Pepa Ramírez-Cobo

2D wavelet-based spectra with applications

A wavelet-based spectral method for estimating the (directional) Hurst parameter in isotropic and anisotropic non-stationary fractional Gaussian fields is proposed. The method can be applied to self-similar images and, in general, to d-dimensional data which scale. In the application part, the problems of denoising 2D fractional Brownian fields and classification of digital mammograms to benign and malignant are considered. In the first application, a Bayesian inference calibrated by information from the wavelet-spectral domain is used to separate the signal from the noise. In the second application, digital mammograms are classified into benign and malignant based on the directional Hurst exponents which prove to be discriminatory summaries.

Bayesian inference for double Pareto lognormal queues

In this article we describe a method for carrying out Bayesian estimation for the double Pareto lognormal (dPlN) distribution which has been proposed as a model for heavy-tailed phenomena. We apply our approach to estimate the dPlN/M/1 and M/dPlN/1 queueing systems. These systems cannot be analyzed using standard techniques due to the fact that the dPlN distribution does not possess a Laplace transform in closed form. This difficulty is overcome using some recent approximations for the Laplace transform of the interarrival distribution for the Pareto/M/1 system. Our procedure is illustrated with applications in internet traffic analysis and risk theory.

A 2D wavelet-based multiscale approach with applications to the analysis of digital mammograms

A wavelet-based multifractal spectrum (MFS) for the analysis of images that possess an erratically changing oscillatory behavior at various scales is constructed and estimated. The methodology is applied to the analysis of mammograms. The key contribution is that the analysis is not focused on microcalcifications, but on the background of the image, thus presenting a new modality to be combined with other diagnostic tools. Differences in image backgrounds between malignant and normal cases are found, in terms of multifractal descriptors. The new tool is compared with another spectral method, based on monofractal descriptors.

A Wavelet‐Based Spectral Method for Extracting Self‐Similarity Measures in Time‐Varying Two‐Dimensional Rainfall Maps

Many environmental time‐evolving spatial phenomena are characterized by a large number of energetic modes, the occurrence of irregularities, and self‐organization over a wide range of space or time scales. Precipitation is a classical example characterized by both strong intermittency and multiscale dynamics, and these features generate persistence, long‐range dependence, and extremes (whether be it droughts or extreme floods). Over the last two decades, time‐frequency or time‐scale transforms have become indispensable tools in the analysis of such phenomena and, as a consequence, a number of wavelet‐based spectral methods are now routinely employed to estimate Hurst exponents and other measures of regularity and scaling. In this article, an ensemble of new wavelet‐based spectral tools for analysis of 2‐D images is proposed. The new scale‐mixing wavelet spectrum is applied to the analysis of time sequences of two‐dimensional spatial rainfall radar images characterized by either convective or frontal systems. Intermittent spatial patterns connected to the precipitation‐formation mechanisms were encoded in low‐dimensional informative descriptors appropriate for classification, discrimination analyses and possible integration with climate models. We found that convective rainfall spatial patterns compared to frontal patterns produce spectral signatures consistent with their generation mechanism.

Robust newsvendor problem with autoregressive demand

This paper explores the single-item newsvendor problem under a novel setting which combines temporal dependence and tractable robust optimization. First, the demand is modeled as a time series which follows an autoregressive process AR(p), p ? 1 . Second, a robust approach to maximize the worst-case revenue is proposed: a robust distribution-free autoregressive method for the newsvendor problem, which copes with non-stationary time series, is formulated. A closed-form expression for the optimal solution is found for p=1; for the remaining values of p, the problem is expressed as a nonlinear convex optimization program, to be solved numerically. The optimal solution under the robust method is compared with those obtained under three versions of the classic approach, in which either the demand distribution is unknown, and autocorrelation is neglected, or it is assumed to follow an AR(p) process with normal error terms. Numerical experiments show that our proposal usually outperforms the previous benchmarks, not only with regard to robustness, but also in terms of the average revenue. Extensions to multiperiod and multiproduct models are also discussed. HighlightsThe single period problem with uncertain and correlated demand values is explored.The demand forecast is estimated by a robust optimization method based on uncertainty sets.The proposed approach usually outperforms the competing methods.A model for the multi-product case with demands correlated along time and between products is proposed.An approach to deal with the multi-period case is outlined.

Failure modeling of an electrical N-component framework by the non-stationary Markovian arrival process

This paper considers the non-stationary version of the Markovian arrival process to model the failures of N electrical components that are considered to be identically distributed, but for which it is not reasonable to assume that the operational times related to each component are independent or identically distributed. We propose a moment matching estimation approach to fit the data via a non-stationary Markovian arrival process. A simulated and a real data set provided by the Spanish electrical group Iberdrola are presented to illustrate the approach.

Time series interpolation via global optimization of moments fitting

Most time series forecasting methods assume the series has no missing values. When missing values exist, interpolation methods, while filling in the blanks, may substantially modify the statistical pattern of the data, since critical features such as moments and autocorrelations are not necessarily preserved.

Analytical issues regarding the lack of identifiability of the non-stationary MAP2

Abstract This paper studies in detail different problems concerning the identifiability of the non-stationary version of the M A P 2 . First, a matrix-based methodology to build equivalent processes is given. Second, a unique, canonical representation of the process, so that the infinite, equivalent versions of a process can be reduced to its canonical counterpart is provided. Finally, a characterization of the process in terms of five descriptors representing moments of the three first inter-event time distributions is given.

Dependence patterns for modeling simultaneous events

In this paper we examine in detail some of the modeling capabilities of the stationary m-state BMAP, with simultaneous events up to size k, noted BMAPm(k). Specifically, we study the forms of the auto-correlation functions of the inter-event times and event sizes. We provide a novel characterization of the functions which is suitable for analyzing the dependence patterns. In particular, this allows one to prove a geometrically decrease to zero of the functions and to identify four correlation patterns, when m=2 . The case m≥3 is illustrated via an extensive simulation study, from which it can be deduced that, as expected, richer structures can be obtained as m increases. In addition, the influence of the dependence patterns for both auto-correlation functions for the BMAP2(2) in the counting process has been explored through an empirical analysis.

A sparsity-controlled vector autoregressive model

Vector autoregressive (VAR) models constitute a powerful and well studied tool to analyze multivariate time series. Since sparseness, crucial to identify and visualize joint dependencies and relevant causalities, is not expected to happen in the standard VAR model, several sparse variants have been introduced in the literature. However, in some cases it might be of interest to control some dimensions of the sparsity, as e.g. the number of causal features allowed in the prediction. To authors extent none of the existent methods endows the user with full control over the different aspects of the sparsity of the solution. In this article, we propose a versatile sparsity-controlled VAR model which enables a proper visualization of potential causalities while allows the user to control different dimensions of the sparsity if she holds some preferences regarding the sparsity of the outcome. The model coefficients are found as the solution to an optimization problem, solvable by standard numerical optimization routines. The tests performed on both simulated and real-life time series show that our approach may outperform a greedy algorithm and different Lasso approaches in terms of prediction errors and sparsity.