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- MakaleYalnız künye2026Minimum covariance determinant-based estimators for estimating population mean using two auxiliary variables
Zaman, Tolga; Islamoglu, Ebrucan; Bulut, Hasan
This study addresses the challenge of outliers in sample surveys, a common issue that can distort results and lead to inaccurate conclusions. To tackle this problem, researchers have developed various robust regression techniques including least trimmed squares, least median of squares, least absolute deviations, Huber’s, Hample’s and Tukey’s maximum likelihood estimators, and Huber’s maximum likelihood estimator for location and scale estimators. We propose a new approach: minimum covariance determinant-based ratio estimators for estimating the population mean in sample surveys. To assess the performance of the proposed minimum covariance determinant-based estimators, we derive their mean square error expressions and determine the conditions under which they surpass existing estimators in efficiency. To validate our theoretical findings, we conduct a numerical illustration using real-world data and perform simulations with R-Programme software. The results demonstrate that our method effectively handles outliers and improves the overall accuracy of survey-based estimations, making it a valuable tool for researchers working with sample survey data.
- MakaleYalnız künye2024An efficient Hartley–Ross type estimators of nonsensitive and sensitive variables using robust regression methods in sample surveys
Zaman, Tolga; Shazad, Usman; Yadav, Vinay Kumar
In sample surveys, the problem of outliers is one of the most frequent and widest, whose solution is required to be obtained using statistical techniques. To overcome this problem, various robust regression methods are being developed such as LTS, LMS, LAD, Huber-M, Hample-M, Tukey-M and Huber-MM methods. This article presents the modified Hartley–Ross type ratio estimators to estimate the population mean in sample surveys. The proposed design is taken into account under the two suppositions one is that the study variable is a non-sensitive variable, which means that measurements on it do not embarrass participants in personal interviews and other is the sensitive variable, which means that measurement errors are introduced as a result of a few dishonest responses. The use of scrambling response models helps to reduce these measurement errors to some extent. The proposed estimator is found to be more efficient than the existing classical estimators. A Numerical illustration was performed on a real data set in R-Program Software to support of our findings.
- MakaleAçık Erişim2020A comparison of alternative curve fitting techniques for different earthquake fault parameters of Iranian earthquakes; [Comparación de técnicas de ajuste de curvas para diferentes parámetros de fallas en terremotos en Irán]
Öztürk, Serkan; Ghassemi, Mohammad R.; Sarı, Mahmut
In this study, we tried to estimate the optimum linear equations among the parameters associated with different earthquake fault mechanisms for Iranian earthquakes. For this purpose, we tested different curve fitting methods in order to present the most proper empirical relationships between several seismic parameters for different fault systems. In the present paper, 46 large and destructive Iranian earthquakes whose magnitudes change between 5.8 and 7.8 from 1900 to 2014 were used for the analyses. A comparison was made by using four types of curve fitting techniques. The estimation procedures are considered as (1) L2 or Least Squares Regression, (2) L1 or Least Sum of Absolute Deviations Regression, (3) Robust Regression and, (4) Orthogonal Regression. Confidence intervals were selected as 95% for all types of regression relationships. In the selection of the best probability distribution, we considered the correlation coefficients of the linear regressions as a powerful and conceptually simple method. Correlation coefficients of all relationships change between 0.299 and 0.986 with Orthogonal regression, between 0.168 and 0.792 with L1 regression, between 0.059 and 0.829 with Robust regression. For Iranian earthquakes, the most suitable and reliable empirical relationships between moment magnitude (Mw) and surface wave magnitude (Ms), Mw and surface rupture length (SRL), Mw and maximum displacement (MD), and SRL and MD were obtained by Orthogonal regression since it supplies stronger correlation coefficients than those of the other regression techniques in most estimates. The results show that estimated empirical relationships among the different fault parameters by using the Orthogonal regression method can be accepted as more up-to-date and more appropriate in comparison with the other regression norms. Consequently, these equations were suggested as more reliable in the estimation of the maximum surface displacement, maximum surface rupture length and associated with the maximum credible earthquakes for different areas of Iran. Furthermore, obtained relationships can be statistically significant for the assessment of seismic, tectonic and geologic activities, and they can be used to evaluate the rupture hazard of the Iranian Plateau.
- MakaleYayıncıda açık erişim2014A New Empirical Relation between Surface Wave Magnitude and Rupture Length for Turkey Earthquakes
Öztürk, Serkan
Many practical problems encountered in quantitative oriented disciplines entail finding the best approximate solution to an over determined system of linear equations. In this study, it is investigated the usage of different regression methods as a theoretical, practical and correct estimation tool in order to obtain the best empirical relationship between surface wave magnitude and rupture length for Turkey earthquakes. For this purpose, a detailed comparison is made among four different regression norms: (1) Least Squares, (2) Least Sum of Absolute Deviations, (3) Total Least Squares or Orthogonal and, (4) Robust Regressions. In order to assess the quality of the fit in a linear regression and to select the best empirical relationship for data sets, the correlation coefficient as a quite simple and very practicable tool is used. A list of all earthquakes where the surface wave magnitude (Ms) and surface rupture length (L) are available is compiled. In order to estimate the empirical relationships between these parameters for Turkey earthquakes, loglinear fit is used and following equations are derived from different norms: Ms = 1.02* LogL + 5.18, for L-2 Norm regression (R-2=0.71), Ms = 1.15* LogL + 4.98, for L-1 Norm regression (R-2=0.92), Ms = 1.04* LogL + 5.15, for Robust regression (R-2=0.75), Ms = 1.25* LogL + 4.86, for Orthogonal regression (R-2=0.68), Consequently, the empirical equation given by the Least Sum of Absolute Deviations regression as Ms = 1.15* LogL + 4.98 with a strong correlation coefficient (R-2=0.92) can be thought as more suitable and more reliable for Turkey earthquakes. Also, local differences in rupture length for a given magnitude can be interpreted in terms of local variation in geologic and seismic efficiencies. Furthermore, this result suggests that seismic efficiency in a region is dependent on rupture length or magnitude.