Juan M Vilar

University of A Coruña | UDC · Department of Mathematics

In this paper, an estimator of the probability of default (PD) in credit risk is proposed. It is derived from a nonparametric conditional survival function estimator based on cure models. Asymptotic expressions for the bias and the variance, as well as the asymptotic normality of the proposed estimator are presented. A simulation study shows the pe...

The survival function of length-of-stay in hospital ward and ICU for COVID-19 patients is studied in this paper. Flexible statistical methods are used to estimate this survival function given relevant covariates such as age, sex, obesity and chronic obstructive pulmonary disease (COPD). A doubly-smoothed Beran’s estimator has been considered to thi...

In this paper, a conditional survival function estimator for censored data is studied. It is based on a double smoothing technique: both the covariate and the variable of interest (usually, the time) are smoothed. Asymptotic expressions for the bias and the variance and the asymptotic normality of the smoothed survival estimator derived from Beran'...

For a fixed time, t, and a horizon time, b, the probability of default (PD) measures the probability that an obligor, that has paid his/her credit until time t, runs into arrears not later that time t+b. This probability is one of the most crucial elements that influences the risk in credits. Previous works have proposed nonparametric estimators fo...

This work proposes a resampling technique to approximate the smoothing parameter of Beran’s estimator. It is based on resampling by the smoothed bootstrap and minimising the bootstrap approximation of the mean integrated squared error to find the bootstrap bandwidth. The behaviour of this method has been tested by simulation on several models. Boot...

The authors would like to correct the errors in the publication of the original article.

In this work a doubly smoothed probability of default (PD) estimator is proposed based on a smoothed version of the survival Beran’s estimator. The asymptotic properties of both the smoothed survival and PD estimators are proved and their behaviour is analyzed by simulation. The results allow us to conclude that the time variable smoothing reduce t...

In this paper, four nonparametric estimators of the probability of default in credit risk are proposed and compared. They are derived from estimators of the conditional survival function for censored data. Asymptotic expressions for the bias and the variance of these probability of default estimators are derived from similar properties for the cond...

A Responsabilidade Social da Empresa (RSE), tamén denominada Responsabilidade Social Corporativa (RSC), formúlase como un factor estratéxico clave na xestión. O obxecto deste traballo é analizar as relacións existentes entre os principios de RSE e a rendibilidade das empresas do sector da construción en Galicia. Para iso realízase unha revisión do...

Purpose: Lumbago, or low back pain (LBP), is a common musculoskeletal complaint among older adults that may also be associated with depression. The study objective was to investigate differences in Beck Depression Inventory depression symptoms scores among older adult patients with and without LBP. Design: This was a case-control study. Methods...

This research applied accelerated bridge construction techniques to the Northern Mexico City Elevated Urban Toll Road. To this end, an 18-m precast combined pile-cap and column element was monitored during production. The recorded high internal temperatures raised concerns, which led to the extraction and testing of concrete cores, yielding satisfa...

Background: Variations in the foot structure related with the high or low arch are identified common lower limb conditions, and it is supposed to be the effect on the quality of life (QoL) associated to foot health in adults. Here we aimed to determine the relationships between relatively high and low feet arches and QoL. Methods: A cross-sectio...

A research project was performed to characterize both the setting and hardening of three high-strength self-consolidating concrete mixes used in the production of precast combined pile-cap and column footings (column footings) of the Elevated Highways in Mexico City. By monitoring an eighteen-meter-high column footing during its production, the wid...

This paper provides two procedures to obtain prediction intervals for electricity demand and price based on functional data. The proposed procedures are related to one day ahead pointwise forecast. In particular, the first method uses a nonparametric autoregressive model and the second one uses a partial linear semi-parametric model, in which exoge...

This paper presents an application of functional additive models in the context of electricity demand and price prediction. Data from the Spanish Electricity Market are used to obtain the pointwise predictions. Also prediction intervals, based on a bootstrap procedure, are computed. This approach is compared with the use of other functional regress...

The Bristol Foot Score is considered an instrument for measuring the impact of foot problems and pain. It was developed and validated in United Kingdom. Therefore, this aim was to perform the transcultural adaptation and validation of the Spanish version. The recommended forward/backward translation protocol was applied for the procedure of transla...

This paper deals with the semi-functional partial linear regression model \(Y={{\varvec{X}}}^\mathrm{T}{\varvec{\beta }}+m({\varvec{\chi }})+\varepsilon \) under \(\alpha \)-mixing conditions. \({\varvec{\beta }} \in \mathbb {R}^{p}\) and \(m(\cdot )\) denote an unknown vector and an unknown smooth real-valued operator, respectively. The covariates...

Background: Low back pain (LBP) is the most common musculoskeletal disorder affecting the general population and it is believed to be associated with depression. Objective: The study aim was to describe and compare the impact in a sample of people with subacute LBP (SLBP) and patients without LBP with normalized reference values in the light of...

Semi-functional partial linear regression model allows to deal with a nonparametric and a linear component within the functional regression. Naïve and wild bootstrap procedures are proposed to approximate the distribution of the estimators for each component in the model, and their asymptotic validities are obtained in the context of dependence dat...

Reading predictors directly contribute to reading accuracy and speed. This study analyses the effect of an instructional programme aimed at improving two of these reading predictors, phonological awareness and naming speed. Participants were 326 children (171 in the experimental group and 155 in the control group) in grades second and third year pr...

Background and purpose Nonspecific low back pain (LBP) is the most prevalent musculoskeletal condition in various age ranges and is associated with depression. The aim of this study was to determine the Beck Depression Inventory (BDI) scores in participants with nonspecific LBP and no-pain by age distribution. Methods A case–control study was carr...

The aim of our study was to evaluate the efficacy and safety of topical cantharidin-podophylotoxin-salicylic acid (CPS) treatment of recalcitrant plantar warts (RPW). This study was carried out in a health center in the city of A Coruña (Spain) between January and December 2013. A total of 75 patients completed all the stages of the research proces...

Hallux valgus (HV) is a highly-prevalent forefoot deformity associated with progressive subluxation and osteoarthritis of the first metatarsophalangeal joint; it is believed to be associated with depression. The aim of the present study was to determine the association of patients with varying degrees of HV involvement to depression using the Beck...

This paper considers naive and wild bootstrap procedures to construct pointwise confidence intervals for a nonparametric regression function when the predictor is of functional nature and when the data are dependent. Assuming α-mixing conditions on the sample, the asymptotic validity of both procedures is obtained. A simulation study shows promisin...

This study proposes two methods for detecting outliers in functional time series. Both methods take dependence in the data into account and are based on robust functional principal component analysis. One method seeks outliers in the series of projections on the first principal component. The other obtains uncontaminated forecasts for each data set...

A functional depth measures the “centrality” of a functional datum (a function observed over a continuum, for example, a curve, an image) with respect to a given functional dataset. This paper proposes a way to detect outliers in functional time series based on functional depth. Ideally, the depth of a functional outlier should be very low but, whe...

El objetivo de este estudio fue analizar el efecto que la intervención conciencia fonológica y velocidad de denominación tiene sobre el aprendizaje de la escritura. Los participantes fueron 271 alumnos, 138 del grupo experimental y 133 del control. Los alumnos del grupo experimental recibieron instrucción en conciencia fonológica y en velocidad de...

A new time series clustering method based on comparing forecast densities for a sequence of $k>1$ consecutive horizons is proposed. The unknown $k$-dimensional forecast densities can be non-parametrically approximated by using bootstrap procedures that mimic the generating processes without parametric restrictions. However, the difficulty of constr...

This paper deals with the prediction of residual demand curves in electricity spot markets, as a tool for optimizing bidding strategies in the short-term. Two functional models are formulated and empirically compared with the naïve method, which is the reference model in most of the practical applications found in industry. The first one is a funct...

Generalised variance function (GVF) models are data analysis techniques often used in large-scale sample surveys to approximate the design variance of point estimators for population means and proportions. Some potential advantages of the GVF approach include operational simplicity, more stable sampling errors estimates and providing a convenient m...

One-day-ahead forecasting of electricity demand and price is an important issue in competitive electric power markets. These problems have been studied in previous works using, for instance, ARIMA models, dynamic regression and neural networks. This paper provides two new methods to address these two prediction setups. They are based on using nonpa...

A bootstrap procedure for testing the equality of several regression curves under dependence conditions is proposed. The errors are assumed to follow different ARMA structures. A test statistic based on the functional distances between nonparametric estimators of the regression functions is considered. The critical test values are obtained using a...

The problem of prediction in time series using nonparametric functional techniques is considered. An extension of the local linear method to regression with functional explanatory variable is proposed. This forecasting method is compared with the functional Nadaraya–Watson method and with finite-dimensional nonparametric predictors for several real...

The problem of residual demand prediction in electricity spot markets is considered in this paper. Hourly residual demand The problem of residual demand prediction in electricity spot markets is considered in this paper. Hourly residual demand curves are predicted using nonparametric regressionwith functional explanatory and functional response var...

This paper describes a Bayesian approach to make inference for aggregate loss models in the insurance framework. A semiparametric model based on Coxian distributions is proposed for the approximation of both the interarrival time between claims and the claim size distributions. A Bayesian density estimation approach for the Coxian distribution is i...

The problem of clustering time series is studied for a general class of non-parametric autoregressive models. The dissimilarity between two time series is based on comparing their full forecast densities at a given horizon. In particular, two functional distances are considered: L1 and L2. As the forecast densities are unknown, they are approximate...

In this paper, a fixed design regression model where the errors follow a strictly stationary process is considered. In this model the conditional mean function and the conditional variance function are unknown curves. Correlated errors when observations are missing in the response variable are assumed. Four nonparametric estimators of the condition...

Credit risk models are used by financial companies to evaluate in advance the insolvency risk caused by credits that enter into default. Many models for credit risk have been developed over the past few decades. In this paper, we focus on those models that can be formulated in terms of the probability of default by using survival analysis technique...

A general nonparametric approach to identify similarities in a set of simultaneously observed time series is proposed. The trends are estimated via local polynomial regression and classified according to standard clustering procedures. The equality of the trends is checked using several nonparametric test statistics whose asymptotic distributions a...

The problem of semiparametric modelling in time series is considered. For this, partial linear regression models are used, that is, regression models where the regression func- tion is the sum of a linear and a nonparametric component. Two estimators for the nonparametric component are shown: one estimator takes into account the depend- ence struct...

This paper describes a nonparametric approach to make inferences for aggregate loss models in the insurance framework. We assume that an insurance company provides a historical sample of claims given by claim occurrence times and claim sizes. Furthermore, information may be incomplete as claims may be censored and/or truncated. In this context, the...

The main objective of this work is the nonparametric estimation of the regression function with correlated errors when observations are missing in the response variable. Two nonparametric estimators of the regression function are proposed. The asymptotic properties of these estimators are studied; expresions for the bias and the variance are obtain...

In this paper, two new tests for heteroscedasticity in nonparametric regression are presented and compared. The first of these tests consists in first estimating nonparametrically the unknown conditional variance function and then using a classical least-squares test for a general linear model to test whether this function is a constant. The second...

Credit risk models are used by financial companies to evaluate in advance the insolvency risk caused by credits that enter into default. Many models for credit risk have been developed over the past few decades. In this paper, we focus on those models that can be formulated in terms of the probability of default by using survival analysis technique...

A regression model whose regression function is the sum of a linear and a nonparametric component is presented. The design is random and the response and explanatory variables satisfy mixing conditions. A new local polynomial type estimator for the nonparametric component of the model is proposed and its asymptotic normality is obtained. Specifical...

The problem of predicting a future value of a time series is considered in this article. If the series follows a stationary Markov process, this can be done by nonparametric estimation of the autoregression function. Two forecasting algorithms are introduced. They only differ in the nonparametric kernel-type estimator used: the Nadaraya-Watson esti...

In this paper, the problem of testing the equality of regression curves with dependent data is studied. Several methods based on nonparametric estimators of the regression function are described. In this setting, the distribution of the test statistic is frequently unknown or difficult to compute, so an approximate test based on the asymptotic dist...

We consider a fixed regression model where the errors are a strictly stationary process and in which both functions, the conditional mean and the conditional variance (volatility), are unknown. Two nonparamerric estimators of the volatility function based on local polynomial fitting are studied. Expressions of the asymptotic bias and variance are g...

Este trabajo desarrolla un modelo teórico que relaciona el margen de beneficio de las entidades financieras con variables estratégicas clave relativas a su tamaño y variables que hacen referencia próxima a los servicios ofrecidos. La importancia del sector bancario en nuestra economía, las modificaciones del sistema financiero y la importancia y el...

This work develops a theoric model that connects the banks and saving banks profit's margin with strategic variables relative with its size and its services offered. The importance of bank sector in our economy and the specific weight of saving banks in it define our basic goal related with tha elaborated model: the verification of posible differen...

Seven of the most popular methods for bandwidth selection in regression estimation are compared by means of a thorough simulation study, when the local polynomial estimator is used and the observations are dependent. The study is completed with two plug-in bandwidths for the generalized local polynomial estimator proposed by Vilar-Fernândez & Franc...

Suppose that data {(x l,i,n , y l,i,n ): l = 1, …, k; i = 1, …, n} are observed from the regression models: Y l,i,n  = m l (x l,i,n ) + ϵ l,i,n , l = 1, …, k, where the regression functions {m l } l=1 k are unknown and the random errors {ϵ l,i,n } are dependent, following an MA(∞) structure. A new test is proposed for testing the hypothesis H 0: m...

This paper presents an overview of the existing literature on the nonparametric local polynomial (LPR) estimator of the regression function and its derivatives when the observations are dependent. When the errors of the regression model are correlated and follow an ARMA process, Vilar-Fernández and Francisco-Fernández (2002) proposed a modification...

Consider the fixed regression model where the error random variables are coming from a strictly stationary, non-white noise stochastic process. In a situation like this, automated bandwidth selection methods for nonparametric regression break down. We present a plug-in method for choosing the smoothing parameter for local least squares estimators o...

In this article, nonparametric estimators of the regression function, and its derivatives, obtained by means of weighted local polynomial fitting are studied. Consider the fixed regression model where the error random variables are coming from a stationary stochastic process satisfying a mixing condition. Uniform strong consistency, along with rate...

The linear regression model Yi=xiθ+εi, where is an unknown parameter vector and the observational errors εi follow an AR(1) model, is considered. In a previous paper, Vilar-Fernández and González-Manteiga (Statist. Papers, to appear) have proposed a two-stage generalized minimum distance estimator (GMD) for θ, which presents the same asymptotic pro...

Consider the fixed regression model with random observation error that follows an AR(1) correlation structure. In this paper, we study the nonparametric estimation of the regression function and its derivatives using a modified version of estimators obtained by weighted local polynomial fitting. The asymptotic properties of the proposed estimators...

In this paper we study a special class of minimum distance estimators, based on nonparametric pilot estimators of the regression function, for a parameter θ ∈ Θ ⊂ R p of a linear regression model of the type Y = Xθ + ε, where X is the design matrix, Y the vector of the response variable and ε the random error vector that follows an AR(1) correlatio...

In this paper, we study the nonparametric estimation of the regression function and its derivatives using weighted local polynomial fitting. Consider the fixed regression model and suppose that the random observation error is coming from a strictly stationary stochastic process. Expressions for the bias and the variance array of the estimators of t...

For broad classes of deterministic and random sampling schemes {[tau]k}, exact mean integrated squared error (MISE) expressions for the kernel estimator of the marginal density of a first-order continuous-time autoregressive process are derived. The obtained expressions show that the effect on MISE due to both the sampling scheme and the sampling r...

Let us consider the fixed regression model, and assume that the random errors, {εt}, follow an ARMA-type dependence structure. The purpose of this paper is to study the application of the bootstrap test to check that the unknown regression function, m, follows a general linear model of the type:with A being a functional of in . In a previous paper,...

In the case of the random design nonparametric regression, one recursive local polynomial smoother is considered. Expressions for the bias and the variance matrix of the estimators of the regression function and its derivatives are obtained under dependence conditions (strongly mixing processes). The obtained Mean Squared Error is shown to be large...

The recursive estimation of the regression function m(x) = E(Y/X = x) and its derivatives is studied under dependence conditions. The examined method of nonparametric estimation is a recursive version of the estimator based on locally weighted polynomial fitting, that in recent articles has proved to be an attractive technique and has advantages ov...

Given the regression model Yi = m(xi) +εi (xi ε C, i = l,…,n, C a compact set in R) where m is unknown and the random errors {εi} present an ARMA structure, we design a bootstrap method for testing the hypothesis that the regression function follows a general linear model: Ho : m ε {mθ(.) = A(.)θ : θ ε ⊝ ⊂ R} with A a functional from R to R. The cr...

Given the regression model Yi = m(xi) + εi, (xiϵC, i = 1, …, n, C a compact set in R), where m is unknown and the random errors {εi} have an MA (∞) structure, we designed a method for testing the hypothesis that the regression function follows a general linear model: with A a functional from R to Rq. The criterion of the test derives from a Crámer-...

Dado el siguiente modelo de regresión de diseño fijo, con correlación serial en los errores: Yi = m(xi) + ei, donde xi Î C, i = 1,..., n, siendo C un conjunto compacto de R, con error aleatorio ei siguiendo una estructura lineal de tipo MA(8), se propone un nuevo método para contrastar la hipótesis de que la función de regresión siga un modelo line...

Summary The problem addressed is that of smoothing parameter selection in kernel density estimation with dependent data (strong mixing), using local criteria. The method proposed is an adaptation of the traditional technique of least squares cross-validation and it generalizes the algorithm developed by Mielniczuket al. (1989), when independence is...

Se define un estimador no paramétrico, recursivo, de la función de regresiónr(x)=E(Y/X=x), que se calcula a partir de un conjunto den observaciones {(X 1,Y i ):i=1,…n} del vector aleatorio (X, Y). Bajo la hipótesis de que los datos son idénticamente distribuidos pero no necesariamente independientes, lo que permite utilizar el estimador definido pa...

Sea X una variable aleatoria con función de distribución F(x) y función de densidad f(x) y X1, X2,..., Xn un conjunto de observaciones de la variable que pueden ser dependientes. Se definen dos estimadores no paramétricos generales (uno recursivo y el otro no recursivo) de la función de distribución. Bajo condiciones aceptables se obtiene el sesgo...

Se estudian modificaciones de las técnicas de validación cruzada de Kullback-Leibler y mínimos cuadrados para obtener el parámetro de suavización asociado a un estimador general no paramétrico de la función de densidad, a partir de la muestra, en el supuesto de que los datos verifican alguna condición débil de dependencia. Se demuestra que los pará...

Let be {X t :t∈Z} a stationary valued in ℝp time series, verifiying the condition α-mixing orL 2-stability. Since a sample of sizen is defined a general class of non-parametric estimators of the density functionf(x) asociated to the process and of the autoregression function in orderk:\(r(\bar y) = E(g(X_{t - k + 1} \ldots X_t ) = \bar y)), \bar y...

Let be{X t}t∈Z+ one stationary time serie that follows the model:X t=λ+⌕Xt−1+et, where {e t} is a sucession of independent and identifically distributed random variables with expectation zero and variance σ2. With an initial sample {X 1,...,Xn} of the process we obtain in a first part nonparametric estimations:\(\hat \tau _n \) and\(\hat \Omega _n...

This article presents a new class of estimators for the parameters θt= (θ1,…,θq) of the stationary autoregressive model \({\text{AR }}\left( {\text{q}} \right),{{\text{x}}_{\text{t}}}{\text{ = }}\mathop \Sigma \limits_{{\text{i = 1}}}^{\text{q}} {{\text{0}}_{\text{i}}}{{\text{x}}_{{\text{t - i}}}}{\text{ + }}{\varepsilon _{\text{t}}},\) with \({\te...

A statistical analysis of the series recording the weekly price (per share in euros) of the banks in the Spanish stock market during 2001 and 2002 is performed by using only nonparametric procedures. The analysis consists in estimating, classifying and testing the equality of the trends and then, once the estimated trends have been removed from the...

The main objective of this work is the nonparametric estimation of the regression function with correlated errors when observations are missing in the response variable. Two nonparametric estimators of the regression function are proposed. The asymptotic properties of these estimators are studied; expresions for the bias and the variance are obtain...

Let X(t) be a stationary continuous-time process. The recursive estimation of the univariate probability distribution function, F(x), given discrete-time samples X(τ 1 ), X(τ 2 ),⋯,X(τ n ), with sampling instants τ i irregularly spaced or random (according to a renewal process), is studied for the process X(t) when the observations satisfy strong m...

Sea X(t) un proceso estacionario en tiempo continuo con función de densidad marginal univariante f(x). A partir de un conjunto de n observaciones; X(t1), X(t2), ..., X(tn) recogidas en instantes muestrales ti, espaciados irregularmente o aletorios, se estudia la estimación no paramétrica de f(x), utilizando un estimador recursivo tipo núcleo. Asumi...