Ana M. Aguilera

University of Granada | UGR · Department Statistics and Operations Research

Biomechanics data are usually curves that represent the human movement when subjects are submitted to multiple conditions. The main objective of this paper is to detect possible differences in gait patterns when a group of children between 8 and 11 years old go to school with different book-bags (walking without bag, carrying a backpack and pulling...

Whitening is a critical normalization method to enhance statistical reduction via reparametrization to unit covariance. This article introduces the notion of whitening for random functions assumed to reside in a real separable Hilbert space. We compare the properties of different whitening transformations stemming from the factorization of a bounde...

The functional logit regression model was proposed by Escabias et al. (2004) with the objective of modeling a scalar binary response variable from a functional predictor. The model estimation proposed in that case was performed in a subspace of L2(T) of squared integrable functions of finite dimension, generated by a finite set of basis functions....

The methodological contribution in this paper is motivated by biomechanical studies where data characterizing human movement are waveform curves representing joint measures such as flexion angles, velocity, acceleration, and so on. In many cases the aim consists of detecting differences in gait patterns when several independent samples of subjects...

Faced with novel coronavirus outbreak, the most hard-hit countries adopted a lockdown strategy to contrast the spread of virus. Many studies have already documented that the COVID-19 control actions have resulted in improved air quality locally and around the world. Following these lines of research, we focus on air quality changes in the urban ter...

Burnout is a serious problem in modern society and early detection methods are needed to successfully handled its multiple effects. The latter refer to working well-being, as well as to the affective, psychological, physiological, and behavioral well-being of workers. However, in many countries official statistics on this topic are not available. F...

Motivated by mapping adverse artifactual events caused by body movements in electroencephalographic (EEG) signals, we present a functional independent component analysis based on the spectral decomposition of the kurtosis operator of a smoothed principal component expansion. A discrete roughness penalty is introduced in the orthonormality constrain...

The aim of this paper is the imputation of missing data of COVID-19 hospitalized and intensive care curves in several Spanish regions. Taking into account that the curves of cases, deceases and recovered people are completely observed, a function-on-function regression model is proposed to estimate the missing values of the functional responses ass...

A new stochastic process was developed by considering the internal performance of macro-states in which the sojourn time in each one is phase-type distributed depending on time. The stationary distribution was calculated through matrix-algorithmic methods and multiple interesting measures were worked out. The number of visits distribution to a dete...

A powerful time series analysis modeling technique is presented to describe cycle-to-cycle variability in memristors. These devices show variability linked to the inherent stochasticity of device operation and it needs to be accurately modeled to build compact models for circuit simulation and design purposes. A new multivariate approach is propose...

In this work, voltage distributions of forming operations are analyzed by using an advanced statistical approach based on phase-type distributions (PHD). The experimental data were collected from batches of 128 HfO2-based RRAM devices integrated in 4-kbit arrays. Three different switching oxides, namely, polycrystalline HfO2, amorphous HfO2, and Al...

A functional linear discriminant analysis approach to classify a set of kinematic data (human movement curves of individuals performing different physical activities) is performed. Kinematic data, usually collected in linear acceleration or angular rotation format, can be identified with functions in a continuous domain (time, percentage of gait cy...

Functional Principal Component Analysis (FPCA) is an important dimension reduction technique to interpret the main modes of functional data variation in terms of a small set of uncorrelated variables. The principal components can not always be simply interpreted and rotation is one of the main solutions to improve the interpretation. In this paper,...

Functional principal component analysis (FPCA) based on Karhunen-Loève (K-L) expansion allows to describe the stochastic evolution of the main characteristics associated to multiple systems and devices. Identifying the probability distribution of the principal component scores is fundamental to characterize the whole process. The aim of this work i...

The homogeneity problem for testing if more than two different samples come from the same population is considered for the case of functional data. The methodological results are motivated by the study of homogeneity of electronic devices fabricated by different materials and active layer thicknesses. In the case of normality distribution of the st...

This work investigates the sources of resistive switching (RS) in recently reported laser-fabricated graphene oxide memristors by means of two numerical analysis tools linked to the Time Series Statistical Analysis and the use of the Quantum Point Contact Conduction model. The application of both numerical procedures points to the existence of a fi...

A functional linear discriminant analysis approach to classify a set of kinematic data (human movement curves of individuals performing different physical activities) is performed. Kinematic data, usually collected in linear acceleration or angular rotation format, can be identified with functions in a continuous domain (time, percentage of gait cy...

Time series statistical analyses (TSSA) have been employed to evaluate the variability of resistive switching memories and to model the set and reset voltages for modeling purposes. The conventional procedures behind time series theory have been used to obtain autocorrelation and partial autocorrelation functions and determine the simplest analytic...

In order to study the device-to-device and cycle-to-cycle variability of switching voltages in 4-kbit RRAM arrays, an alternative statistical approach has been adopted by using experimental data collected from a batch of 128 devices switched along 200 cycles. The statistical distributions of switching voltages have been usually studied by using the...

Resistive Random Access Memories (RRAMs) are being studied by the industry and academia because it is widely accepted that they are promising candidates for the next generation of high density nonvolatile memories. Taking into account the stochastic nature of mechanisms behind resistive switching, a new technique based on the use of functional data...

A new statistical approach has been developed to analyze Resistive Random Access Memory (RRAM) variability. The stochastic nature of the physical processes behind the operation of resistive memories makes variability one of the key issues to solve from the industrial viewpoint of these new devices. The statistical features of variability have been...

A multivariate analysis of the parameters that characterize the reset process in Resistive Random Access Memory (RRAM) has been performed. The different correlations obtained can help to shed light on the current components that contribute in the Low Resistance State (LRS) of the technology considered. In addition, a screening method for the Quantu...

Traditionally gait analysis has examined discrete measures as descriptors of gait to compare different experimental situations. Functional data analysis (FDA) uses information from the entire curves and trajectories, thus revealing the nature of the movement. The aim of our study is to develop some repeated measures FDA methodologies to analyze kin...

This paper is focus on spatial functional variables whose observations are a set of spatially correlated sample curves obtained as realizations of a spatio-temporal stochastic process. In this context, as alternative to other geostatistical techniques (kriging, kernel smoothing, among others), a new method to predict the curves of temporal evolutio...

Least squares estimation of the functional linear regression model with scalar response is an ill-posed problem due to the infinite dimension of the functional predictor. Dimension reduction approaches as principal component regression or partial least squares regression are proposed and widely used in applications. In both cases the interpretation...

In many statistical applications data are curves measured as functions of a continuous parameter as time. Despite of their functional nature and due to discrete-time observation, these type of data are usually analyzed with multivariate statistical methods that do not take into account the high correlation between observations of a single curve at...

The power of functional linear regression to estimate a set of curves from others involved is studied in this work in the context of life sciences. The objective is to determine the relationship between the degree of lupus and the level of stress for patients suffering this autoimmune disease. Daily stress and lupus curves have a strong local behav...

This is a discussion of the paper “Overview of object oriented data analysis” by J. Steve Marron and Andrés M. Alonso.

The sample observations of a functional variable are functions that come from the observation of a statistical variable in a continuous argument that in most cases is the time. But in practice, the sample functions are observed in a finite set of points. Then, the first step in functional data analysis is to reconstruct the functional form of sampl...

The problem of multicollinearity associated with the estimation of a functional logit model can be solved by using as predictor variables a set of functional principal components. The functional parameter estimated by functional principal component logit regression is often nonsmooth and then difficult to interpret. To solve this problem, different...

Functional principal component analysis (FPCA) is a dimension reduction technique that explains the dependence structure of a functional data set in terms of uncorrelated variables. In many applications the data are a set of smooth functions observed with error. In these cases the principal components are difficult to interpret because the estimate...

The aim of this paper is to improve the quality of cookies production by classifying them as good or bad from the curves of resistance of dough observed during the kneading process. As the predictor variable is functional, functional classification methodologies such as functional logit regression and functional discriminant analysis are considered...

The objective of this paper is to present a review of different calibration and classification methods for functional data in the context of chemometric applications. In chemometric, it is usual to measure certain parameters in terms of a set of spectrometric curves that are observed in a finite set of points (functional data). Although the predict...

The intensity of a doubly stochastic Poisson process (DSPP) is also a stochastic process whose integral is the mean process of the DSPP. From a set of sample paths of the Cox process we propose a numerical method, preserving the monotone character of the mean, to estimate the intensity on the basis of the functional PCA. A validation of the estimat...

High levels of airborne olive pollen represent a problem for a large proportion of the population because of the many allergies it causes. Many attempts have been made to forecast the concentration of airborne olive pollen, using methods such as time series, linear regression, neural networks, a combination of fuzzy systems and neural networks, and...

The problem of multicollinearity associated with the estimation of a functional logit model can be solved by using as predictor variables a set of functional principal components. The functional parameter estimated by functional principal component logit regression is often unsmooth. To solve this problem we propose two penalized estimations of the...

There are many chemometric applications, such as spectroscopy, where the objective is to explain a scalar response from a functional variable (the spectrum) whose observations are functions of wavelengths rather than vectors. In this paper, PLS regression is considered for estimating the linear model when the predictor is a functional random variab...

A solution to the problem of calibrating a counting device from observed data, is developed in this paper by means of a Cox process model. The stochastic intensity of the process for counting emitted particles is estimated by functional principal components analysis and confidence bands are provided for two radioactive isotopes, 226Ra and 137Cs. A...

Biometría es una asignatura troncal de primer curso del grado de Farmacia. Últimamente, los profesores tratan de adaptarla al espíritu del EEES. El mayor esfuerzo se enfoca hacia el desarrollo de la capacidad de auto-crítica, auto-aprendizaje y de una evaluación adecuada. Algunos métodos tradicionales ya lo pretendían, como la provisión de resúmene...

La implantación del EEES en las titulaciones en Farmacia va a significar la potenciación del autoaprendizaje por parte del alumno. Esto va a poner a prueba la capacidad de aplicar conocimientos adquiridos en unas materias, para entender y conocer otras. Entre dichos conocimientos, se encuentran las técnicas de modelado matemático, incluidas en el c...

Biometrics is a mandatory subject in the first course of the Pharmacy degree. In the last few years, its professors try to adapt it to the EEES spirit. The biggest effort is focused on developing the selfcriticisim, self-learning competences and a suitable evaluation method. Some of the traditional teaching methods already aimed that, such us provi...

A functional regression model to forecast the cypress pollen concentration during a given time interval, considering the air temperature in a previous interval as the input, is derived by means of a two-step procedure. This estimation is carried out by functional principal component (FPC) analysis and the residual noise is also modeled by FPC regre...

The relationship between time evolution of stress and flares in Systemic Lupus Erythematosus patients has recently been studied. Daily stress data can be considered as observations of a single variable for a subject, carried out repeatedly at different time points (functional data). In this study, we propose a functional logistic regression model w...

Difierent functional logit models to estimate a multicategory response variable from a functional predictor will be formulated in terms of difierent types of logit transformations as base-line category logits for nominal responses or cumulative, adjacent-categories or continuation-ratio logits for ordinal responses. Estimation procedures of functio...

A linear regression model to estimate a sample of response curves (realizations of a functional response) from a sample of predictor curves (functional predictor) is considered. Difierent procedures for estimating the parameter function of the model based on wavelets expansions and functional principal component decomposition of both the predictor...

A transfer function model with multiplicative intervention variable is proposed in this paper in order to forecast air pollen concentration using the temperature as input series. The inertia process is at the same time modelled by means of a principal component analysis (PCA) after a suitable time rescaling. The final model is tested with cypress p...

In order to forecast time evolution of a binary response variable from a related continuous time series a functional logit model is proposed. The estimation of this model from discrete time observations of the predictor is solved by using functional principal component analysis and ARIMA modelling of the associated discrete time series of principal...

Functional logistic regression is one of the methods that have raised great interest in the emerging statistical field of functional data analysis and par-ticularly the one of functional regression analysis when the predictor is functional and the response is binary. The aim of this paper is to generalize the solutions exposed in the literature to...

Functional logistic regression has been developed to forecast a binary response variable from a functional predictor. In order to fit this model, it is usual to assume that the functional observations and the parameter function of the model belong to a same finite space generated by a basis of functions. This consideration turns the functional mode...

Computing estimates in functional principal component analysis (FPCA) from discrete data is usually based on the approximation of sample curves in terms of a basis (splines, wavelets, trigonometric functions, etc.) and a geometrical structure in the data space (L 2 spaces, Sobolev spaces, etc.). Until now, the computational efforts have been focuse...

The characteristic functional (c.fl.) of a doubly stochastic Poisson process (DSPP) is studied and it provides us the finite dimensional distributions of the process and so its moments. It is also studied the case of a DSPP which intensity is a narrow-band process. The Karhunen–Loève expansion of its intensity is used to obtain the probability dist...

A new procedure for estimating the mean process of a doubly stochastic Poisson process is intro- duced. The proposed estimation is based on monotone piecewise cubic interpolation of the sample paths of the mean. In order to estimate the continuous time structure of the mean process functional principal component analysis is applied to its trajector...

The logistic regression model is used to predict a binary response variable in terms of a set of explicative ones. The estimation of the model parameters is not too accurate and their interpretation in terms of odds ratios may be erroneous, when there is multicollinearity (high dependence) among the predictors. Other important problem is the great...

Summary The number of mortgages in Spain is a counting process that can be modelled as a doubly stochastic Poisson process (DSPP). A modelling method for the intensity of a DSPP is proposed. A first step consists on estimating discrete sample paths of it from observed ones of the DSPP, then a continuous modelling is derived by means of Functional P...

In recent years, many studies have dealt with predicting a response variable based on the information provided by a functional variable. When the response variable is binary, different problems arise, such as multicollinearity and high dimensionality, which prejudice the estimation of the model and the interpretation of its parameters. In this arti...

This paper studies the response to the compound doubly stochastic Poisson process which is called filtered CDSPP. The characteristic functional is given and therefore is possible to derive several statistics very difficult to obtain by other methods, as the m-dimensional distribution of the process or the mean, variance and covariance.

This paper deals with the doubly stochastic Poisson process (DSPP) with mean a truncated Gaussian distribution at any instant of time. The expression of its probability mass function is derived in this paper and it is also proved that the value of the process with maximum probability can be found in a known bounded interval. Furthermore, this paper...

This paper introduces an improvement on the forecasting models previously developed by the authors for continuous time series based on the PCA of the stochastic process by cutting series in seasonal periods. The new approach consists of modelling principal components as ARIMA processes and then to formulate a mixed PC-ARIMA model for the time serie...

An estimator for the intensity process of a doubly stochastic Poisson process is presented, having no statistical previous knowledge of it. In order to give a statistical structure of the intensity, a functional Principal Components Analysis is applied to/c estimated sample paths of the intensity built from/c observed sample paths of the point proc...

In this paper, we present a methodology to model the number of domestic car registrations in European countries by a doubly stochastic Poisson process which mean is a truncated Normal variable. On the basis of previous work about this statistical model, we extend the study of its moments. Also, we forecast the mentioned real process for 2000 and 20...

En este artículo presentamos una modelización para la matriculación de vehículos en países de Europa mediante un proceso de Poisson Doblemente Estocástico con media aleatoria Normal truncada. Apoyándonos en trabajos previos acerca de este proceso, se amplía el estudio de características de éste. Asímismo, se hace una predicción de este proceso para...

The objective of this paper is to develop an extension of principal component regression for multiple logistic regression with continuous covariates. A practical application with simulated data will be included where the accuracy of the proposed principal component logistic regression model will be evaluated starting from the estimated parameters a...

The functional principal components analysis (PCA) involves new considerations on the mechanism of measuring distances (the norm). Some properties arising in functional framework (e.g., smoothing) could be taken into account through an inner product in the data space. But this proposed inner product could make, for example, interpretational or (and...

The objective of this paper is to apply functional principal component analysis to model and forecast "nancial prices of the banking in Madrid Stock Market from weekly observations of a random sample of banks. It is well known that direct statistical analysis of stock prices is di$cult, therefore principal component prediction models for weekly ret...

The objective of this paper is to apply functional principal component analysis to model and forecast financial prices of the banking in Madrid Stock Market from weekly observations of a random sample of banks. It is well known that direct statistical analysis of stock prices is difficult, therefore principal component prediction models for weekly...

In this paper a functional principal component model is applied to forecast a continuous time series that has been observed only at discrete time points not necessarily equally spaced. To take into account the natural order among the sample paths obtained after cutting the series into pieces, a weighted estimation of the principal components is pro...

A method for exploring the structure of populations of complex objects, such as images, is considered. The objects are summarized by feature vectors. The statistical backbone is Principal Component Analysis in the space of feature vectors. Visual insights come from representing the results in the original data space. In an ophthalmological example,...

The Principal Component Regression model of multiple responses is extended to forccast a continuous-time stochastic process. Orthogonal projection on a subspace of trigonometric functions is applied in order to estimate the principal components using discrete-time observations from a sample of regular curves. The forecasts provided by this approach...

The aim of this paper is to approximate the estimates in the principal component analysis of a continuous time stochastic process (functional PCA) by using wavelet methods. A short review of estimating in the functional PCA leads to the problem of solving the integral equation with the covariance function as kernel. An estimating procedure based on...

On the basis of functional principal components analysis (FPCA), two forecasting approaches for time series are developed. The first one uses weighted multiple linear regression among principal components whereas the second one applies Kalman filtering on approximate state-space models. The forecasting performance of both methods is discussed on a...

In this paper, a linear model for forecasting a continuous-time stochastic process in a future interval in terms of its evolution in a past interval is developed. This model is based on linear regression of the principal components in the future against the principal components in the past. In order to approximate the principal factors from discret...

A sufficient condition for a random vector to be Gaussian is formulated by applying Skitovich's theorem to the principal component analysis of the random vector. An application to a standard Brownian motion simulated in discrete times, and a simulation study on non-normal data are also included.

The objective of this paper is to estimate the principal factors of a continuous time real valued process when we have a collection of independent sample functions which are observed only at discrete time points. We propose to approximate the Principal Component Analysis (PCA) of the process, when the sample functions are regular, by means of the P...

El ACP de un número finito de variables puede ser generalizado para manejar datos que evolucionan en el tiempo. El objetivo de este trabajo es la estimación de los factores principales de procesos aleatorios con funciones muestrales escalonadas. Ante la imposibilidad de obtener una solución exacta a este problema, proponemos estimar el ACP de un pr...

In many real life situations information about a continuous time series is given by discrete-time observations not always evenly spaced. Our purpose is to develop a forecasting model for such a time series avoiding some of the restrictive hypotheses imposed by classical approaches. If the original series x(t) is cut in periods of amplitude h (h > 0...

After performing a review of the classical procedures for estimation in the principal component analysis (PCA) of a second order stochastic process, two alternative procedures have been developed to approach such estimates. The first is based on the orthogonal projection method and uses cubic interpolating splines when the data are discrete. The se...

The distribution of expenses generated by foreign students of the University of Granada in subjects such as maintenance, idleness, etc., is analyzed in this paper, depending upon the residence form in the town. Likewise, the economic incidence of this group in Granada is also discussed.

Over the last few years many methods have been developed for analyzing functional data with different objectives. The purpose of this paper is to predict a binary response variable in terms of a functional variable whose sample information is given by a set of curves measured without error. In order to solve this problem we formulate a functional l...

Currently, most universities offer a wide range of online courses which are taught on the web through a virtual learning environment such as Moodle. The goal of virtual teaching is to provide access to those people who would not be able to attend a physical campus, for reasons such as distance and flexibility. In virtual education, the protagonist...