Tomotaka Momozaki, Tomoyuki Nakagawa, Kiyotaka Iki, S. Tomizawa
For square contingency tables with ordered categories, an index based on Cressie and Read's power divergence (or Patil and Taillie's diversity index) has been proposed in order to measure the degree of departure from symmetry. Although there are two types of maximum asymmetry (i.e., whether (1) all the observations concentrate in the top-right cell in the table, or (2) they concentrate in the bottom-left cell), the existing index cannot distinguish the two directions of maximum asymmetry. This paper proposes a directional index based on an arc-cosine function in order to simultaneously represent the degree and directionality of asymmetry.The proposed index would be useful for comparing degrees of asymmetry for several square contingency tables. Numerical examples show the utility of the proposed index using some datasets. We evaluate the usefulness of the proposed index by applying it to real data of the clinical study. The proposed index provides analysis results that are easier to interpret than the existing index.
{"title":"An Index for the Degree and Directionality of Asymmetry for Square Contingency Tables with Ordered Categories","authors":"Tomotaka Momozaki, Tomoyuki Nakagawa, Kiyotaka Iki, S. Tomizawa","doi":"10.17713/ajs.v52i1.1382","DOIUrl":"https://doi.org/10.17713/ajs.v52i1.1382","url":null,"abstract":"\u0000\u0000\u0000For square contingency tables with ordered categories, an index based on Cressie and Read's power divergence (or Patil and Taillie's diversity index) has been proposed in order to measure the degree of departure from symmetry. Although there are two types of maximum asymmetry (i.e., whether (1) all the observations concentrate in the top-right cell in the table, or (2) they concentrate in the bottom-left cell), the existing index cannot distinguish the two directions of maximum asymmetry. This paper proposes a directional index based on an arc-cosine function in order to simultaneously represent the degree and directionality of asymmetry.The proposed index would be useful for comparing degrees of asymmetry for several square contingency tables. Numerical examples show the utility of the proposed index using some datasets. We evaluate the usefulness of the proposed index by applying it to real data of the clinical study. The proposed index provides analysis results that are easier to interpret than the existing index.\u0000\u0000\u0000","PeriodicalId":51761,"journal":{"name":"Austrian Journal of Statistics","volume":"1 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90867617","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The quality of life, well-being and deprivation are significant factors affecting the ageing European population. The fifth (2013) wave of the Survey of Health, Ageing and Retirement in Europe (SHARE) covers the two indices of (material and social) deprivation along with various life quality and satisfaction indicators measuring (subjective and objective) well-being. Using the SHARE data, the present paper examines the 50+ population in 13 EU member states and Switzerland, emphasizing the relationships between distinctive characteristics. The gender gap is quantified for both the whole sample and particular age groups. Statistical comparisons between old and new EU countries are limited since only three of the latter (Estonia, Slovenia and the Czech Republic) took part in the 2013 SHARE survey.
{"title":"The Quality of Life of the European Population: SHARE Data-based Analysis","authors":"I. Malá","doi":"10.17713/ajs.v52i1.1101","DOIUrl":"https://doi.org/10.17713/ajs.v52i1.1101","url":null,"abstract":"The quality of life, well-being and deprivation are significant factors affecting the ageing European population. The fifth (2013) wave of the Survey of Health, Ageing and Retirement in Europe (SHARE) covers the two indices of (material and social) deprivation along with various life quality and satisfaction indicators measuring (subjective and objective) well-being. Using the SHARE data, the present paper examines the 50+ population in 13 EU member states and Switzerland, emphasizing the relationships between distinctive characteristics. The gender gap is quantified for both the whole sample and particular age groups. Statistical comparisons between old and new EU countries are limited since only three of the latter (Estonia, Slovenia and the Czech Republic) took part in the 2013 SHARE survey.","PeriodicalId":51761,"journal":{"name":"Austrian Journal of Statistics","volume":"14 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82993146","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The Rayleigh distribution has recently become popular as a model for a range of phenomena. As a result, a number of goodness-of-fit tests have been developed for this distribution. In this paper, we provide the first overview of goodness-of-fit tests for the Rayleigh distribution and compare these tests in a Monte-Carlo study to identify the tests that provide the highest powers against a wide range of alternatives. Our findings suggest that two recently developed tests as well as a test based on the Laplace transform and a test based on the Hellinger distance are the better performing tests.
{"title":"A Review of Goodness-of-Fit Tests for the Rayleigh Distribution","authors":"S. Liebenberg, J. Allison","doi":"10.17713/ajs.v52i1.1322","DOIUrl":"https://doi.org/10.17713/ajs.v52i1.1322","url":null,"abstract":"The Rayleigh distribution has recently become popular as a model for a range of phenomena. As a result, a number of goodness-of-fit tests have been developed for this distribution. In this paper, we provide the first overview of goodness-of-fit tests for the Rayleigh distribution and compare these tests in a Monte-Carlo study to identify the tests that provide the highest powers against a wide range of alternatives. Our findings suggest that two recently developed tests as well as a test based on the Laplace transform and a test based on the Hellinger distance are the better performing tests.","PeriodicalId":51761,"journal":{"name":"Austrian Journal of Statistics","volume":"41 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87322034","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The recent low water levels of Lake Neusiedl have raised concern about the lake's future and have sparked interest on how meteorological variables impact the water level. Data from the last 50 years are used to study the impact of rain and temperature on the cyclical changes of the water levels. Linear and nonlinear regression models are used to describe how rainfall and temperature change the water level, and to assess the future progression of the water level under three scenarios. For average 2022 meteorological conditions the water levels in 2022 may not recover for a dry 2021 autumn, but will recover substantially for a wet ending to the year 2021.
{"title":"A Statistical Analysis of the Water Levels at Lake Neusiedl","authors":"Peter Hackl, Johannes Ledolter","doi":"10.17713/ajs.v52i1.1444","DOIUrl":"https://doi.org/10.17713/ajs.v52i1.1444","url":null,"abstract":"The recent low water levels of Lake Neusiedl have raised concern about the lake's future and have sparked interest on how meteorological variables impact the water level. Data from the last 50 years are used to study the impact of rain and temperature on the cyclical changes of the water levels. Linear and nonlinear regression models are used to describe how rainfall and temperature change the water level, and to assess the future progression of the water level under three scenarios. For average 2022 meteorological conditions the water levels in 2022 may not recover for a dry 2021 autumn, but will recover substantially for a wet ending to the year 2021.","PeriodicalId":51761,"journal":{"name":"Austrian Journal of Statistics","volume":"144 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136245379","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Type I doubly left-censored data often arise in environmental studies. In this paper, the power of the most frequently used goodness-of-fit tests (Kolmogorov-Smirnov, Cramér-von Mises, Anderson-Darling) is studied considering various sample sizes and degrees of censoring. Attention is paid to testing of the composite hypothesis that the data has a specific distribution with unknown parameters, which are estimated using the maximum likelihood method. Performance of the tests is assessed by means of Monte Carlo simulations for several distributions, specifically the Weibull, lognormal and gamma distributions, which are among the most frequently used distributions for modelling of environmental data. Finally, the tests are used for identification of the distribution of musk concentrations if fish tissue.
{"title":"Statistical Power of Goodness-of-Fit Tests for Type~I Left-Censored Data","authors":"M. Fusek","doi":"10.17713/ajs.v52i1.1348","DOIUrl":"https://doi.org/10.17713/ajs.v52i1.1348","url":null,"abstract":"Type I doubly left-censored data often arise in environmental studies. In this paper, the power of the most frequently used goodness-of-fit tests (Kolmogorov-Smirnov, Cramér-von Mises, Anderson-Darling) is studied considering various sample sizes and degrees of censoring. Attention is paid to testing of the composite hypothesis that the data has a specific distribution with unknown parameters, which are estimated using the maximum likelihood method. Performance of the tests is assessed by means of Monte Carlo simulations for several distributions, specifically the Weibull, lognormal and gamma distributions, which are among the most frequently used distributions for modelling of environmental data. Finally, the tests are used for identification of the distribution of musk concentrations if fish tissue.","PeriodicalId":51761,"journal":{"name":"Austrian Journal of Statistics","volume":"1 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74958173","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The multilevel and poststratification approach is commonly used to draw valid inference from (non-probabilistic) surveys. This Bayesian approach includes varying regression coefficients for which prior distributions of their variance parameter must be specified. The choice of the distribution is far from being trivial and many contradicting recommendations exist in the literature. The prior choice may be even more challenging when data results from a highly selective inclusion mechanism, such as applied by volunteer panels. We conduct a Monte Carlo simulation study to evaluate the effect of different distribution choices on bias in the estimation of a proportion based on a sample that is subject to a highly selective inclusion mechanism.
{"title":"Prior Choice for the Variance Parameter in the Multilevel Regression and Poststratification Approach for Highly Selective Data. A Monte Carlo Simulation Study.","authors":"Christiane Bruch, Barbara Felderer","doi":"10.17713/ajs.v51i4.1361","DOIUrl":"https://doi.org/10.17713/ajs.v51i4.1361","url":null,"abstract":"The multilevel and poststratification approach is commonly used to draw valid inference from (non-probabilistic) surveys. This Bayesian approach includes varying regression coefficients for which prior distributions of their variance parameter must be specified. The choice of the distribution is far from being trivial and many contradicting recommendations exist in the literature. The prior choice may be even more challenging when data results from a highly selective inclusion mechanism, such as applied by volunteer panels. We conduct a Monte Carlo simulation study to evaluate the effect of different distribution choices on bias in the estimation of a proportion based on a sample that is subject to a highly selective inclusion mechanism.","PeriodicalId":51761,"journal":{"name":"Austrian Journal of Statistics","volume":"1 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78319675","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider an expression for the probability R=P(Y
我们考虑概率R=P(Y
{"title":"Effect of Dependency on the Estimation of P[Y","authors":"D. Patil, U. V. Naik-Nimbalkar, M. M. Kale","doi":"10.17713/ajs.v51i4.1293","DOIUrl":"https://doi.org/10.17713/ajs.v51i4.1293","url":null,"abstract":"We consider an expression for the probability R=P(Y<X) where the random variables X and Y denote strength and stress, respectively. Our aim is to study the effect of the dependency between X and Y on R. We assume that X and Y follow exponential distributions and their dependency is modeled by a copula with the dependency parameter theta. We obtain a closed-form expression for R for Farlie-Gumbel-Morgenstern (FGM), Ali-Mikhail-Haq (AMH), Gumbel's bivariate exponential copulas and compute R for Gumbel-Hougaard (GH) copula using a Monte-Carlo integration technique. We plot a graph of R versus theta to study the effect of dependency on R. We estimate R by plugging in the estimates of the marginal parameters and theta in its expression. The estimates of the marginal parameters are based on the marginal likelihood. The estimates of theta are obtained from two different methods; one is based on the conditional likelihood and the other on the method of moments using Blomqvist's beta. Asymptotic distribution of both the estimators of R is obtained. For illustration purpose, we apply our results to a real data set.","PeriodicalId":51761,"journal":{"name":"Austrian Journal of Statistics","volume":"14 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88372239","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Several authors have studied fractional cointegration in time series data, but little or no consideration has been extended to panel data settings. Therefore, in this paper, we compare the finite sample behaviour of existing fractional cointegration time-series test procedures in panel data settings. This comparison is performed to determine the best tests that can be adapted to fractional cointegration in panel data settings. Specifically, simulation studies and real-life data analysis were performed to study the changes in the empirical type I error rate and power of six semiparametric fractional cointegration tests in panel settings. The various results revealed the limitations of the tests in the nonstationary and low or high correlation of the residual errors conditions. Also, two of the test procedures were recommended for testing the null hypothesis of no fractional cointegration in both time series and panel data settings.
{"title":"A Comparative Analysis of Semiparametric Tests for Fractional Cointegration in Panel Data Models","authors":"S. F. Olaniran, M. Ismail","doi":"10.17713/ajs.v51i4.1170","DOIUrl":"https://doi.org/10.17713/ajs.v51i4.1170","url":null,"abstract":"Several authors have studied fractional cointegration in time series data, but little or no consideration has been extended to panel data settings. Therefore, in this paper, we compare the finite sample behaviour of existing fractional cointegration time-series test procedures in panel data settings. This comparison is performed to determine the best tests that can be adapted to fractional cointegration in panel data settings. Specifically, simulation studies and real-life data analysis were performed to study the changes in the empirical type I error rate and power of six semiparametric fractional cointegration tests in panel settings. The various results revealed the limitations of the tests in the nonstationary and low or high correlation of the residual errors conditions. Also, two of the test procedures were recommended for testing the null hypothesis of no fractional cointegration in both time series and panel data settings.","PeriodicalId":51761,"journal":{"name":"Austrian Journal of Statistics","volume":"25 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83148704","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In statistical literature, various probability distributions exist with advantageous properties, while others are considered pathological since their properties are counterintuitive. A well-known pathological probability distribution is the Cauchy distribution, and it has applications in areas related to environmental and financial research. Both the log-Cauchy and half-Cauchy distributions, which have close connections to the Cauchy distribution, are pathological distributions. This paper considers another pathological model called the Cauchy Birnbaum-Saunders distribution. Some of the statistical properties of this distribution are discussed briefly, and its parameters are estimated using eight frequentist estimation methods, including the maximum likelihood, least-squares-based, and minimum distance estimation methods. Monte Carlo simulations are carried out to compare and examine the performance of each estimator numerically. Furthermore, a recent climate data set is analyzed to show the practical applicability of this model.
{"title":"On Comparing Different Methods of Estimation for the Parameters of a Pathological Distribution with Application to Climate Data","authors":"F. Alam","doi":"10.17713/ajs.v51i4.1331","DOIUrl":"https://doi.org/10.17713/ajs.v51i4.1331","url":null,"abstract":"In statistical literature, various probability distributions exist with advantageous properties, while others are considered pathological since their properties are counterintuitive. A well-known pathological probability distribution is the Cauchy distribution, and it has applications in areas related to environmental and financial research. Both the log-Cauchy and half-Cauchy distributions, which have close connections to the Cauchy distribution, are pathological distributions. This paper considers another pathological model called the Cauchy Birnbaum-Saunders distribution. Some of the statistical properties of this distribution are discussed briefly, and its parameters are estimated using eight frequentist estimation methods, including the maximum likelihood, least-squares-based, and minimum distance estimation methods. Monte Carlo simulations are carried out to compare and examine the performance of each estimator numerically. Furthermore, a recent climate data set is analyzed to show the practical applicability of this model.","PeriodicalId":51761,"journal":{"name":"Austrian Journal of Statistics","volume":"59 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89539209","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
When comparing two or more multidimensional scaling (MDS) configurations, one usually first eliminates meaningless differences by Procrustean transformations. Such fittings lead to a number of unresolved issues such as the typical shrinkage of the fitted configuration relative to the target or how to interpret major similarity measures under various conditions of noise in the data. We here prove that the shrinkage ratio is equivalent to the correlation of the coordinates of the target and the fitted configuration. Thus, in real-life applications, the fitted configuration is always smaller than the target configuration. Both coefficients approach 0 as the noise level goes up. The congruence coefficient of the configurations' distances, in contrast, remains at a high level even in case of pure noise, falsely suggesting that the configurations are somewhat similar. This is important information for the user of Procrustean analyses.
{"title":"A Note on Procrustean Fittings of Noisy Configurations","authors":"I. Borg, P. Mair","doi":"10.17713/ajs.v51i4.1423","DOIUrl":"https://doi.org/10.17713/ajs.v51i4.1423","url":null,"abstract":"When comparing two or more multidimensional scaling (MDS) configurations, one usually first eliminates meaningless differences by Procrustean transformations. Such fittings lead to a number of unresolved issues such as the typical shrinkage of the fitted configuration relative to the target or how to interpret major similarity measures under various conditions of noise in the data. We here prove that the shrinkage ratio is equivalent to the correlation of the coordinates of the target and the fitted configuration. Thus, in real-life applications, the fitted configuration is always smaller than the target configuration. Both coefficients approach 0 as the noise level goes up. The congruence coefficient of the configurations' distances, in contrast, remains at a high level even in case of pure noise, falsely suggesting that the configurations are somewhat similar. This is important information for the user of Procrustean analyses.","PeriodicalId":51761,"journal":{"name":"Austrian Journal of Statistics","volume":"1 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75563666","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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