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A Bootstrap Comparison of Robust Regression Estimators
Kalina, Jan; Janáček, Patrik
2022 - English
The ordinary least squares estimator in linear regression is well known to be highly vulnerable to the presence of outliers in the data and available robust statistical estimators represent more preferable alternatives. It has been repeatedly recommended to use the least squares together with a robust estimator, where the latter is understood as a diagnostic tool for the former. In other words, only if the robust estimator yields a very different result, the user should investigate the dataset closer and search for explanations. For this purpose, a hypothesis test of equality of the means of two alternative linear regression estimators is proposed here based on nonparametric bootstrap. The performance of the test is presented on three real economic datasets with small samples. Robust estimates turn out not to be significantly different from non-robust estimates in the selected datasets. Still, robust estimation is beneficial in these datasets and the experiments illustrate one of possible ways of exploiting the bootstrap methodology in regression modeling. The bootstrap test could be easily extended to nonlinear regression models.
Keywords:
linear regression; robust estimation; nonparametric bootstrap; bootstrap hypothesis testing
Fulltext is available at external website.
A Bootstrap Comparison of Robust Regression Estimators
The ordinary least squares estimator in linear regression is well known to be highly vulnerable to the presence of outliers in the data and available robust statistical estimators represent more ...
A Measure of Variability WIthin Parametric Families of Continuous Distributions
Fabián, Zdeněk
2022 - English
A continuous probability measure on an open interval of the real line induces in it a unique geometry, "center of gravity" of which is the typical value of the distribution. In the paper is identified a score variance as a finite measure of variability of distributions with respect to the typical value and discussed its properties and methods of estimation. Itroducing a generalized Rao distance in the sample space one can appraise the precision of the estimate of the typical value.
Keywords:
scalar-valued score; score mean; score variance; distance in the sample space
Available at various institutes of the ASCR
A Measure of Variability WIthin Parametric Families of Continuous Distributions
A continuous probability measure on an open interval of the real line induces in it a unique geometry, "center of gravity" of which is the typical value of the distribution. In the paper is identified ...
Score correlation for skewed distributions
Fabián, Zdeněk
2022 - English
Based on the new concept of the scalar-valued score function of continuous distributions we introduce the score correlation coefficient ”tai-lored” to the assumed probabilistic model and study its properties by means of simulation experiments. It appeared that the new correlation method is useful for enormously skewed distributions.
Keywords:
Scalar-valued score; score coefficient of variation; Monte Carlo
Available at various institutes of the ASCR
Score correlation for skewed distributions
Based on the new concept of the scalar-valued score function of continuous distributions we introduce the score correlation coefficient ”tai-lored” to the assumed probabilistic model and study its ...
Introduction to statistical inference based on scalar-valued scores
Fabián, Zdeněk
2022 - English
In the report we maintain consistently the following point of view: Given a continuous model, there are not the observed values, which are to be used in probabilistic and statistical considerations, but their ”treated forms”,the values of the scalar-valued score function corresponding to the model. Based on this modified concept of the score function, we develop theory of score random variables, study their geometry and define their new characteristics, finite even in cases of heavy-tailed models. A generalization for parametric families provides a new approach to parametric point estimation.
Keywords:
continuous distributions; score mean; score variance; score moment estimation method; score distance
Available at various institutes of the ASCR
Introduction to statistical inference based on scalar-valued scores
In the report we maintain consistently the following point of view: Given a continuous model, there are not the observed values, which are to be used in probabilistic and statistical considerations, ...
Scalar-Valued Score Functions and their use in Parametric Estimation
Fabián, Zdeněk
2022 - English
In the paper we describe and explain a new direction in probabilistic and statistical reasoning, the approach based on scalar-valued score functions of continuous random variables. We show basic properties of score functions of standard distributions, generalize the approach for parametric families and show how to use them for solutions of problems of parametric statistics.
Keywords:
core random variable; score mean; score variance; score distance; score correlation
Available on request at various institutes of the ASCR
Scalar-Valued Score Functions and their use in Parametric Estimation
In the paper we describe and explain a new direction in probabilistic and statistical reasoning, the approach based on scalar-valued score functions of continuous random variables. We show basic ...
A New Look to Information and Uncertainty of Continuous Distributions
Fabián, Zdeněk
2022 - English
We define information and uncertainty function of a family of continuous distributions. Their values are relative information and uncertainty of an observation from the given parametric family, their mean values are the generalized Fisher information and a new measure of variability, the score variance. In a series of examples we show why to use new concepts instead of the differential entropy.
Keywords:
Differential entropy; information function; uncertainty function; mean information of distribution
Available at various institutes of the ASCR
A New Look to Information and Uncertainty of Continuous Distributions
We define information and uncertainty function of a family of continuous distributions. Their values are relative information and uncertainty of an observation from the given parametric family, their ...
Large Perimeter Objects Surrounded by a 1.5D Terrain
Keikha, Vahideh
2022 - English
Given is a 1.5D terrain T , i.e., an x-monotone polygonal chain in R2. Our objective is to approximate the largest area or perimeter convex polygon with at most k vertices inside T . For a constant k > 0, we design an FPTAS that efficiently approximates such polygons within a factor (1 − ǫ). For the special case of the´largest-perimeter contained triangle in T , we design an O(n log n) time exact algorithm that matches the same result for the area measure.
Available in digital repository of the ASCR
Large Perimeter Objects Surrounded by a 1.5D Terrain
Given is a 1.5D terrain T , i.e., an x-monotone polygonal chain in R2. Our objective is to approximate the largest area or perimeter convex polygon with at most k vertices inside T . For a constant k ...
Recent Trends in Machine Learning with a Focus on Applications in Finance
Kalina, Jan; Neoral, Aleš
2022 - English
Machine learning methods penetrate to applications in the analysis of financial data, particularly to supervised learning tasks including regression or classification. Other approaches, such as reinforcement learning or automated machine learning, are not so well known in the context of finance yet. In this paper, we discuss the advantages of an automated data analysis, which is beneficial especially if a larger number of datasets should be analyzed under a time pressure. Important types of learning include reinforcement learning, automated machine learning, or metalearning. This paper overviews their principles and recalls some of their inspiring applications. We include a discussion of the importance of the concept of information and of the search for the most relevant information in the field of mathematical finance. We come to the conclusion that a statistical interpretation of the results of theautomatic machine learning remains crucial for a proper understanding of the knowledge acquired by the analysis of the given (financial) data.
Keywords:
statistical learning; automated machine learning; metalearning; financial data analysis; stock market investing
Fulltext is available at external website.
Recent Trends in Machine Learning with a Focus on Applications in Finance
Machine learning methods penetrate to applications in the analysis of financial data, particularly to supervised learning tasks including regression or classification. Other approaches, such as ...
The 2020 Election In The United States: Beta Regression Versus Regression Quantiles
Kalina, Jan
2021 - English
The results of the presidential election in the United States in 2020 desire a detailed statistical analysis by advanced statistical tools, as they were much different from the majority of available prognoses as well as from the presented opinion polls. We perform regression modeling for explaining the election results by means of three demographic predictors for individual 50 states: weekly attendance at religious services, percentage of Afroamerican population, and population density. We compare the performance of beta regression with linear regression, while beta regression performs only slightly better in terms of predicting the response. Because the United States population is very heterogeneous and the regression models are heteroscedastic, we focus on regression quantiles in the linear regression model. Particularly, we develop an original quintile regression map, such graphical visualization allows to perform an interesting interpretation of the effect of the demographic predictors on the election outcome on the level of individual states.
Keywords:
elections results; electoral demography; quantile regression; heteroscedasticity; outliers
Fulltext is available at external website.
The 2020 Election In The United States: Beta Regression Versus Regression Quantiles
The results of the presidential election in the United States in 2020 desire a detailed statistical analysis by advanced statistical tools, as they were much different from the majority of available ...
DC 5.3 Základní statistický model velkého měřítka
Brabec, Marek; Malý, Marek; Malá, I.; Hladká, Adéla
2021 - Czech
BIBLIOGRAFICKÉ ÚDAJE: Výzkumná zpráva č. SS02030031-V94, evidenční č. ENV/2021/118018. Praha: ICS CAS, 2021. 47 s. ANOTACE: Obsahem tohoto dokumentu je popis prostorového statistického modelu velkého měřítka vyvinutého z dosavadních dat poskytnutých ČHMÚ. Prostorový model bude (po nezbytných aktualizacích a případných modifikacích daných jak časovým vývojem samotného znečištění, který lze očekávat např. v souvislosti s dopady pandemie covid-19, tak dalším vývojem statistické metodologie) v dalších letech používán jako podklad pro vývoj algoritmu prostorové optimalizace umístění měřicích stanic na základě statistického designu. Jde o několik variantních řešení, která zohledňují různé aspekty statistického chování pole koncentrací vybraných znečišťujících látek. This document describes suite of fundamental large-scale statistical models developed from data provided by CHMI (Czech Hydrometeorological Institute). The models were constructed in several variants, differing in complexity, detail and computational demands. Spatial models will be, after some further developments and modifications (necessary not only from the natural model evolution but also due to systematic changes brought e.g. by covid outbreak influences) used as the main input for optimization algorithms constructed for selection of measurement stations on the principles of statistical design theory and methods.
Keywords:
spatial field of pollutant concentration; geostatistics; GAM; INLA; spatially varying covariance model; Bayesian modeling
Available in digital repository of the ASCR
DC 5.3 Základní statistický model velkého měřítka
BIBLIOGRAFICKÉ ÚDAJE: Výzkumná zpráva č. SS02030031-V94, evidenční č. ENV/2021/118018. Praha: ICS CAS, 2021. 47 s. ANOTACE: Obsahem tohoto dokumentu je popis prostorového statistického modelu velkého ...
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