Aydin Erar - Academia.edu (original) (raw)

Papers by Aydin Erar

Research paper thumbnail of Otokorelasyonlu Doğrusal Olmayan Regresyon Çözümlemesinde Model Seçimi

Research paper thumbnail of Bayesian approach to linear regression with multicollinearity

Research paper thumbnail of A simulation study for some biased estimation methods

Research paper thumbnail of Variable selection criteria in robust regression

Research paper thumbnail of Bayesian Variable Selection in Linear Regression and a Comparison

Hacettepe Journal of Mathematics and Statistics, Dec 1, 2001

In this study, Bayesian approaches, such as Zellner, Occam's Window and Gibbs sampling, have been... more In this study, Bayesian approaches, such as Zellner, Occam's Window and Gibbs sampling, have been compared in terms of selecting the correct subset for the variable selection in a linear regression model. The aim of this comparison is to analyze Bayesian variable selection and the behavior of classical criteria by taking into consideration the different values of β and σ and prior expected levels.

Research paper thumbnail of Variable Selection with Akaike Information Criteria : A Comparative Study

Hacettepe Journal of Mathematics and Statistics, 2001

In this paper, the problem of variable selection in linear regression is considered. This problem... more In this paper, the problem of variable selection in linear regression is considered. This problem involves choosing the most appropriate model from the candidate models. Variable selection criteria based on estimates of the Kullback-Leibler information are most common. Akaike’s AIC and bias corrected AIC belong to this group of criteria. The reduction of the bias in estimating the Kullback-Leibler information can lead to better variable selection. In this study we have compared the Akaike Criterion based on Fisher Information and AIC criteria based on Kullback-Leibler.

Research paper thumbnail of Aykiri Değer Varliğinda Doğrusal Regresyonda Deği̇şken Seçi̇mi̇ne Gi̇bbs Örneklemesi̇ Yaklaşimi

gazi university journal of science, Aug 11, 2010

In this study, Gibbs sampling has been applied to the variable selection in the linear regression... more In this study, Gibbs sampling has been applied to the variable selection in the linear regression model with outlier values. Gibbs sampling has been compared with classical variable selection criteria by using dummy data with different β and priors.

Research paper thumbnail of An alternative method correcting BDR type of heteroskedasticity by the weighting re-estimated absolute residuals

Communications in Statistics - Theory and Methods, 2017

The aim of this paper is to introduce a new method which corrects residuals variances for the but... more The aim of this paper is to introduce a new method which corrects residuals variances for the butterfly distributed residuals (BDR). Distribution theory, confidence intervals and tests of hypotheses are valid and meaningful only if the standard regression assumptions are satisfied. Heteroscedasticity is one of the violations of these assumptions and BDR is another type of heteroscedasticity. This study reveals an alternative approach to correct BDR type of heteroscedasticity by the weighting re-estimated absolute residuals (WRAR). After giving brief information about heteroscedasticity and BDR type of heteroscedasticity, WRAR is introduced. WRAR and the usual variance stabilizing techniques are compared on multiple and simple regression models.

Research paper thumbnail of Gibbs Sampling Approach to Variable Selection in Linear Regression with Outlier Values

In this study, Gibbs sampling has been applied to the variable selection in the linear regression... more In this study, Gibbs sampling has been applied to the variable selection in the linear regression model with outlier values. Gibbs sampling has been compared with classical variable selection criteria by using dummy data with different β

Research paper thumbnail of Bibliometrics or Informetrics: Displaying Regularity in Scientific Patterns by Using Statistical Distributions

The application of Statistical and Mathematical methods in Library and Information Sciences is ca... more The application of Statistical and Mathematical methods in Library and Information Sciences is called Bibliometrics or Informetrics. The fundamental topic in this area is the study of distributions which display regularity in scientiflc patterns, such as in the productivity of authors, or in articles, words or citations. In this study these distributions will be summarized and discussed after describing brie∞y the concept of Informetrics. Also an original applications will be given where the flt of the data to these distributions is tested.

Research paper thumbnail of Variable selection with genetic algorithm and multivariate adaptive regression splines in the presence of multicollinearity

International Journal of ADVANCED AND APPLIED SCIENCES, 2016

In this paper, it is aimed to determine the true regressors explaining the dependent variable in ... more In this paper, it is aimed to determine the true regressors explaining the dependent variable in multiple linear regression models and also to find the best model by using two different approaches in the presence of low, medium and high multicollinearity. These approaches compared in this study are genetic algorithm and multivariate adaptive regression splines. A comprehensive Monte Carlo experiment is performed in order to examine the performance of these approaches. This study exposes that nonparametric methods can be preferred for variable selection in order to obtain the best model when there is a multicollinearity problem in the small, medium or large data sets.

Research paper thumbnail of Değişken Dönüşümlerinin Kelebek Dağılan Artıklar için Değişen Varyanslılığa Etkileri

Afyon Kocatepe University Journal of Sciences and Engineering, 2013

Klasik doğrusal regresyon analizinde varsayımlar gerçeklenmediğinde, ağırlıklandırma ve dönüşümle... more Klasik doğrusal regresyon analizinde varsayımlar gerçeklenmediğinde, ağırlıklandırma ve dönüşümler kullanılarak varsayım bozulmaları giderilmeye çalışılır. Değişen varyanslılık varsayım bozulmalarından biridir ve kelebek dağılan artıklar da değişen varyanslılığın özel bir halidir. Bu çalışmanın amacı, regresyon eşitliğinde yer alan değişkenlere uygulanan dönüşümlerin kelebek dağılan artıklar için etkilerinin incelenmesidir.

Research paper thumbnail of Regression error characteristic curves based on the choice of best estimation method

Selcuk Journal of Applied Mathematics, Jun 18, 2016

Research paper thumbnail of Bibliometrics or informetrics: Displaying regularity in scientific patterns by using statistical distributions

Hacettepe University Bulletin of Natural Sciences and Engineering Series B Mathematics and Statistics, 2002

Research paper thumbnail of Sağlam Cp Kriterinin Uygulanması Üzerine Bir Çalışma

Anadolu Universitesi Bilim Ve Teknoloji Dergisi a Uygulamalı Bilimler Ve Muhendislik, 2000

Research paper thumbnail of Kütüphanecilik ve Bilgibilim Alanlarında İstatistik Yöntemlerin Kullanımı

Research paper thumbnail of Two-Stage Genetic Algorithm in the Analysis of Biochemical Relations

Turkiye Klinikleri Journal of Biostatistics, 2012

... (17:21) Dicle Nörolojide asistanlar "sorun" yaşıyor. (15:59) "Kürtaj Kurulu&qu... more ... (17:21) Dicle Nörolojide asistanlar "sorun" yaşıyor. (15:59) "Kürtaj Kurulu" çalışmalara başlıyor, kurulda hangi branşlar olacak? ... (12:24) Doktorlar arasındaki bıçaklı kavgada 1 doktor tutuklandı. (11:34) Diyanet İşleri Başkanı Görmez'den 'kürtaj' açıklaması. ...

Research paper thumbnail of FRI0422 A possible source of error in the method of cancer risk estimation in patients with rheumatoid arthritis

Annals of the Rheumatic Diseases, 2012

ABSTRACT Background The magnitude of the association of cancer with rheumatoid arthritis, especia... more ABSTRACT Background The magnitude of the association of cancer with rheumatoid arthritis, especially after anti-TNF use, remains in dispute. We recently proposed (1) an important selection bias was potentially inherent in the registry data especially when the comparator for the sought cancer incidence in RA was the cancer incidence in the “mother population”, the population from which the registry is derived from. In a mother population within a given time there would be many patients with cancer who would not have the chance to develop RA since a. a sizeable fraction would die from their disease before having the chance to develop RA; b. The cancer treatment could potentially prevent the development of RA or finally, and particularly in the case of anti-TNF registries, c. If they remained alive and developed cancer the likelihood of them being included in such a registry would be small. All 3 factors could render the incidence ratio (incidence in the registry/incidence in the mother population) less than unity even if biologically there are no real differences in the cancer frequencies between the 2 populations. Lastly this ratio would decrease in time as was observed in the Taiwan registry (1). Objectives We formally surveyed whether the same potential selection bias was present in other manuscripts reporting similar data. Methods We conducted a PubMed search with the search terms “registry” “cancer” and “rheumatoid arthritis” among 7 high-impact rheumatology journals between 2001 and May-2011 (inclusive). First, articles that reported cancer incidence in patients with RA were retrieved in full-text. Among these, those manuscripts which reported an incidence ratio at 2 or more time-points were included in this survey. We specifically sought a. whether the comparisons were made between the registry and a “mother population” and b. the changes in the above described ratio between the first and last time points. Results We retrieved 36 articles among 1274 search results. In 6/36 the incidence ratio comparisons were made between at least one RA registry and its mother population at more than 1 time point. The number of time-points ranged from 3 to 11. Sampling-period-length ranged from 8 to 40 years. In 5 of the 6 articles when a comparison was made with the mother population there was a reduction over time in the incidence ratio which ranged from 29 to 99%. In the remaining study there was no appreciable change in the incidence ratio. Conclusions There are many important methodological issues for a fair assessment of cancer incidence in RA especially with the use of anti-TNF agents (2) We propose that the selection bias we try to highlight here should be included in this list of issues especially when we compare the cancer in a RA cohort with that in the mother population. Disclosure of Interest None Declared

Research paper thumbnail of Research Into Multiple Outliers in Linear Regression Analysis

mat.hacettepe.edu.tr

Studying the observations in regression analysis it is seen that the output of regression is affe... more Studying the observations in regression analysis it is seen that the output of regression is affected from outliers in the direction of the dependent and / or the independent variables. In this paper multiple outliers are examined in two real data sets. The results concerned with which method can determine multiple outliers better are examined with the help of some statistics and REC curve which can be used for determining efficiency. Also, the results are tried to support by using Monte Carlo Simulation.

Research paper thumbnail of Comparison of the Least Square Estimators with Their Robust Versions in Linear Calibration Problems

mat.hacettepe.edu.tr

... Keywords: Linear calibration, Classical estimator, Inverse estimator, Nazsodi esti-mator, Ali... more ... Keywords: Linear calibration, Classical estimator, Inverse estimator, Nazsodi esti-mator, Ali and Singh estimator, Srivastava and Singh estimator, Robust calibration ... Aitchison and Dunsmore [1] used the following equation, which is similar to Halperin's estimator, to estimate x0. ...

Research paper thumbnail of Otokorelasyonlu Doğrusal Olmayan Regresyon Çözümlemesinde Model Seçimi

Research paper thumbnail of Bayesian approach to linear regression with multicollinearity

Research paper thumbnail of A simulation study for some biased estimation methods

Research paper thumbnail of Variable selection criteria in robust regression

Research paper thumbnail of Bayesian Variable Selection in Linear Regression and a Comparison

Hacettepe Journal of Mathematics and Statistics, Dec 1, 2001

In this study, Bayesian approaches, such as Zellner, Occam's Window and Gibbs sampling, have been... more In this study, Bayesian approaches, such as Zellner, Occam's Window and Gibbs sampling, have been compared in terms of selecting the correct subset for the variable selection in a linear regression model. The aim of this comparison is to analyze Bayesian variable selection and the behavior of classical criteria by taking into consideration the different values of β and σ and prior expected levels.

Research paper thumbnail of Variable Selection with Akaike Information Criteria : A Comparative Study

Hacettepe Journal of Mathematics and Statistics, 2001

In this paper, the problem of variable selection in linear regression is considered. This problem... more In this paper, the problem of variable selection in linear regression is considered. This problem involves choosing the most appropriate model from the candidate models. Variable selection criteria based on estimates of the Kullback-Leibler information are most common. Akaike’s AIC and bias corrected AIC belong to this group of criteria. The reduction of the bias in estimating the Kullback-Leibler information can lead to better variable selection. In this study we have compared the Akaike Criterion based on Fisher Information and AIC criteria based on Kullback-Leibler.

Research paper thumbnail of Aykiri Değer Varliğinda Doğrusal Regresyonda Deği̇şken Seçi̇mi̇ne Gi̇bbs Örneklemesi̇ Yaklaşimi

gazi university journal of science, Aug 11, 2010

In this study, Gibbs sampling has been applied to the variable selection in the linear regression... more In this study, Gibbs sampling has been applied to the variable selection in the linear regression model with outlier values. Gibbs sampling has been compared with classical variable selection criteria by using dummy data with different β and priors.

Research paper thumbnail of An alternative method correcting BDR type of heteroskedasticity by the weighting re-estimated absolute residuals

Communications in Statistics - Theory and Methods, 2017

The aim of this paper is to introduce a new method which corrects residuals variances for the but... more The aim of this paper is to introduce a new method which corrects residuals variances for the butterfly distributed residuals (BDR). Distribution theory, confidence intervals and tests of hypotheses are valid and meaningful only if the standard regression assumptions are satisfied. Heteroscedasticity is one of the violations of these assumptions and BDR is another type of heteroscedasticity. This study reveals an alternative approach to correct BDR type of heteroscedasticity by the weighting re-estimated absolute residuals (WRAR). After giving brief information about heteroscedasticity and BDR type of heteroscedasticity, WRAR is introduced. WRAR and the usual variance stabilizing techniques are compared on multiple and simple regression models.

Research paper thumbnail of Gibbs Sampling Approach to Variable Selection in Linear Regression with Outlier Values

In this study, Gibbs sampling has been applied to the variable selection in the linear regression... more In this study, Gibbs sampling has been applied to the variable selection in the linear regression model with outlier values. Gibbs sampling has been compared with classical variable selection criteria by using dummy data with different β

Research paper thumbnail of Bibliometrics or Informetrics: Displaying Regularity in Scientific Patterns by Using Statistical Distributions

The application of Statistical and Mathematical methods in Library and Information Sciences is ca... more The application of Statistical and Mathematical methods in Library and Information Sciences is called Bibliometrics or Informetrics. The fundamental topic in this area is the study of distributions which display regularity in scientiflc patterns, such as in the productivity of authors, or in articles, words or citations. In this study these distributions will be summarized and discussed after describing brie∞y the concept of Informetrics. Also an original applications will be given where the flt of the data to these distributions is tested.

Research paper thumbnail of Variable selection with genetic algorithm and multivariate adaptive regression splines in the presence of multicollinearity

International Journal of ADVANCED AND APPLIED SCIENCES, 2016

In this paper, it is aimed to determine the true regressors explaining the dependent variable in ... more In this paper, it is aimed to determine the true regressors explaining the dependent variable in multiple linear regression models and also to find the best model by using two different approaches in the presence of low, medium and high multicollinearity. These approaches compared in this study are genetic algorithm and multivariate adaptive regression splines. A comprehensive Monte Carlo experiment is performed in order to examine the performance of these approaches. This study exposes that nonparametric methods can be preferred for variable selection in order to obtain the best model when there is a multicollinearity problem in the small, medium or large data sets.

Research paper thumbnail of Değişken Dönüşümlerinin Kelebek Dağılan Artıklar için Değişen Varyanslılığa Etkileri

Afyon Kocatepe University Journal of Sciences and Engineering, 2013

Klasik doğrusal regresyon analizinde varsayımlar gerçeklenmediğinde, ağırlıklandırma ve dönüşümle... more Klasik doğrusal regresyon analizinde varsayımlar gerçeklenmediğinde, ağırlıklandırma ve dönüşümler kullanılarak varsayım bozulmaları giderilmeye çalışılır. Değişen varyanslılık varsayım bozulmalarından biridir ve kelebek dağılan artıklar da değişen varyanslılığın özel bir halidir. Bu çalışmanın amacı, regresyon eşitliğinde yer alan değişkenlere uygulanan dönüşümlerin kelebek dağılan artıklar için etkilerinin incelenmesidir.

Research paper thumbnail of Regression error characteristic curves based on the choice of best estimation method

Selcuk Journal of Applied Mathematics, Jun 18, 2016

Research paper thumbnail of Bibliometrics or informetrics: Displaying regularity in scientific patterns by using statistical distributions

Hacettepe University Bulletin of Natural Sciences and Engineering Series B Mathematics and Statistics, 2002

Research paper thumbnail of Sağlam Cp Kriterinin Uygulanması Üzerine Bir Çalışma

Anadolu Universitesi Bilim Ve Teknoloji Dergisi a Uygulamalı Bilimler Ve Muhendislik, 2000

Research paper thumbnail of Kütüphanecilik ve Bilgibilim Alanlarında İstatistik Yöntemlerin Kullanımı

Research paper thumbnail of Two-Stage Genetic Algorithm in the Analysis of Biochemical Relations

Turkiye Klinikleri Journal of Biostatistics, 2012

... (17:21) Dicle Nörolojide asistanlar "sorun" yaşıyor. (15:59) "Kürtaj Kurulu&qu... more ... (17:21) Dicle Nörolojide asistanlar "sorun" yaşıyor. (15:59) "Kürtaj Kurulu" çalışmalara başlıyor, kurulda hangi branşlar olacak? ... (12:24) Doktorlar arasındaki bıçaklı kavgada 1 doktor tutuklandı. (11:34) Diyanet İşleri Başkanı Görmez'den 'kürtaj' açıklaması. ...

Research paper thumbnail of FRI0422 A possible source of error in the method of cancer risk estimation in patients with rheumatoid arthritis

Annals of the Rheumatic Diseases, 2012

ABSTRACT Background The magnitude of the association of cancer with rheumatoid arthritis, especia... more ABSTRACT Background The magnitude of the association of cancer with rheumatoid arthritis, especially after anti-TNF use, remains in dispute. We recently proposed (1) an important selection bias was potentially inherent in the registry data especially when the comparator for the sought cancer incidence in RA was the cancer incidence in the “mother population”, the population from which the registry is derived from. In a mother population within a given time there would be many patients with cancer who would not have the chance to develop RA since a. a sizeable fraction would die from their disease before having the chance to develop RA; b. The cancer treatment could potentially prevent the development of RA or finally, and particularly in the case of anti-TNF registries, c. If they remained alive and developed cancer the likelihood of them being included in such a registry would be small. All 3 factors could render the incidence ratio (incidence in the registry/incidence in the mother population) less than unity even if biologically there are no real differences in the cancer frequencies between the 2 populations. Lastly this ratio would decrease in time as was observed in the Taiwan registry (1). Objectives We formally surveyed whether the same potential selection bias was present in other manuscripts reporting similar data. Methods We conducted a PubMed search with the search terms “registry” “cancer” and “rheumatoid arthritis” among 7 high-impact rheumatology journals between 2001 and May-2011 (inclusive). First, articles that reported cancer incidence in patients with RA were retrieved in full-text. Among these, those manuscripts which reported an incidence ratio at 2 or more time-points were included in this survey. We specifically sought a. whether the comparisons were made between the registry and a “mother population” and b. the changes in the above described ratio between the first and last time points. Results We retrieved 36 articles among 1274 search results. In 6/36 the incidence ratio comparisons were made between at least one RA registry and its mother population at more than 1 time point. The number of time-points ranged from 3 to 11. Sampling-period-length ranged from 8 to 40 years. In 5 of the 6 articles when a comparison was made with the mother population there was a reduction over time in the incidence ratio which ranged from 29 to 99%. In the remaining study there was no appreciable change in the incidence ratio. Conclusions There are many important methodological issues for a fair assessment of cancer incidence in RA especially with the use of anti-TNF agents (2) We propose that the selection bias we try to highlight here should be included in this list of issues especially when we compare the cancer in a RA cohort with that in the mother population. Disclosure of Interest None Declared

Research paper thumbnail of Research Into Multiple Outliers in Linear Regression Analysis

mat.hacettepe.edu.tr

Studying the observations in regression analysis it is seen that the output of regression is affe... more Studying the observations in regression analysis it is seen that the output of regression is affected from outliers in the direction of the dependent and / or the independent variables. In this paper multiple outliers are examined in two real data sets. The results concerned with which method can determine multiple outliers better are examined with the help of some statistics and REC curve which can be used for determining efficiency. Also, the results are tried to support by using Monte Carlo Simulation.

Research paper thumbnail of Comparison of the Least Square Estimators with Their Robust Versions in Linear Calibration Problems

mat.hacettepe.edu.tr

... Keywords: Linear calibration, Classical estimator, Inverse estimator, Nazsodi esti-mator, Ali... more ... Keywords: Linear calibration, Classical estimator, Inverse estimator, Nazsodi esti-mator, Ali and Singh estimator, Srivastava and Singh estimator, Robust calibration ... Aitchison and Dunsmore [1] used the following equation, which is similar to Halperin's estimator, to estimate x0. ...