Testing for Concordance Ordering

We propose inference tools to analyse the concordance (or correlation) order of random vectors. The analysis in the bivariate case relies on tests for upper and lower quadrant dominance of the true distribution by a parametric or semiparametric model, i.e. for a parametric or semiparametric model to give a probability that two variables are simultaneously small or large at least as great as it would be were they left unspecified. Tests for its generalisation in higher dimensions, namely joint lower and upper orthant dominance, are also analysed. The parametric and semiparametric settings are based on the copula representation for multivariate distribution, which allows for disentangling behaviour of margins and dependence structure. A distance test and an intersection-union test for inequality constraints are developed depending on the definition of null and alternative hypotheses. An empirical illustration is given for US insurance claim dat

RecordTest: An R Package to Analyze Non-Stationarity in the Extremes Based on Record-Breaking Events

The study of non-stationary behavior in the extremes is important to analyze data in environmental sciences, climate, finance, or sports. As an alternative to the classical extreme value theory, this analysis can be based on the study of record-breaking events. The R package RecordTest provides a useful framework for non-parametric analysis of non-stationary behavior in the extremes, based on the analysis of records. The underlying idea of all the non-parametric tools implemented in the package is to use the distribution of the record occurrence under series of independent and identically distributed continuous random variables, to analyze if the observed records are compatible with that behavior. Two families of tests are implemented. The first only requires the record times of the series, while the second includes more powerful tests that join the information from different types of records: upper and lower records in the forward and backward series. The package also offers functions that cover all the steps in this type of analysis such as data preparation, identification of the records, exploratory analysis, and complementary graphical tools. The applicability of the package is illustrated with the analysis of the effect of global warming on the extremes of the daily maximum temperature series in Zaragoza, Spain

Statistical analysis of extreme and record-breaking daily maximum temperatures in peninsular Spain during 1960–2021

This work analyses the effects of global warming in the upper extremes of daily temperature series over Spain. This objective implies specific analysis, since time evolution of mean temperature is not always parallel to evolution of the extremes. We propose the use of several record tests to study the behavior of the extreme and record-breaking events in different temperature signals, at different time and spatial scales. The underlying idea of the tests is to compare the occurrence of the extreme events in the observed series and the occurrence in a stationary climate. Given that under global warming, an increasing trend, or an increasing variability, can be expected, the alternative is that the probability of the extremes is higher than in a stationary climate. Some of the tests, based on a permutation approach, can be applied to sets of correlated series and this allows the analysis of short periods of time and regional analysis, where series are measured in close days and/or locations. Using these tests, we evaluate and compare the effects of climate change in temperature extreme and record-breaking events using 36 series of daily maximum temperature from 1960 to 2021, all over peninsular Spain. We also compare the behavior in different Spanish regions, in different periods of the year, and in different signals such as the annual maximum temperature. Significant evidences of the effect of an increasing trend in the occurrence of upper extremes are found in most of Spain. The effects are heterogeneous within the year, being autumn the season where the effects are weaker and summer where they are stronger. Concerning the spatial variability, the Mediterranean and the North Atlantic region are the areas where the effects are more and less clear, respectively

Record tests to detect non-stationarity in the tails with an application to climate change

The analysis of trends and other non-stationary behaviours at the extremes of a series is an important problem in global warming. This work proposes and compares several statistical tools to analyse that behaviour, using the properties of the occurrence of records in i.i.d. series. The main difficulty of this problem is the scarcity of information in the tails, so it is important to obtain all the possible evidence from the available data. First, different statistics based on upper records are proposed, and the most powerful is selected. Then, using that statistic, several approaches to join the information of four types of records, upper and lower records of forward and backward series, are suggested. It is found that these joint tests are clearly more powerful. The suggested tests are specifically useful in analysing the effect of global warming in the extremes, for example, of daily temperature. They have a high power to detect weak trends and can be widely applied since they are non-parametric. The proposed statistics join the information of M independent series, which is useful given the necessary split of the series to arrange the data. This arrangement solves the usual problems of climate series (seasonality and serial correlation) and provides more series to find evidence. These tools are used to analyse the effect of global warming on the extremes of daily temperature in Madrid

Distribución de la sequía más severa en un intervalo de tiempo dado

Ponencia presentada en: III Congreso de la Asociación Española de Climatología “El agua y el clima”, celebrado en Palma de Mallorca del 16 al 19 de junio de 2002.[ES]El objetivo de este trabajo es caracterizar la máxima sequía que cabe esperar en un determinado periodo de tiempo. Para ello es necesario disponer de un modelo estocástico que describa el proceso de sequias (proponemos un proceso Poisson cluster para describir la ocurrencia y tres series de variables aleatorias, Longitud, Déficit e Intensidad Máxima, para describir la severidad) y desarrollar los resultados teóricos necesarios sobre la distribución del máximo en una muestra de tamaño Poisson.[EN]This work aims to characterize the largest drought event to occur in a given period of time. A Poisson cluster process is used to model drought occurrence and three series of random variables (Length, Deficit and Maximum Intensity) to describe their severity. Some theoretical results on the distribution of the maximum in a random Poisson size sample are developed for describing the largest drought events

Bayesian variable selection in generalized extreme value regression: modeling annual maximum temperature

In many applications, interest focuses on assessing relationships between covariates and the extremes of the distribution of a continuous response. For example, in climate studies, a usual approach to assess climate change has been based on the analysis of annual maximum data. Using the generalized extreme value (GEV) distribution, we can model trends in the annual maximum temperature using the high number of available atmospheric covariates. However, there is typically uncertainty in which of the many candidate covariates should be included. Bayesian methods for variable selection are very useful to identify important covariates. However, such methods are currently very limited for moderately high dimensional variable selection in GEV regression. We propose a Bayesian method for variable selection based on a stochastic search variable selection (SSVS) algorithm proposed for posterior computation. The method is applied to the selection of atmospheric covariates in annual maximum temperature series in three Spanish stations

Nuevas técnicas de regresión: métodos de regularización y otros

El trabajo de fin de grado que se presenta a continuación lleva el título de "Nuevas técnicas de regresión: métodos de regularización". Los métodos estadísticos clásicos, como la regresión por mínimos cuadrados, fueron pensados para ser utilizados con cantidades relativamente pequeñas de datos. Sin embargo, en la actualidad es posible el acceso a una considerable cantidad de datos. La universalización de las páginas web, redes sociales, dispositivos móviles y otros usos hace que la cantidad de datos recopilados y almacenados no deje de crecer, por lo que la tarea de analizarlos se vuelve cada vez más complicada. Por ello es necesario desarrollar nuevas técnicas estadísticas como los métodos de regularización. En este trabajo explicaremos estas nuevas metodologías, aplicadas a modelos lineales y extendidas a modelos lineales generalizados. A través de los métodos explicados en el trabajo aplicados a un modelo de regresión logística se modelizará el ingreso en los hospitales de los infectados por Covid-19 y se determinará cuáles son los factores más influyentes para la necesidad de dicho ingreso.<br /

Model-based tools for assessing space and time change in daily maximum temperature: an application to the Ebro basin in Spain

There is continuing interest in the investigation of change in temperature over space and time. We offer a set of tools to illuminate such change temporally, at desired temporal resolution, and spatially, according to region of interest, using data generated from suitable space-time models. These tools include predictive spatial probability surfaces and spatial extents for an event. Working with exceedance events around the center of the temperature distribution, the probability surfaces capture the spatial variation in the risk of an exceedance event, while the spatial extents capture the expected proportion of incidence of a given exceedance event for a region of interest. Importantly, the proposed tools can be used with the output from any suitable model fitted to any set of spatially referenced time series data. As an illustration, we employ a dataset from 1956 to 2015 collected at 18 stations over Arag\'{o}n in Spain, and a collection of daily maximum temperature series obtained from posterior predictive simulation of a Bayesian hierarchical daily temperature model. The results for the summer period show that although there is an increasing risk in all the events used to quantify the effects of climate change, it is not spatially homogeneous, with the largest increase arising in the center of Ebro valley and Eastern Pyrenees area. The risk of an increase of the average temperature between 1966-1975 and 2006-2015 higher than $1^\circ$C is higher than 0.5 all over the region, and close to 1 in the previous areas. The extent of daily temperature higher than the reference mean has increased 3.5% per decade. The mean of the extent indicates that 95% of the area under study has suffered a positive increment of the average temperature, and almost 70% higher than $1^{\circ}$C.Comment: 23 pages main manuscript and 7 pages supplemen

Spatial quantile autoregression for season within year daily maximum temperature data

Regression is the most widely used modeling tool in statistics. Quantile regression offers a strategy for enhancing the regression picture beyond customary mean regression. With time-series data, we move to quantile autoregression and, finally, with spatially referenced time series, we move to space-time quantile regression. Here, we are concerned with the spatiotemporal evolution of daily maximum temperature, particularly with regard to extreme heat. Our motivating data set is 60 years of daily summer maximum temperature data over Aragón in Spain. Hence, we work with time on two scales—days within summer season across years—collected at geocoded station locations. For a specified quantile, we fit a very flexible, mixed-effects autoregressive model, introducing four spatial processes. We work with asymmetric Laplace errors to take advantage of the available conditional Gaussian representation for these distributions. Further, while the autoregressive model yields conditional quantiles, we demonstrate how to extract marginal quantiles with the asymmetric Laplace specification. Thus, we are able to interpolate quantiles for any days within years across our study region

Desarrollo de modelos estocásticos para la proyección de la ocurrencia de extremos: Aplicación a extremos de temperatura

Presentamos la modelización del proceso de ocurrencias de extremos de temperatura enlas series de máximas y mínimas diarias del Balneario de Panticosa. Se propone un procesoCPSP, que equivale a la estimación de tres procesos de Poisson No Homogéneos independientes.Estudiamos su evolución en el tiempo y dependencia con algunos predictores de temperatura. Seestablecen diferentes herramientas que validan nuestro modelo como una aproximación correctaa los datos disponibles. Este modelo se presenta finalmente como una herramienta útil para lareducción de escala temporal de proyecciones de temperatura. Se obtienen estimaciones de laintensidad del proceso para el siglo XXI a partir de las trayectorias de modelos climáticos globalespara diferentes escenarios de cambio climático, observando un incremento del número medio deextremos bajo todos los escenarios, más acentuado en la serie de temperaturas máximas.<br /