Tolga ZAMAN | Cankiri Karatekin University (original) (raw)

Papers by Tolga ZAMAN

Mathematical Problems in Engineering

Many authors defined the modified version of the mean estimator by using two auxiliary variables.... more Many authors defined the modified version of the mean estimator by using two auxiliary variables. These proposed estimators highly depend on the calculated regression coefficients. In the presence of outliers, these estimators do not give satisfactory results. In this study, we improve the suggested estimators using several robust regression techniques while obtaining the regression coefficients. We compared the efficiencies between the suggested estimators and the estimators presented in the literature. We used two numerical examples and a simulation study to support these theoretical results. Empirical results show that the modified ratio estimator performs well in the presence of outliers when adopting robust regression techniques.

Mathematical Problems in Engineering

New class of exponential estimators for finite population mean in two-phase sampling New class of exponential estimators for finite population mean in two-phase sampling, 2019

This paper suggests a new family of exponential estimators in the two-phase sampling using the in... more This paper suggests a new family of exponential estimators in the two-phase sampling using the information of an auxiliary attribute. Theoretically, we obtain the mean square error (MSE) for these estimators. We compare the MSE equations of the proposed exponential ratio families of estimators with the MSE equations of the ratio estimators in literature. As a result of these comparisons, we observe that the proposed families of estimators give more efficient results than the estimators in literature for the determined conditions obtained in theory. In addition, these theoretical results are supported by an application with original data sets.

Novel family of exponential estimators using information of auxiliary attribute Novel family of exponential estimators using information of auxiliary attribute, 2019

In this article, we propose a family of exponential ratio estimators for the estimation of the po... more In this article, we propose a family of exponential ratio estimators for the estimation of the population mean of the study variable using the information of the population proportion possessing the certain attributes. We obtain the mean squared error (MSE) equations for all proposed ratio exponential estimators and find theoretical conditions that make the proposed estimators more efficient than the Naik and Gupta (1996) estimator and the ratio exponential estimator suggested by Singh et al. (2007). In addition, these conditions are supported by an application with original data sets. Subject Classification: 62D05, 62G05

IMPROVED ESTIMATORS USING COEFFICIENT OF SKEWNESS OF AUXILIARY ATTRIBUTE, 2019

In this paper, some ratio estimators for the population mean using known coefficient of skewness ... more In this paper, some ratio estimators for the population mean using known coefficient of skewness based on auxiliary attribute have been proposed and these have been developed by combining ratio estimators for estimating population mean of variate of study using the procedure given in Kadilar and Cingi (2006). The mean square error (MSE) equations for suggested estimators have been derived and it has been concluded that the suggested estimators always perform better than the ratio estimators, given in Sections 1 and 2. The results are also supported by the three original datasets.

EFFICIENT ESTIMATORS OF POPULATION MEAN USING AUXILIARY ATTRIBUTE IN STRATIFIED RANDOM SAMPLING, 2019

This paper suggests new ratio estimators in stratified random sampling using the information of a... more This paper suggests new ratio estimators in stratified random sampling using the information of an auxiliary attribute. Theoretically, it is obtained the bias and mean square error (MSE) for these estimators and compare them with the MSE of classical combined ratio estimator. By these comparisons, it is demonstrated that proposed estimators are more efficient than the considered estimators. In addition, these theoretical results are supported with the aid of numerical examples.

Investigating the Significance of a Correlation Coefficient using Bootstrap Estimates, 2019

Resampling methods offers effective estimates of parameters and its asymptotic distribution. In ... more Resampling methods offers effective estimates of parameters and its asymptotic distribution. In this study, it is recommended to use the bootstrap method as an alternative to the classical and knife (one exclusion procedure) test statistics in evaluating the significance of the Pearson correlation coefficient by applying the bootstrap method to the simple linear regression model. This procedure provides an effective alternative to test the significance of the Pearson correlation coefficient. In the application, the model parameters, standard errors, Pearson coefficients of correlation, bias and % 95 confidence intervals belonging to bootstrap and jackknife methods in estimated with the help of a real data and the obtained results are interpreted. As a result, the test statistic obtained by the bootstrap method is proposed as an alternative to the classical and jackknife test statistics.

Improvement in Estimating the Population Mean in Simple Random Sampling using Coefficient of Skewness of Auxiliary Attribute, 2019

This paper suggested a new family of estimators for the population mean in the simple random samp... more This paper suggested a new family of estimators for the population mean in the simple random sampling using the information of an auxiliary attribute. Theoretically, the mean square error (MSE) equations were obtained and it was shown that all the suggested ratio estimators are more efficient than some known estimators. These results were also supported by two original data sets.

This article proposes new regression-type estimators by considering Tukey-M, Hampel M, Huber MM, ... more This article proposes new regression-type estimators by considering Tukey-M, Hampel M, Huber MM, LTS, LMS and LAD robust methods and MCD and MVE robust covariance matrices in stratified sampling. Theoretically, we obtain the mean square error (MSE) for these esti-mators. We compare the efficiencies based on MSE equations, between the proposed estimators and the traditional combined and separate regression estimators. As a result of these comparisons, we observed that our proposed estimators give more efficient results than traditional approaches. And, these theoretical results are supported with the aid of numerical examples and simulation based on data sets that include outliers.

COMPARISON OF RESAMPLING METHODS IN MULTIPLE LINEAR REGRESSION, 2019

In order to estimate model parameters in multiple regression models, resampling methods of bootst... more In order to estimate model parameters in multiple regression models, resampling methods of bootstrap and jackknife are used. Resampling methods are used as an alternative readjustment method to the least squares method (OLS) especially when assumptions belonging to error term in regression analysis are not met. Data used in the study are taken from 25 advertisements in Sahibinden.com website and the price of beetle car brand is accepted as dependent variable for multiple linear regression models. It is aimed that price variable taken is tried to be explained with the help of variables of fuel, case type, salesman, sunroof, wind shield, upholstery, age and engine size. When we examined the variables, it is seen that categorical variables are in question and dummy variable must be used. Firstly, model parameters of this obtained data are estimated using OLS and significances of parameters are tested, then, model parameters, significances of estimated parameters, coefficient of determination, and standard error of the model and % 90 confidence intervals are estimated using one of the resampling methods, bootstrap and jackknife method and results belonging to these three methods are compared. Also, generalization condition, which is to the population, of parameter estimation results belonging to explanatory variables used in this study are reviewed with the help of jackknife resampling method ve It has been seen that the salesman and upholstery independent variables have a considerable effect at a significance level of .10 on the dependent variable of price dependence of decision making (p < .10) and Jackknife have confirmed these generalization.

Determining the Factors that Influence Gini Coefficient by Beta Regression Method, 2019

Öz Bu çalışmanın amacı bazı gelişmiş ve gelişmekte olan ülkelere ait, Gini katsayısı üzerinde etk... more Öz Bu çalışmanın amacı bazı gelişmiş ve gelişmekte olan ülkelere ait, Gini katsayısı üzerinde etkisi olan makroekonomik değişkenleri belirlemektir. Bir ülkede milli gelirin dağılımının eşit olup olmadığını ölçmeye yarayan Gini Katsayısı, 0 ila 1sayıları arasında değerler alır. Çalışmada bağımlı değişken olan Gini katsayısı 0-1 aralığında oransal değerler aldığı için modelleme aşamasında Beta Regresyon Analizi uygulanmıştır. Analiz sonuçlarına göre ilgilenilen ülkelerin Gini katsayıları üzerinde anlamlı etkisi bulunan değişkenler tespit edilip, çeşitli yorumlamalar yapılmıştır. Analiz R programlama dili yardımıyla gerçekleştirilmiştir. Abstract The purpose of this study is to identify the macroeconomic variables of some developed and developing countries that have an impact on the Gini coefficient. The Gini Coefficient, which measures the distribution of income in a country, is between 0 and 1. Beta Regression Analysis was applied at the modeling stage since the Gini coefficient, which is dependent variable in the study, received the proportional values on the interval 0-1. According to the results of the analysis, the variables that have a significant effect on the Gini coefficients of the countries concerned were determined and various interpretations were made. The analysis was performed with the aid of the R programming language.

New family of estimators using two auxiliary attributes, Dec 7, 2018

Utilizing the estimators in Singh and Malik (Appl. Math. Computed. 219, (2013), 10948) and Kadila... more Utilizing the estimators in Singh and Malik (Appl. Math. Computed. 219, (2013), 10948) and Kadilar and Cingi (Appl. Math. Computed. 162 (2005), 902), It is proposed estimators using two auxiliary attributes in simple random sampling. It is obtained mean square error (MSE) equation of these estimators. Theoretically, it is compared with the MSE of proposed estimators and the MSE of traditional regression estimators using two auxiliary attributes. As a result of these comparisons, It is observed that the proposed estimators give more efficient results than the traditional regression estimators. Also, under all conditions, all of the proposed estimators more efficient than the traditional regression estimators. And, these theoretical results are supported by an application with original data.

This study examines robust regression methods which are used for the solution of problems caused ... more This study examines robust regression methods which are used for the solution of problems caused by the situations in which the assumptions of LSM technique, which is commonly used for the prediction of linear regression models, cannot be used. Robust estimators are not influenced by small deviations and discrepancies. For this purpose, some robust regression techniques which are used in situations in which the assumptions cannot be made were introduced and parameter estimation algorithms of these techniques were analyzed. Regression models of the methods of Lad, Weighted –M regression, Theil regression and Least Median Squares, coefficients of determination and average absolute deviations were calculated and the results were discussed as to which of these methods gave better results.
Özet Bu çalışmada doğrusal regresyon modellerinin tahmininde yaygın olarak kullanılan EKK tekniğinin varsayımlarının sağlanmamasından kaynaklanan problemlerin çözümü için kullanılan Robust regresyon yöntemleri incelenmiştir. Robust tahmin ediciler küçük sapmalardan, aykırılıklardan etkilenmezler. Bu amaçla, çalışmada varsayımların sağlanmadığı durumlarda kullanılan bazı robust regresyon teknikleri tanıtılmıştır ve bu tekniklere ait parametre tahmin algoritmaları incelenmiştir. Uygulamada Lad, Ağırlıklı –M regresyon, Theil regresyon ve En küçük Medyan Kareler yöntemlerine ait regresyon modeli, belirleme katsayıları ve ortalama mutlak sapmalar hesaplanmış olup, bu tahmin edicilerden hangisinin daha iyi sonuç verdiği tartışılmıştır.

The purpose of this study was to examine the burnout levels of research assistants in Ondokuz May... more The purpose of this study was to examine the burnout levels of research assistants in Ondokuz Mayıs University and to examine the results of multiple linear regression model based on the results obtained from Maslach Burnout Scale with Jackknife Method in terms of validity and genera-lizability. To do this, a questionnaire was given to 11 research assistants working at Ondokuz Mayıs University and the burnout scores of this questionnaire were taken as the dependent variable of the multiple linear regression model. The variable of burnout was explained with the variables of age, weekly hours of classes taught, monthly average credit card debt, numbers of published articles and reports, gender, marital status, number of children and the departments of the research assistants. Dummy variables were assigned to the variables of gender, marital status, number of children and the departments of the research assistants and thus, they were made quantitative. The significance of the model as a result of multiple linear regressions was examined through backward elimination method. After this, for the five explanatory variables which influenced the variable of burnout, standardized model coefficients and coefficients of determination, and 95% confidence intervals of these values were estimated through Jackknife Method and the ge-neralizability of the parameter estimation results of these variables on population was researched.

In this study, the use of taylor series method in the calculation of some means with single auxil... more In this study, the use of taylor series method in the calculation of some means with single auxiliary variable developed in a simple random sampling and mean square error unit ratio estimators having certain properties was investigated. An application was performed in respect thereof. The study population (mass) included 111 secondary schools from 18 districts of Trabzon province. Auxiliary variable (x) was taken as the number of students whereas the main variable (y) was taken as the number of teachers. Sample size was calculated as 45 for unit ratio that has certain features. Afterwards, theoretically proposed mean and units ratio estimators having certain properties were compared numerically. Random sampling was performed using the SPSS 20 program thus giving an equal chance to the units sampled and variability in the population was protected.

Modified ratio estimators using robust regression methods, 2018

Whenthereisanoutlierinthedataset,theefficiencyoftraditionalmethodsdecreases.Inordertosolvethispro... more Whenthereisanoutlierinthedataset,theefficiencyoftraditionalmethodsdecreases.Inordertosolvethisproblem,Kadilaretal.(2007)adapted Huber-M method which is only one of robust regression methods to ratio-typeestimatorsanddecreasedtheeffectofoutlierproblem.Inthis study,newratio-typeestimatorsareproposedbyconsideringTukey-M, HampelM,HuberMM,LTS,LMSandLADrobustmethodsbasedonthe Kadilaretal.(2007).Theoretically,weobtainthemeansquareerror(MSE) fortheseestimators.WecomparedwithMSEvaluesofproposedestimatorsandMSEvaluesofestimatorsbasedonHuber-MandOLSmethods. As a result of these comparisons, we observed that our proposed estimators give more efficient results than both Huber M approach which wasproposedbyKadilaretal.(2007)andOLSapproach.Also,underall conditions,alloftheotherproposedestimatorsexceptLadmethodare more efficient than robust estimators proposed by Kadilar et al. (2007). And,thesetheoreticalresultsaresupportedwiththeaidofanumerical exampleandsimulationbybasingondatathatincludesanoutlier.

Bu çalışmanın amacı Türkiye'de " Vosvos " ya da " Kaplumbağa " olarak da adlandırılan Beetle araç... more Bu çalışmanın amacı Türkiye'de " Vosvos " ya da " Kaplumbağa " olarak da adlandırılan Beetle araçların fiyatını etkileyen faktörleri belirlemektir. Beetle özellikle ikinci el piyasasında son model araçlardan daha pahalı olabilmektedir. Aracın tercih edilmesindeki temek etken diğer otomobiller gibi kişisel konfor, güvenlik, uygun fiyat vb. özelliklerden ziyade, tamamen kişisel haz duygusu ve estetik kaygılardır. Bu bakımdan otomobil özel bir hayran kitlesine sahiptir. Beetle araçların fiyatını etkileyen faktörlerin belirlenmesinde hedonik fiyat model yaklaşımı tercih edilmiştir. Çünkü hedonik fiyat modeli kişisel haz duygusunu tatmin etmek için satın alınan heterojen malların fiyatını etkileyen faktörlerin belirlenmesinde kullanılmaktadır. Ancak Türkiye piyasasında bulunan araçların hem yaşları, hem özellikleri hem de restorasyon durumları çok farklı olduğundan fiyatlar arasında büyük farklılıklar vardır. Bu durumun veri setinde aykırı değer sorununa neden olabileceği düşünüldüğünden çalışmada klasik ve robust hedonik fiyat modellerinden yararlanılmıştır. Ayrıca çalışmadan elde edilen sonuçlar ile bir fiyat tahmin robotu oluşturulmuştur. Böylece çalışmanın sonuçlarının teorik olarak başarılı olmasının yanı sıra, günlük hayata ve ekonomiye de katkı sağlayacağı düşünülmektedir. Abstract The aim of this study is to determine the factors which affects the price of Beetle vehicles named also " Vosvos " or " Kaplumbağa " (Tortoise) in Turkey. It is also possible for Beetle to be more expensive than the top model cars especially in the spot market. The main reason of fondness of the beetle is entirely related to personal pleasure and aesthetics rather than to features such as personal comfort, security, affordable price etc. like in other cars. In this regard, this car has a special fan base. Hedonic price model approach is used to determine the factors which affects the prices of Beetle model cars. Because hedonic price model is used to determine the factor which affects the prices of heterogeneous goods that are bought to satisfy personal pleasure. However, since the cars in Turkey market are different in the sense of their ages, features and restoration states, there are wide differences among prices of them. The fact that this situation can cause outlier problem in the data set is the reason which we used classical and robust hedonic price model in the study for. Also, the results obtained from the study is used to create a price estimator robot. Therefore, results of the study are not only theoretically successful but also a support to daily life and the economy.

This paper proposes some ratio estimators for population mean using known skewness coefficient of... more This paper proposes some ratio estimators for population mean using known skewness coefficient of auxiliary attribute. Theoretically, it is obtained mean square error (MSE) equations for all proposed estimators. The efficiency between the suggested estimators and some known estimators is compared. The theoretical findings are also supported by a numerical examples using original data sets.

T h e r e a r e s e v e r a l r a ti o e s ti m a t o r s t h a t e s ti m a t e t h e p o p u l ... more T h e r e a r e s e v e r a l r a ti o e s ti m a t o r s t h a t e s ti m a t e t h e p o p u l a ti o n m e a n o f s t u d y v a r i a b l e b y u s i n g information about a population proportion possessing certain attributes. However when there are outliers in the data, the efficiency of the estimators decreases. F o r t h i s r e a s o n , w e a d a p t l e a s t m e d i a n o f s q u ares ( L M S ) e s ti m a ti o n t o t h e p r o p o s e d e s ti m a t o r s b y S i n g h e t a l. ( R a ti o E s ti m a t o r s i n S i m p l e R a n d o m Sampling Using Informati on on Auxiliary Attribute, Pak. J.stat.oper.res , 2 0 0 8 ). T h e o r e ti c a ll y , w e o b t a i n the mean square error (MSE) for these estimators and w e c o m p a r e M S E e q u a ti o n s o f o u r s u g g e s t e d estimators and the proposed estimators by Singh et al. (2008). As a result of these comparisons, we observe t h a t s u g g e s t e d e s ti m a t e s g i v e m o r e e f fi c i e n t r e s u lt s t h a n e s ti m a t e s o f S i n g e t. a l. ( 2 0 0 8 ) a n d t h e s e theo r e ti c a l r e s u lt s a r e s u p p o r t e d w it h t h e a i d o f a numerical example and simulation by basing on data that includes an outlier.

A stochastic model consisting of two heterogeneous channels and having no waiting room in front o... more A stochastic model consisting of two heterogeneous channels and having no waiting room in front of each is considered. A customer who has completed his service in channel 1 while channel 2 is busy blocks channel 1 with probability í µí± or leaves the system with 1−í µí± probability. This model was analysed: expected number of customer and loss probability of customer are calculated and optimal ordering of channels minimizing parameters has been found. Additionally, this model was simulated; furthermore, simulated and exact results of loss probabilities of customers were given in the tables.