PLS Path modelling: computation of latent variables with the estimation mode B

PLS Path modelling has several interesting advantages compared to other existing approaches traditionally used for structural modelling. However, the lack of convergence properties of the existing iterative procedures for the computation of the latent variables, has always been considered as a major drawback. The convergence is stated only in practice. The present paper shows that when the estimation mode B is chosen for all blocks, the iterative procedure for the computation of latent variables proposed by Wold (in Encyclopaedia of statistical sciences, vol 6. Wiley, New York, pp. 581–591, 1985) is monotonically convergent.     

On the modelling of nested risk-neutral stochastic processes with applications in insurance

We propose a modelling framework for risk-neutral stochastic processes nested in a real-world stochastic process. The framework is important for insurers that deal with the valuation of embedded options and in particular at future points in time. We make use of the class of State Space Hidden Markov models for modelling the joint behaviour of the parameters of a risk-neutral model and the dynamics of option market instruments. This modelling concept enables us to perform non-linear estimation, forecasting and robust calibration. The proposed method is applied to the Heston model for which we find highly satisfactory results. We use the estimated Heston model to compute the required capital of an insurance company under Solvency II and we find large differences compared to a basic calibration method.     

Estimation of stress-strength reliability based on tail-modelling

In probabilistic design it is common to use parametric statistical models to calculate the probability of failure (P_f) obtained from stress-strength interference theory. In this respect, it is well known that P_f is sensitive to the shape of the upper and lower tails of the stress and strength distributions respectively and also to their interference. If the true shapes of these tails could be discovered, it would be possible to improve the existing techniques. However, in practice there is seldom sufficient real data available to establish these tails with statistical significance. Moreover, often one or both variables are expensive to sample. Thus a separate tail estimation may not always be possible. Motivated to define a theoretical safety factor, the author presents a method here which provides a general solution to the problem by considering the tail estimation for a sample of increased sized. This is obtained by a reformulation of the problem in terms of excesses over a threshold, and by breaking the analysis into two parts; estimation of the number of exceedances and modelling the excesses. The analysis is carried out by non-parametric estimation of the former and parametric modelling of the latter based on data from the critical region.     

Adjoining batch Markov arrival processes of a Markov chain

A batch Markov arrival process (BMAP) X* = (N, J) is a 2-dimensional Markov process with two components, one is the counting process N and the other one is the phase process J. It is proved that the phase process is a time-homogeneous Markov chain with a finite state-space, or for short, Markov chain. In this paper, a new and inverse problem is proposed firstly: given a Markov chain J, can we deploy a process N such that the 2-dimensional process X* = (N, J) is a BMAP? The process X* = (N, J) is said to be an adjoining BMAP for the Markov chain J. For a given Markov chain the adjoining processes exist and they are not unique. Two kinds of adjoining BMAPs have been constructed. One is the BMAPs with fixed constant batches, the other one is the BMAPs with independent and identically distributed (i.i.d) random batches. The method we used in this paper is not the usual matrix-analytic method of studying BMAP, it is a path-analytic method. We constructed directly sample paths of adjoining BMAPs. The expressions of characteristic (D _k , k = 0, 1, 2 · · ·) and transition probabilities of the adjoining BMAP are obtained by the density matrix Q of the given Markov chain J. Moreover, we obtained two frontal Theorems. We present these expressions in the first time.     

A GREEDY ALGORITHM FOR SPARSE PRECISION MATRIX APPROXIMATION

Precision matrix estimation is an important problem in statistical data analysis.This paper proposes a sparse precision matrix estimation approach,based on CLIME estimator and an efficient algorithm GISSρ that was originally proposed for l1 sparse signal recov-ery in compressed sensing.The asymptotic convergence rate for sparse precision matrix estimation is analyzed with respect to the new stopping criteria of the proposed GISSρ algorithm.Finally,numerical comparison of GISSρ with other sparse recovery algorithms,such as ADMM and HTP in three settings of precision matrix estimation is provided and the numerical results show the advantages of the proposed algorithm.     

A two-way analysis of variance model with positive definite interaction for homologous factors

A special type of modelling of interaction is investigated in the framework of two-way analysis of variance models for homologous factors. Factors are said to be homologous when their levels are in a meaningful one-to-one relationship, which arise in a wide variety of contexts, as recalled by McCullagh (J. Roy. Statist. Soc. B 62 (2000) 209). The classical linear context for analysis of interaction is extended by positive definiteness restrictions on the interaction parameters. These restrictions aim to provide a spatial representation of the interaction. Properties of the maximum likelihood estimators are derived for a given dimensionality of the model. When the dimension is unknown, an alternative procedure is proposed based on a penalty approach. This approach relies heavily on random matrix theory arguments but we focus on their statistical consequences especially on the reduction of over-fitting problems in the maximum likelihood estimation. Confidence ellipses are provided for an illustrative example.     

Discussion of “Copulas: Tales and facts”, by Thomas Mikosch

As Prof. Mikosch correctly points out, there exists very little sound statistical theory on modelling dependence using copulas. In this contribution, an open problem is presented concerning the efficient estimation of the parameter of a copula when no parametric assumptions are made regarding the marginal distributions.     

Mathematical justification of a heuristic for statistical correlation of real-life time series

Many of the analyses of time series that arise in real-life situations require the adoption of various simplifying assumptions so as to cope with the complexity of the phenomena under consideration. Whilst accepting that these simplifications lead to heuristics providing less accurate processing of information compared to the solution of analytical equations, the intelligent choice of the simplifications coupled with the empirical verification of the resulting heuristic has proven itself to be a powerful systems modelling paradigm. In this study, we look at the theoretical underpinning of a successful heuristic for estimation of urban travel times from lane occupancy measurements. We show that by interpreting time series as statistical processes with a known distribution it is possible to estimate travel time as a limit value of an appropriately defined statistical process. The proof of the theorem asserting the above, supports the conclusion that it is possible to design a heuristic that eliminates the adverse effect of spurious readings without loosing temporal resolution of data (as implied by the standard method of data averaging). The original contribution of the paper concerning the link between the analytical modelling and the design of heuristics is general and relevant to a broad spectrum of applications.     

Online state of charge estimation of Li-ion battery based on an improved unscented Kalman filter approach

An improved unscented Kalman filter approach is proposed to enhance online state of charge estimation in terms of both accuracy and robustness. The goal is to address the drawback associated with the unscented Kalman filter in terms of its requirement for an accurate model and a priori noise statistics. Firstly, Li-ion battery modelling and offline parameter identification is performed. Secondly, a sensitivity analysis experiment is designed to verify which model parameter has the greatest influence on state of charge estimation accuracy, in order to provide an appropriate parameter for the model adaptive algorithm. Thirdly, an improved unscented Kalman filter approach, composed of a model adaptive algorithm and a noise adaptive algorithm, is introduced. Finally, the results are discussed, which reveal that the proposed approach’s estimation error is less than 1.79% with acceptable robustness and time complexity.     

Prediction of Euclidean distances with discrete and continuous outcomes

The objective of this paper is first to predict generalized Euclidean distances in the context of discrete and quantitative variables and then to derive their statistical properties. We first consider the simultaneous modelling of discrete and continuous random variables with covariates and obtain the likelihood. We derive an important property useful for its practical maximization. We then study the prediction of any Euclidean distances and its statistical proprieties, especially for the Mahalanobis distance. The quality of distance estimation is analyzed through simulations. This results are applied to our motivating example: the official distinction procedure of rapeseed varieties.     

Forecasting model with asymmetric market response and its application to pricing of consumer package goods

This paper presents a dynamic forecasting model that accommodates asymmetric market responses to marketing mix variable—price promotion—by threshold models. As a threshold variable to generate a mechanism for different market responses, we use the counterpart to the concept of a price threshold applied to a representative consumer in a store. A Bayesian approach is taken for statistical modelling because of advantages that it offers over estimation and forecasting. The proposed model incorporates the lagged effects of a price variable. Thereby, myriad pricing strategies can be implemented in the time horizon. Their effectiveness can be evaluated using the predictive density. We intend to improve the forecasting performance over conventional linear time series models. Furthermore, we discuss efficient dynamic pricing in a store using strategic simulations under some scenarios suggested by an estimated structure of the models. Empirical studies illustrate the superior forecasting performance of our model against conventional linear models in terms of the root mean square error of the forecasts. Useful information for dynamic pricing is derived from its structural parameter estimates. This paper develops a dynamic forecasting model that accommodates asymmetric market responses to marketing mix variable—price promotion—by the threshold models. Copyright © 2005 John Wiley & Sons, Ltd.     

Bayesian estimation of NIG models via Markov chain Monte Carlo methods

The normal inverse Gaussian (NIG) distribution is a promising alternative for modelling financial data since it is a continuous distribution that allows for skewness and fat tails. There is an increasing number of applications of the NIG distribution to financial problems. Due to the complicated nature of its density, estimation procedures are not simple. In this paper we propose Bayesian estimation for the parameters of the NIG distribution via an MCMC scheme based on the Gibbs sampler. Our approach makes use of the data augmentation provided by the mixture representation of the distribution. We also extend the model to allow for modelling heteroscedastic regression situations. Examples with financial and simulated data are provided. Copyright © 2004 John Wiley & Sons, Ltd.     

A hierarchical model for the joint mortality analysis of pension scheme data with missing covariates

A hierarchical model is developed for the joint mortality analysis of pension scheme datasets. The proposed model allows for a rigorous statistical treatment of missing data. While our approach works for any missing data pattern, we are particularly interested in a scenario where some covariates are observed for members of one pension scheme but not the other. Therefore, our approach allows for the joint modelling of datasets which contain different information about individual lives. The proposed model generalizes the specification of parametric models when accounting for covariates. We consider parameter uncertainty using Bayesian techniques. Model parametrization is analysed in order to obtain an efficient MCMC sampler, and address model selection. The inferential framework described here accommodates any missing-data pattern, and turns out to be useful to analyse statistical relationships among covariates. Finally, we assess the financial impact of using the covariates, and of the optimal use of the whole available sample when combining data from different mortality experiences.     

Simulation of ECB decisions and forecast of short term Euro rate with an adaptive fuzzy expert system

The elaboration of optimal monetary policy strategies, and the statistical estimation of monetary policy rules followed by European Central Bank (ECB) in the new currency area of the Euro, are difficult to follow with the standard statistical models. For this reason we have developed an adaptive fuzzy expert system in order to mimic the framework on which the monetary policy strategy of the ECB is based. The expert system knowledge base consists of a set of fuzzy and crisp rules located at two different hierarchical levels. The high-level of the system receives some intermediate output values from the low-level and processes this information by means of a set of crisp rules. The low-level prepares these intermediate output values with the use of a fuzzy inference engine applied to economic input variables. The use of an expert system allows for modelling the ECB behaviour with the use of wider scope of knowledge, when compared with more traditional computational techniques. Rules at different hierarchical levels and at different intra-level groups, allow for managing the potentially contradictory structure of the ECB strategy. The system has been tested on the economic and financial time series going from the January 1999 to September 2000. The system’s correct prediction was estimated to overall 70% and, considering the complexity of the task, the results obtained are promising.     

Wavelet-based analysis of non-Gaussian long-range dependent processes and estimation of the hurst parameter

In this contribution, the statistical performance of the wavelet-based estimation procedure for the Hurst parameter is studied for non-Gaussian long-range dependent processes obtained from point transformations of Gaussian processes. The statistical properties of the wavelet coefficients and the estimation performance are compared both for processes having the same covariance but different marginal distributions and for processes having the same covariance and same marginal distributions but obtained from different point transformations, analyzed using mother wavelets with different number of vanishing moments. It is shown that the reduction of the dependence range from long to short by increasing the number of vanishing moments, observed for Gaussian processes, and at the origin of the popularity of the wavelet-based estimator, does not hold in general for non-Gaussian processes. Crucially, it is also observed that the Hermite rank of the point transformation impacts significantly the statistical properties of the wavelet coefficients and the estimation performance and also that processes having identical marginal distributions and covariance function can yet yield significantly different estimation performance. These results are interpreted in the light of central and noncentral limit theorems that are fundamental when dealing with long-range dependent processes. Moreover, it will be shown that, on condition that estimation is performed using a range of scales restricted to the coarsest practically available, an approximate, yet analytical and simple to use in practice, formula can be proposed for the evaluation of the variance of the wavelet-based estimator of the Hurst parameter.     

Integrodifferential approaches to frequency analysis and control design for compressible fluid flow in a pipeline element

In this study, modelling, frequency analysis, and optimization of control processes are considered for the fluid flow in pipeline systems. A mathematical model of controlled pipeline elements with distributed parameters is proposed to describe the dynamical behaviour of compressible fluid which is transported in a long rigid tube. By exploiting specific functions representing cross-sectional forces and effective displacements as well as linear approximations of fluidic resistances, the original problem with non-uniform parameters is reduced to a partial differential equation (PDE) system with constant coefficients and homogeneous initial and boundary conditions. Three numerical approaches are applied to an efficient analysis of natural vibrations and reliable control-oriented modelling of pipeline elements. The conventional Galerkin method is compared with the method of integrodifferential relations based on a weak formulation of the constitutive laws. In the latter approach, the original initial-boundary value problem is reduced to the minimization of an error functional which provides explicit energy estimates of the solution quality. A novel projection approach is implemented on the basis of the Petrov–Galerkin method combined with the method of integrodifferential relations. This technique benefits from the advantages of the above-mentioned projection and variational approaches, namely sufficient numerical stability, a lower differential order, and an explicit quality estimation. Numerical optimization procedures, making use of a modified finite element technique, are proposed to obtain a feedforward control strategy for changing the pressure and mass flow inside the pipeline system to a desired operating state. At this given finite point of time, residual elastic oscillations inside the pipeline are minimized. Numerical results, obtained for ideal as well as viscous fluid models, are analysed and discussed.     

Regularized Adaptation of Fuzzy Inference Systems. Modelling the Opinion of a Medical Expert about Physical Fitness: An Application

This study presents a new approach to adaptation of Sugeno type fuzzy inference systems using regularization, since regularization improves the robustness of standard parameter estimation algorithms leading to stable fuzzy approximation. The proposed method can be used for modelling, identification and control of physical processes. A recursive method for on-line identification of fuzzy parameters employing Tikhonov regularization is suggested. The power of approach was shown by applying it to the modelling, identification, and adaptive control problems of dynamic processes. The proposed approach was used for modelling of human-decisions (experience) with a fuzzy inference system and for the fuzzy approximation of physical fitness with real world medical data.     

Practical Extreme Value Modelling of Hydrological Floods and Droughts: A Case Study

Estimation of flood and drought frequencies is important for reservoir design and management, river pollution, ecology and drinking water supply. Through an example based on daily streamflow observations, we introduce a stepwise procedure for estimating quantiles of the hydrological extremes floods and droughts. We fit the generalised extreme value (GEV) distribution by the method of block maxima and the generalised Pareto (GP) distribution by applying the peak over threshold method. Maximum likelihood, penalized maximum likelihood and probability weighted moments are used for parameter estimation. We incorporate trends and seasonal variation in the models instead of splitting the data, and investigate how the observed number of extreme events, the chosen statistical model, and the parameter estimation method effect parameter estimates and quantiles. We find that a seasonal variation should be included in the GEV distribution fitting for floods using block sizes less than one year. When modelling droughts, block sizes of one year or less are not recommended as significant model bias becomes visible. We conclude that the different characteristics of floods and droughts influence the choices made in the extreme value modelling within a common inferential strategy.This revised version was published online in March 2005 with corrections to the cover date.     

Time series analysis

Current univariate and multivariate time series modelling procedures are reviewed. Areas of disagreement are discussed, such as the choice of a forecasting method, whether to use time series analysis or econometrics for economic data, the merits of prior seasonal adjustment, and the advisability of prewhitening in multivariate modelling. Some recent developments in model identification, estimation and model criticism are described. It is argued that too little attention has been paid to allowing for departures from the model; this leads to a discussion of exploratory and robust techniques. Finally, it is pointed out that little has been done on modelling positive and discrete-valued time series of importance in OR such as lifetimes and counts; some recent proposals are described.     

Comment détecter le délit d'initiés?

This Note uses the enlargement of filiations for modelling the observation of a financial market by an insider trader. A characterization of admissible strategies and a criterium for optimization are given. Then a statistical test is proposed to test the unknown of the future against its knowledge.