Reversing the Stein Effect

The Reverse Stein Effect is identified and illustrated: A statistician who shrinks his/her data toward a point chosen without reliable knowledge about the underlying value of the parameter to be estimated but based instead upon the observed data will not be protected by the minimax property of shrinkage estimators such as that of James and Stein, but instead will likely incur a greater error than if shrinkage were not used.Comment: Published in at http://dx.doi.org/10.1214/09-STS278 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Real estate portfolio construction and estimation risk

The use of MPT in the construction real estate portfolios has two serious limitations when used in an ex-ante framework: (1) the intertemporal instability of the portfolio weights and (2) the sharp deterioration in performance of the optimal portfolios outside the sample period used to estimate asset mean returns. Both problems can be traced to wide fluctuations in sample means Jorion (1985). Thus the use of a procedure that ignores the estimation risk due to the uncertain in mean returns is likely to produce sub-optimal results in subsequent periods. This suggests that the consideration of the issue of estimation risk is crucial in the use of MPT in developing a successful real estate portfolio strategy. Therefore, following Eun & Resnick (1988), this study extends previous ex-ante based studies by evaluating optimal portfolio allocations in subsequent test periods by using methods that have been proposed to reduce the effect of measurement error on optimal portfolio allocations

Statistical Methodologies of Functional Data Analysis for Industrial Applications

This thesis stands as one of the first attempt to connect the statistical object oriented data analysis (OODA) methodologies with the industry field. Indeed, the aim of this thesis is to develop statistical methods to tackle industrial problems through the paradigm of the OODA. The new framework of Industry 4.0 requires factories that are equipped with sensor and advanced acquisition systems that acquire data with a high degree of complexity. OODA can be particularly suitable to deal with this increasing complexity as it considers each statistical unit as an atom or a data object assumed to be a point in a well-defined mathematical space. This idea allows one to deal with complex data structure by changing the resolution of the analysis. Indeed, from standard methods where the atom is represented by vector of numbers, the focus now is on methodologies where the objects of the analysis are whole complex objects. In particular, this thesis focuses on functional data analysis (FDA), a branch of OODA that considers as the atom of the analysis functions defined on compact domains. The cross-fertilization of FDA methods to industrial applications is developed into three parts in this dissertation. The first part presents methodologies developed to solve specific applicative problems. In particular, a first consistent portion of this part is focused on \textit{profile monitoring} methods applied to ship CO\textsubscript{2} emissions. A second portion deals with the problem of predicting the mechanical properties of an additively manufactured artifact given the particle size distribution of the powder used for its production. And, a third portion copes with the cluster analysis for the quality assessment of metal sheet spot welds in the automotive industry based on observations of dynamic resistance curve. Stimulated by these challenges, the second part of this dissertation turns towards a more methodological line that addresses the notion of \textit{interpretability} for functional data. In particular, two new interpretable estimators of the coefficient function of the function-on-function linear regression model are proposed, which are named S-LASSO and AdaSS, respectively. Moreover, a new method, referred to as SaS-Funclust, is presented for sparse clustering of functional data that aims to classify a sample of curves into homogeneous groups while jointly detecting the most informative portions of domain. In the last part, two ongoing researches on FDA methods for industrial application are presented. In particular, the first one regards the definition of a new robust nonparametric functional ANOVA method (Ro-FANOVA) to test differences among group functional means by being robust against the presence of outliers with an application to additive manufacturing. The second one sketches a new methodological framework for the real-time profile monitoring

Exploiting Robust Multivariate Statistics and Data Driven Techniques for Prognosis and Health Management

This thesis explores state of the art robust multivariate statistical methods and data driven techniques to holistically perform prognostics and health management (PHM). This provides a means to enable the early detection, diagnosis and prognosis of future asset failures. In this thesis, the developed PHM methodology is applied to wind turbine drive train components, specifically focussed on planetary gearbox bearings and gears. A novel methodology for the identification of relevant time-domain statistical features based upon robust statistical process control charts is presented for high frequency bearing accelerometer data. In total, 28 time-domain statistical features were evaluated for their capabilities as leading indicators of degradation. The results of this analysis describe the extensible multivariate “Moments’ model” for the encapsulation of bearing operational behaviour. This is presented, enabling the early degradation of detection, predictive diagnostics and estimation of remaining useful life (RUL). Following this, an extended physics of failure model based upon low frequency SCADA data for the quantification of wind turbine gearbox condition is described. This extends the state of the art, whilst defining robust performance charts for quantifying component condition. Normalisation against loading of the turbine and transient states based upon empirical data is performed in the bivariate domain, with extensibility into the multivariate domain if necessary. Prognosis of asset condition is found to be possible with the assistance of artificial neural networks in order to provide business intelligence to the planning and scheduling of effective maintenance actions. These multivariate condition models are explored with multivariate distance and similarity metrics for to exploit traditional data mining techniques for tacit knowledge extraction, ensemble diagnosis and prognosis. Estimation of bearing remaining useful life is found to be possible, with the derived technique correlating strongly to bearing life (r = .96

Stein-Like Estimation and Inference.

The dissertation addresses three issues in the use of Stein-like estimators of the classical normal linear regression model. The St. Louis equation is used to generate out-of-sample forecasts using least squares. These forecasts are compared to those produced by restricted least squares, pretest, and members of a general family of minimax shrinkage estimators using the root-mean-square error criterion. Bootstrap confidence intervals and ellipsoids are constructed which are centered at least squares and James-Stein estimators and their coverage probability and size is explored in a Monte Carlo experiment. A Stein-like estimator of the probit regression model is suggested and its quadratic risk properties are explored in a Monte Carlo experiment

25 Years of IIF Time Series Forecasting: A Selective Review

We review the past 25 years of time series research that has been published in journals managed by the International Institute of Forecasters (Journal of Forecasting 1982-1985; International Journal of Forecasting 1985-2005). During this period, over one third of all papers published in these journals concerned time series forecasting. We also review highly influential works on time series forecasting that have been published elsewhere during this period. Enormous progress has been made in many areas, but we find that there are a large number of topics in need of further development. We conclude with comments on possible future research directions in this field.Accuracy measures; ARCH model; ARIMA model; Combining; Count data; Densities; Exponential smoothing; Kalman Filter; Long memory; Multivariate; Neural nets; Nonlinearity; Prediction intervals; Regime switching models; Robustness; Seasonality; State space; Structural models; Transfer function; Univariate; VAR.