evaluate GPS SRP regarding accuracy, as the equivalent of a real time kinematic (RTK) network and to address the practicality of using either a continuously operating reference stations (CORS) or a passive control point for providing accurate positioning control. The precision of an observed 3D relative position between two global navigation satellite systems (GNSS) antennas, and how it depends on the distance between these antennas and on the duration of the observing session, was studied. We analyze the performance of the software for each of the six chosen ranges of length in each of the four scenarios created, considering different intervals of observation time. An intermediate inference level technique (Tamhane and Dunlop, Statistics and data analysis: from elementary to intermediate, Prentice Hall, New Jersey, 2000), an analysis of variance, establishes the evidence of relation between observing time and baseline length.

The work described in this article results from a problem proposed by the company EDP—Energy Solutions Operator, in the framework of ESGI 119th, European Study Group with Industry, during July 2016. Markets for electricity have two characteristics: the energy is mainly no-storable and volatile prices at exchanges are issues to take into consideration. These two features, between others, contribute significantly to the risk of a planning process. The aim of the problem is the short-term forecast of hourly energy prices. In the present work, GLM is considered a useful technique to obtain a predictive model where its predictive power is discussed. The results show that in the GLM framework the season of the year, month, or winter/summer period revealed significant explanatory variables in the different estimated models. The in-sample forecast is promising, conducting to adequate measures of performance.

When \(\left (X_t\right )_{t\geq 0}\) is an ergodic process, the density function of X _t converges to some invariant density as t →∞. We will compute and study some asymptotic properties of pseudo moments estimators obtained from this invariant density, for a specific class of ergodic processes. In this class of processes we can find the Cox-Ingersoll & Ross or Dixit & Pindyck processes, among others. A comparative study of the proposed estimators with the usual estimators obtained from discrete approximations of the likelihood function will be carried out.

The aim of this work is the statistical modelling of counts assuming low values and exhibiting sudden and large bursts that occur randomly in time. It is well known that bilinear processes capture these kind of phenomena. In this work the integer-valued bilinear INBL(1,0,1,1) model is discussed and some properties are reviewed. Classical and Bayesian methodologies are considered and compared through simulation studies, namely to obtain estimates of model parameters and to calculate point and interval predictions. Finally, an empirical application to real epidemiological count data is also presented to attest for its practical applicability in data analysis.

For the purpose of modeling the demand of Engineering Courses in Portugal we analyzed the possible regression models for panel count data models by establishing a comparison between the estimators obtained and then finding the most appropriate ones for our dataset. A precise quantification of the demand for each academic program is facilitated by the rules of access to higher education, in National Contest for Access and Admission to Higher Education, where candidates must list up to six preferences of institution and program. The data used in this paper covers the results of the national contest from 1997 to 2015 provided by the Portuguese Ministry of Education and Science. Multivariate methodologies were performed in order to allow a better understanding of the students’ allocation behavior. The results seem to indicate that the negative binomial estimates fit better the dataset analyzed.

Text data has been growing dramatically in the last years, mainly due to the advance of web related technologies that enable people to produce an overwhelming amount of data. Many knowledge about the world is encoded in text data available through blogs, tweets, web pages, articles, and books.

This paper introduces some general techniques for text data mining, based on text retrieval models, that can be applicable to any text in any natural language. The techniques are targeted to problems requiring minimum or no human effort. These techniques, which can be used in many applications, allow the measurement of similarity of contexts, as well as the co-occurrence of terms in text data with different levels of granularity.