En los meses previos al dia de las elecciones, es una practica usual que diversos actores politic... more En los meses previos al dia de las elecciones, es una practica usual que diversos actores politicos y ciudadanos soliciten la realizacion de cierto tipo de estudios con el proposito de conocer con anticipacion como van perfilandose las preferencias electorales. Antes del dia de la eleccion es posible recurrir a diversos tipos de encuestas consistentes en preguntar a un subconjunto (muestra) de los posibles votantes cual es su preferencia electoral, realizar un analisis estadistico de la informacion recabada y hacer inferencias sobre el posible resultado de la eleccion. El dia de la eleccion tambien es posible recurrir a otro tipo de ejercicios para inferir el resultado de la misma, antes de que se conozca el resultado del recuento total de votos emitidos varios dias despues: la encuesta de salida y el conteo rapido. En Mexico y algunos otros paises es comun que empresas encuestadoras, politicos, analistas y hasta autoridades electorales hablen de que en un momento dado existe “empat...
Abstract Assessment of rock formation permeability is a complicated and chal-lenging problem that... more Abstract Assessment of rock formation permeability is a complicated and chal-lenging problem that plays a key role in oil reservoir modeling, production forecast, and the optimal exploitation management. Generally, permeability evaluation is per-formed using ...
Se presenta una introduccion a conceptos y resultados basicos sobre copulas, y su utilidad par... more Se presenta una introduccion a conceptos y resultados basicos sobre copulas, y su utilidad para estudiar y medir dependencia de variables aleatorias, como consecuencia del Teorema de Sklar (1959).
Se realiza un análisis estad́ıstico de las estimaciones del conteo rápido institucional desde la ... more Se realiza un análisis estad́ıstico de las estimaciones del conteo rápido institucional desde la perspectiva ideal de los resultados de los cómputos distritales de la elección de gobernador del Estado de México del año 2017, particularmente aspectos como la precisión de las estimaciones, el nivel de confianza de los intervalos, el posible sesgo respecto al cómputo distrital y las conclusiones que se derivaron y reportaron, con el objetivo de determinar el grado de cumplimiento de los objetivos de este ejercicio estad́ıstico de carácter informativo.
It is argued that the concept of "technical tie" in electoral polls and quick counts ha... more It is argued that the concept of "technical tie" in electoral polls and quick counts has no probabilistic basis, and that instead the uncertainty associated with these statistical exercises should be expressed in terms of a probability of victory of the leading candidate. ----- Se argumenta que el concepto de "empate t\'ecnico" en encuestas y conteos r\'apidos electorales no tiene fundamento probabil\'istico, y que en su lugar la incertidumbre asociada a dichos ejercicios estad\'isticos debiera expresarse en t\'erminos de una probabilidad de triunfo del candidato puntero.
An electoral quick count is a statistical procedure whose main objective is to obtain a relativel... more An electoral quick count is a statistical procedure whose main objective is to obtain a relatively small but representative sample of all the polling stations in a certain election, and to measure the uncertainty about the final result before the total count of votes. A stratified sampling design is commonly preferred to reduce estimation variability. The present work shows that dependence among strata and among candidates should be taken into consideration for statistical inferences therein, and a copula based model is proposed and applied to Mexico's 2006, 2012, and 2018 presidential elections data.
A statistical analysis of an electoral quick count based on the total count of votes in the elect... more A statistical analysis of an electoral quick count based on the total count of votes in the election of the State of Mexico's governor in 2017 is performed in order to verify precision, confidence level of interval estimations, possible bias and derived conclusions therein, with the main purpose of checking compliance with the objectives of such statistical procedure. ----- Se realiza un an\'alisis estad\'istico de las estimaciones del conteo r\'apido institucional desde la perspectiva ideal de los resultados de los c\'omputos distritales de la elecci\'on de gobernador del Estado de M\'exico del a\~no 2017, particularmente aspectos como la precisi\'on de las estimaciones, el nivel de confianza de los intervalos, el posible sesgo respecto al c\'omputo distrital y las conclusiones que se derivaron y reportaron, con el objetivo de determinar el grado de cumplimiento de los objetivos de este ejercicio estad\'istico de car\'acter informativo.
Revista de Métodos Cuantitativos para la Economía y la Empresa, 2017
The so-called risk diversification principle is analyzed, showing that its convenience depends on... more The so-called risk diversification principle is analyzed, showing that its convenience depends on individual characteristics of the risks involved and the dependence relationship among them. ------------------------------------ Se analiza el principio de diversificacion de riesgos y se demuestra que no siempre resulta mejor que no diversificar, pues esto depende de caracteristicas individuales de los riesgos involucrados, asi como de la relacion de dependencia entre los mismos.
A statistical test based on the geometric mean is proposed to determine if a predictive model sho... more A statistical test based on the geometric mean is proposed to determine if a predictive model should be rejected or not, when the quantity of interest is a strictly positive continuous random variable. A simulation study is performed to compare test power performance against an alternative procedure, and an application to insurance claims reserving is illustrated.
In this brief note we prove that linear B-spline copulas is not a new family of copulas since the... more In this brief note we prove that linear B-spline copulas is not a new family of copulas since they are equivalent to checkerboard copulas, and discuss in particular how they are used to extend empirical subcopulas to copulas.
In this paper we analyze some properties of the discrete copulas in terms of permutations. We obs... more In this paper we analyze some properties of the discrete copulas in terms of permutations. We observe the connection between discrete copulas and the empirical copulas, and then we analyze a statistic that indicates when the discrete copula is symmetric and obtain its main statistical properties under independence. The results obtained are useful in designing a nonparametric test for symmetry of copulas.
The so-called risk diversification principle is analyzed, showing that its convenience depends on... more The so-called risk diversification principle is analyzed, showing that its convenience depends on individual characteristics of the risks involved and the dependence relationship among them. ----- Se analiza el principio de diversificaci\'on de riesgos y se demuestra que no siempre resulta mejor que no diversificar, pues esto depende de caracter\'isticas individuales de los riesgos involucrados, as\'i como de la relaci\'on de dependencia entre los mismos.
In petrophysics, assesment of formation permeability is a complex and challenging problem that pl... more In petrophysics, assesment of formation permeability is a complex and challenging problem that plays a key role in reservoir forecasts and optimal reservoir management. In heterogeneous carbonate reservoirs, permeability evaluation is commonly performed using permeability-porosity relationships, which often seem to be nonlinear and complex. Copulas are marginal-free dependence functions that may capture such nonlinear relationships. In the present work we make use of a nonparametric copula approach for bivariate modeling of permeability- porosity real data, and its application for a spatial median regression.
Abstract In many naturally fractured reservoirs, fractures play a crucial role in their flow and ... more Abstract In many naturally fractured reservoirs, fractures play a crucial role in their flow and transport properties. An approach that has recently gained popularity for modeling fracture systems is the Discrete Fracture Network (DFN) model. This approach consists in applying a stochastic boolean simulation method, also known as object simulation method, where fractures are represented as simplified geometric objects (line segments in 2D and polygons in 3D). One of the shortcomings of this approach is that it usually does not consider the dependence relationships that may exist between geometric properties of fractures (direction, length, aperture), that is, each property is simulated independently. In this work a method for modeling such dependencies by copula theory is introduced. In particular, a nonparametric model using Bernstein copulas for direction-length fracture dependency in 2D is presented. The application of this method is illustrated in an example which shows high agreement between data and simulation, both graphically and in its descriptive statistics, both marginally and jointly, and in the DFN as a whole.
In this paper we analyze some properties of the empirical diagonal and we obtain its exact distri... more In this paper we analyze some properties of the empirical diagonal and we obtain its exact distribution under independence for the two and three- dimensional cases, but the ideas proposed in this paper can be carried out to higher dimensions. The results obtained are useful in designing a nonparametric test for independence, and therefore giving solution to an open problem proposed by Alsina, Frank and Schweizer [2].
En los meses previos al dia de las elecciones, es una practica usual que diversos actores politic... more En los meses previos al dia de las elecciones, es una practica usual que diversos actores politicos y ciudadanos soliciten la realizacion de cierto tipo de estudios con el proposito de conocer con anticipacion como van perfilandose las preferencias electorales. Antes del dia de la eleccion es posible recurrir a diversos tipos de encuestas consistentes en preguntar a un subconjunto (muestra) de los posibles votantes cual es su preferencia electoral, realizar un analisis estadistico de la informacion recabada y hacer inferencias sobre el posible resultado de la eleccion. El dia de la eleccion tambien es posible recurrir a otro tipo de ejercicios para inferir el resultado de la misma, antes de que se conozca el resultado del recuento total de votos emitidos varios dias despues: la encuesta de salida y el conteo rapido. En Mexico y algunos otros paises es comun que empresas encuestadoras, politicos, analistas y hasta autoridades electorales hablen de que en un momento dado existe “empat...
Abstract Assessment of rock formation permeability is a complicated and chal-lenging problem that... more Abstract Assessment of rock formation permeability is a complicated and chal-lenging problem that plays a key role in oil reservoir modeling, production forecast, and the optimal exploitation management. Generally, permeability evaluation is per-formed using ...
Se presenta una introduccion a conceptos y resultados basicos sobre copulas, y su utilidad par... more Se presenta una introduccion a conceptos y resultados basicos sobre copulas, y su utilidad para estudiar y medir dependencia de variables aleatorias, como consecuencia del Teorema de Sklar (1959).
Se realiza un análisis estad́ıstico de las estimaciones del conteo rápido institucional desde la ... more Se realiza un análisis estad́ıstico de las estimaciones del conteo rápido institucional desde la perspectiva ideal de los resultados de los cómputos distritales de la elección de gobernador del Estado de México del año 2017, particularmente aspectos como la precisión de las estimaciones, el nivel de confianza de los intervalos, el posible sesgo respecto al cómputo distrital y las conclusiones que se derivaron y reportaron, con el objetivo de determinar el grado de cumplimiento de los objetivos de este ejercicio estad́ıstico de carácter informativo.
It is argued that the concept of "technical tie" in electoral polls and quick counts ha... more It is argued that the concept of "technical tie" in electoral polls and quick counts has no probabilistic basis, and that instead the uncertainty associated with these statistical exercises should be expressed in terms of a probability of victory of the leading candidate. ----- Se argumenta que el concepto de "empate t\'ecnico" en encuestas y conteos r\'apidos electorales no tiene fundamento probabil\'istico, y que en su lugar la incertidumbre asociada a dichos ejercicios estad\'isticos debiera expresarse en t\'erminos de una probabilidad de triunfo del candidato puntero.
An electoral quick count is a statistical procedure whose main objective is to obtain a relativel... more An electoral quick count is a statistical procedure whose main objective is to obtain a relatively small but representative sample of all the polling stations in a certain election, and to measure the uncertainty about the final result before the total count of votes. A stratified sampling design is commonly preferred to reduce estimation variability. The present work shows that dependence among strata and among candidates should be taken into consideration for statistical inferences therein, and a copula based model is proposed and applied to Mexico's 2006, 2012, and 2018 presidential elections data.
A statistical analysis of an electoral quick count based on the total count of votes in the elect... more A statistical analysis of an electoral quick count based on the total count of votes in the election of the State of Mexico's governor in 2017 is performed in order to verify precision, confidence level of interval estimations, possible bias and derived conclusions therein, with the main purpose of checking compliance with the objectives of such statistical procedure. ----- Se realiza un an\'alisis estad\'istico de las estimaciones del conteo r\'apido institucional desde la perspectiva ideal de los resultados de los c\'omputos distritales de la elecci\'on de gobernador del Estado de M\'exico del a\~no 2017, particularmente aspectos como la precisi\'on de las estimaciones, el nivel de confianza de los intervalos, el posible sesgo respecto al c\'omputo distrital y las conclusiones que se derivaron y reportaron, con el objetivo de determinar el grado de cumplimiento de los objetivos de este ejercicio estad\'istico de car\'acter informativo.
Revista de Métodos Cuantitativos para la Economía y la Empresa, 2017
The so-called risk diversification principle is analyzed, showing that its convenience depends on... more The so-called risk diversification principle is analyzed, showing that its convenience depends on individual characteristics of the risks involved and the dependence relationship among them. ------------------------------------ Se analiza el principio de diversificacion de riesgos y se demuestra que no siempre resulta mejor que no diversificar, pues esto depende de caracteristicas individuales de los riesgos involucrados, asi como de la relacion de dependencia entre los mismos.
A statistical test based on the geometric mean is proposed to determine if a predictive model sho... more A statistical test based on the geometric mean is proposed to determine if a predictive model should be rejected or not, when the quantity of interest is a strictly positive continuous random variable. A simulation study is performed to compare test power performance against an alternative procedure, and an application to insurance claims reserving is illustrated.
In this brief note we prove that linear B-spline copulas is not a new family of copulas since the... more In this brief note we prove that linear B-spline copulas is not a new family of copulas since they are equivalent to checkerboard copulas, and discuss in particular how they are used to extend empirical subcopulas to copulas.
In this paper we analyze some properties of the discrete copulas in terms of permutations. We obs... more In this paper we analyze some properties of the discrete copulas in terms of permutations. We observe the connection between discrete copulas and the empirical copulas, and then we analyze a statistic that indicates when the discrete copula is symmetric and obtain its main statistical properties under independence. The results obtained are useful in designing a nonparametric test for symmetry of copulas.
The so-called risk diversification principle is analyzed, showing that its convenience depends on... more The so-called risk diversification principle is analyzed, showing that its convenience depends on individual characteristics of the risks involved and the dependence relationship among them. ----- Se analiza el principio de diversificaci\'on de riesgos y se demuestra que no siempre resulta mejor que no diversificar, pues esto depende de caracter\'isticas individuales de los riesgos involucrados, as\'i como de la relaci\'on de dependencia entre los mismos.
In petrophysics, assesment of formation permeability is a complex and challenging problem that pl... more In petrophysics, assesment of formation permeability is a complex and challenging problem that plays a key role in reservoir forecasts and optimal reservoir management. In heterogeneous carbonate reservoirs, permeability evaluation is commonly performed using permeability-porosity relationships, which often seem to be nonlinear and complex. Copulas are marginal-free dependence functions that may capture such nonlinear relationships. In the present work we make use of a nonparametric copula approach for bivariate modeling of permeability- porosity real data, and its application for a spatial median regression.
Abstract In many naturally fractured reservoirs, fractures play a crucial role in their flow and ... more Abstract In many naturally fractured reservoirs, fractures play a crucial role in their flow and transport properties. An approach that has recently gained popularity for modeling fracture systems is the Discrete Fracture Network (DFN) model. This approach consists in applying a stochastic boolean simulation method, also known as object simulation method, where fractures are represented as simplified geometric objects (line segments in 2D and polygons in 3D). One of the shortcomings of this approach is that it usually does not consider the dependence relationships that may exist between geometric properties of fractures (direction, length, aperture), that is, each property is simulated independently. In this work a method for modeling such dependencies by copula theory is introduced. In particular, a nonparametric model using Bernstein copulas for direction-length fracture dependency in 2D is presented. The application of this method is illustrated in an example which shows high agreement between data and simulation, both graphically and in its descriptive statistics, both marginally and jointly, and in the DFN as a whole.
In this paper we analyze some properties of the empirical diagonal and we obtain its exact distri... more In this paper we analyze some properties of the empirical diagonal and we obtain its exact distribution under independence for the two and three- dimensional cases, but the ideas proposed in this paper can be carried out to higher dimensions. The results obtained are useful in designing a nonparametric test for independence, and therefore giving solution to an open problem proposed by Alsina, Frank and Schweizer [2].
An electoral quick count is a statistical procedure whose main objective is to obtain a relativel... more An electoral quick count is a statistical procedure whose main objective is to obtain a relatively small but representative sample of all the polling stations in a certain election, and to measure the uncertainty about the final result before the total count of votes. A stratified sampling design is commonly preferred to reduce estimation variability. The present work shows that dependence among strata and among candidates should be taken into consideration for statistical inferences therein, and a copula based model is proposed and applied to Mexico's 2006, 2012, and 2018 presidential elections data.
En los meses previos al día de las elecciones, es una práctica usual que diversos actores polític... more En los meses previos al día de las elecciones, es una práctica usual que diversos actores políticos y ciudadanos soliciten la realización de cierto tipo de estudios con el propósito de conocer con anticipación cómo van perfilándose las preferencias electorales. Antes del día de la elección es posible recurrir a diversos tipos de encuestas consistentes en preguntar a un subconjunto (muestra) de los posibles votantes cuál es su preferencia electoral, realizar un análisis estadístico de la información recabada y hacer inferencias sobre el posible resultado de la elección. El día de la elección también es posible recurrir a otro tipo de ejercicios para inferir el resultado de la misma, antes de que se conozca el resultado del recuento total de votos emitidos varios días después: la encuesta de salida y el conteo rápido. En México y algunos otros países es común que empresas encuestadoras, políticos, analistas y hasta autoridades electorales hablen de que en un momento dado existe “empate técnico” entre dos candidatos punteros y, por tanto, no es estadísticamente posible inferir un ganador. El presente trabajo tiene por objetivo argumentar que el empleo de la expresión “empate técnico” no tiene sustento probabilístico, por lo que no debiera utilizarse en inferencias estadísticas derivadas de encuestas y conteos rápidos electorales, consecuentemente la incertidumbre sobre el posible resultado de una elección debiera expresarse mediante la estimación de la probabilidad de triunfo del candidato puntero.
In the months leading up to the day of the elections, it is common practice among political actors and citizens to request the execution of certain types of studies with the purpose of knowing in advance how the electoral preferences are shaping up. Before the day of the election it is possible to resort to various types of electoral surveys consisting of asking a subset (sample) of the possible voters what their electoral preference is, performing a statistical analysis of the information collected and making inferences about the possible outcome. On the day of the election it is also possible to resort to another type of exercises to infer the outcome, before several days later the result of the total count of votes cast is known: the exit poll and the quick count. In Mexico and some other countries, it is common for polling companies, politicians, analysts and even electoral authorities to speak of a “technical tie” between two leading candidates at a given moment and, therefore, it is not statistically possible to infer a winner. The present work aims to argue that the use of the expression “technical tie” has no probabilistic foundations and therefore should not be used in statistical inferences derived from polls and quick counts, and that uncertainty about the possible outcome of an election should be expressed by estimating the probability of victory of the leading candidate.
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Papers by Arturo Erdely
In the months leading up to the day of the elections, it is common practice among political actors and citizens to request the execution of certain types of studies with the purpose of knowing in advance how the electoral preferences are shaping up. Before the day of the election it is possible to resort to various types of electoral surveys consisting of asking a subset (sample) of the possible voters what their electoral preference is, performing a statistical analysis of the information collected and making inferences about the possible outcome. On the day of the election it is also possible to resort to another type of exercises to infer the outcome, before several days later the result of the total count of votes cast is known: the exit poll and the quick count. In Mexico and some other countries, it is common for polling companies, politicians, analysts and even electoral authorities to speak of a “technical tie” between two leading candidates at a given moment and, therefore, it is not statistically possible to infer a winner. The present work aims to argue that the use of the expression “technical tie” has no probabilistic foundations and therefore should not be used in statistical inferences derived from polls and quick counts, and that uncertainty about the possible outcome of an election should be expressed by estimating the probability of victory of the leading candidate.