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1.
We propose a new ratio type estimator for estimating the finite population mean using two auxiliary variables in stratified two-phase sampling. Expressions for bias and mean squared error of the proposed estimator are derived up to the first order of approximation. The proposed estimator is more efficient than the usual stratified sample mean estimator, traditional stratified ratio estimator and some other stratified estimators including Bahl and Tuteja (1991 Bahl, S., Tuteja, R. K. (1991). Ratio and product type exponential estimators. Information and Optimization Sciences 12:159163. [Google Scholar]), Chami et al. (2012 Chami, P. S., Singh, B., Thomas, D. (2012). A two-prameter ratio-product-ratio estimator using auxiliary information. ISRN Probability and Statistics 2012:115, doi: 10.5402/2012/103860.[Crossref] [Google Scholar]), Chand (1975 Chand, L. (1975) Some Ratio Type Estimator Based on two or more Auxiliary Variables, Ph.D. dissertation, Iowa State University, Ames, Iowa (unpublished). [Google Scholar]), Choudhury and Singh (2012 Choudhury, S., Singh, B. K. (2012). A class of chain ratio-product type estimators with two auxiliary variables under double sampling scheme. Journal of the Korean Statistical Society 41:247256. [Google Scholar]), Hamad et al. (2013 Hamad, N., Hanif, M., Haider, N. (2013). A regression type estimator with two auxiliary variables for two-phase sampling. Open Journal of Statistics, 3:7478. [Google Scholar]), Vishwakarma and Gangele (2014 Vishwakarma, G. K., Gangele, R. K. (2014). A class of chain ratio-type exponential estimators in double sampling using two auxiliary variates. Applied Mathematics and Computation 227:171175. [Google Scholar]), Sanaullah et al. (2014 Sanaullah, A., Ali, H. M., Noor ul Amin, M., Hanif, M. (2014). Generalized exponential chain ratio estimators under stratified two-phase random sampling. Applied Mathematics and Computation 226:541547. [Google Scholar]), and Chanu and Singh (2014 Chanu, W. K., Singh, B. K. (2014). Improved class of ratio-cum-product estimators of finite population mean in two phase sampling. Global Journal of Science Frontier Research: F Mathematics and Decision Sciences 14(2):114. [Google Scholar]).  相似文献   

2.
When a sufficient correlation between the study variable and the auxiliary variable exists, the ranks of the auxiliary variable are also correlated with the study variable, and thus, these ranks can be used as an effective tool in increasing the precision of an estimator. In this paper, we propose a new improved estimator of the finite population mean that incorporates the supplementary information in forms of: (i) the auxiliary variable and (ii) ranks of the auxiliary variable. Mathematical expressions for the bias and the mean-squared error of the proposed estimator are derived under the first order of approximation. The theoretical and empirical studies reveal that the proposed estimator always performs better than the usual mean, ratio, product, exponential-ratio and -product, classical regression estimators, and Rao (1991 Rao, T.J. (1991). On certail methods of improving ration and regression estimators. Commun. Stat. Theory Methods 20(10):33253340.[Taylor &; Francis Online], [Web of Science ®] [Google Scholar]), Singh et al. (2009 Singh, R., Chauhan, P., Sawan, N., Smarandache, F. (2009). Improvement in estimating the population mean using exponential estimator in simple random sampling. Int. J. Stat. Econ. 3(A09):1318. [Google Scholar]), Shabbir and Gupta (2010 Shabbir, J., Gupta, S. (2010). On estimating finite population mean in simple and stratified random sampling. Commun. Stat. Theory Methods 40(2):199212.[Taylor &; Francis Online], [Web of Science ®] [Google Scholar]), Grover and Kaur (2011 Grover, L.K., Kaur, P. (2011). An improved estimator of the finite population mean in simple random sampling. Model Assisted Stat. Appl. 6(1):4755. [Google Scholar], 2014) estimators.  相似文献   

3.
ABSTRACT

This paper addresses the problem of estimating the population mean on the current occasion in two occasion successive sampling. Based on all the readily available information from first and second occasions, a class of estimators is proposed with its properties. It is identified that the estimator recently suggested by Singh and Homa (Journal of Statistical Theory and Practice, 7: 1, 146–155, 2013) is a member of the suggested class of estimators. The correct expression of the mean squared error/variance of the Singh and Homa (2013 Singh, G.N., Homa, F. (2013). Effective rotation patterns in successive sampling over two – occasions. J. Stat. Theor. Pract. 7:146155.[Taylor & Francis Online] [Google Scholar]) estimator is given. The superiority of the suggested class of estimators is discussed with the sample mean estimator when there is no matching, the best combined estimator given in Cochran (1977 Cochran, W.G. (1977). Sampling Techniques. Third edition, New York: Wiley Eastern Limited. [Google Scholar], p.346) and Singh and Homa (2013 Singh, G.N., Homa, F. (2013). Effective rotation patterns in successive sampling over two – occasions. J. Stat. Theor. Pract. 7:146155.[Taylor & Francis Online] [Google Scholar]) estimator. Optimum replacement policy has been discussed. Numerical illustration is given in support of the present study.  相似文献   

4.
This paper considers the estimation of parameters of AR(p) models for time series with t-distribution via EM-based algorithms. The paper develops asymptotic properties for the estimation to show that the estimators are efficient. Also testing theory for the estimators is considered. The robustness of the estimators and various tests to deviations from an assumed model is investigated. The study shows that the algorithms have equal estimation efficiency even if the error distribution is miss-specified or perturbed by outliers. Interestingly, the estimators from these algorithms performed better than that of the Modified Maximum Likelihood (MML) considered in Tiku et al. (2000 Tiku, M. L., Wong, W. K., Vaughan, D. C., Bian, G. (2000). Time series models in non-normal situations: Symmetric innovations. Journal of Time Series Analysis, 21: 571596. [Google Scholar]).  相似文献   

5.
This article considers the problem of estimating the population mean on the current (second) occasion using multi-auxiliary information in successive sampling over two occasions. A general class of estimators is proposed for estimating population mean on the current occasion and expressions for bias and mean square error for these estimators are obtained up to first degree of approximation. The minimum variance bound estimator in the proposed class is discussed. Many popular estimators have been shown to belong to this class. Optimum replacement policy is also discussed. Finally, the superiority of the proposed class of estimators over multivariate version of chain type ratio estimator envisaged by Singh (2005 Singh, G.N. (2005). On the use of chain type ratio estimator in successive sampling. Stat Transition 7:2126. [Google Scholar]) is established empirically.  相似文献   

6.
This article addresses the problem of estimating the finite population mean in stratified random sampling using auxiliary information. Motivated by Singh (1967 Singh , M. P. ( 1967 ). Ratio cum product method of estimation . Metrika 12 : 3442 .[Crossref] [Google Scholar]) and Bahl and Tuteja (1991 Bahl , S. , Tuteja , R. K. ( 1991 ). Ratio and product type exponential estimator . Inform. Optimiz. Sci. 12 ( 1 ): 159163 .[Taylor &; Francis Online] [Google Scholar]) a ratio-cum-product type exponential estimator has been suggested and its bias and mean squared error have been derived under large sample approximation. Suggested estimator has been compared with usual unbiased estimator of population mean in stratified random sampling, combined ratio estimator, combined product estimator, ratio and product type exponential estimator of Singh et al. (2008 Singh , R. , Kumar , M. , Singh , R. D. , Chaudhary , M. K. ( 2008 ). Exponential ratio type estimators in stratified random sampling. Presented in International Symposium on Optimisation and Statistics (I.S.O.S) at A.M.U., Aligarh, India, during 29–31 Dec . [Google Scholar]). Conditions under which suggested estimator is more efficient than other considered estimators have been obtained. A numerical illustration is given in support of the theoretical findings.  相似文献   

7.
This article considers some classes of estimators of the population median of the study variable using information on an auxiliary variable with their properties under large sample approximation. Asymptotic optimum estimator (AOE) in each class of estimators has been investigated along with the approximate mean square error formulae. It has been shown that the proposed classes of estimators are better than these considered by Gross (1980 Gross , T. S. ( 1980 ). Median estimation in sample surveys. Proc. Surv. Res. Meth. Sect. Amer. Statist. Assoc. 181–184 . [Google Scholar]), Kuk and Mak (1989 Kuk , A. Y. C. , Mak , T. K. ( 1989 ). Median estimation in the presence of auxiliary information . J. Roy. Statist. Soc. Ser. B51 : 261269 . [Google Scholar]), Singh et al. (2003a Singh , H. P. , Singh , S. , Joarder , A. H. ( 2003a ). Estimation of population median when mode of an auxiliary variable is known . J. Statist. Res. 37 ( 1 ): 5763 . [Google Scholar]), and Al and Cingi (2009 Al , S. , Cingi , H. ( 2009 ). New estimators for the population median in simple random sampling. Tenth Islamic Countries Conference on Statistical Sciences, held in New Cairo, Egypt . [Google Scholar]). An empirical study is carried out to judge the merits of the suggested class of estimators over other existing estimators.  相似文献   

8.
ABSTRACT

The article suggests a class of estimators of population mean in stratified random sampling using auxiliary information with its properties. In addition, various known estimators/classes of estimators are identified as members of the suggested class. It has been shown that the suggested class of estimators under optimum condition performs better than the usual unbiased, usual combined ratio, usual combined regression, Kadilar and Cingi (2005 Kadilar, C., Cingi, H. (2005). A new ratio estimator in stratified sampling. Commun. Stat. Theory Methods 34:597602.[Taylor & Francis Online], [Web of Science ®] [Google Scholar]), Singh and Vishwakarma (2006 Singh, H.P., Vishwakarma, G.K. (2006). Combined ratio-product estimator of finite population mean in stratified sampling. Metodologia de Encuestas Monografico: Incidencias en el trabjo de Campo 7(1):3240. [Google Scholar]) estimators and the members belonging to the classes of estimators envisaged by Kadilar and Cingi (2003 Kadilar, C., Cingi, H. (2003). Ratio estimator in stratified sampling. Biomet. J. 45:218225.[Crossref], [Web of Science ®] [Google Scholar]), Singh, Tailor et al. (2008 Singh, H.P., Agnihotri, N. (2008). A general procedure of estimating population mean using auxiliary information in sample surveys. Stat. Trans. 9(1):7187. [Google Scholar]), Singh et al. (2009 Singh, R., Kumar, M., Chaudhary, M.K., Kadilar, C. (2009). Improved exponential estimator in stratified random sampling. Pak. J. Stat. Oper. Res. 5(2):6782.[Crossref] [Google Scholar]), Singh and Vishwakarma (2010 Singh, H.P., Vishwakarma, G.K. (2010). A general procedure for estimating the population mean in stratified sampling using auxiliary information. METRON 67(1):4765.[Crossref] [Google Scholar]) and Koyuncu and Kadilar (2010) Koyuncu, N., Kadilar, C. (2010). On improvement in estimating population mean in stratified random sampling. J. Appl. Stat. 37(6):9991013.[Taylor & Francis Online], [Web of Science ®] [Google Scholar].  相似文献   

9.
This paper addresses the problem of estimating a general parameter using information on an auxiliary variable X. We have suggested a class of exponential-type ratio estimators for the parameter and its properties are studied. It is identified that the estimators due to Upadhyaya et al. [Journal of Statistical Theory and Practice (2011), 5(2), 285–302] and Yadav and Kadilar [Revista Columbiana de Estadistica, (2013), 36(1), 145–152] are members of the proposed estimator. We have also shown that the suggested estimator is more efficient than the estimators of Upadhyaya et al. (2011 Upadhyaya, L.N., Singh, H.P., Chatterjee, S., Yadav, R. (2011). Improved ratio and product exponential type estimators. J. Stat. Theo. Pract. 5 (2): 285302.[Taylor &; Francis Online] [Google Scholar]) and Yadav and Kadilar (2013 Yadav, S.K., Kadilar, C. (2013). Improved exponential type ratio estimator of population variance. Revis. Colum. de Estadist. 36(1): 145152. [Google Scholar]). Numerical illustration is provided in support of the present study.  相似文献   

10.
This paper aimed at providing an efficient new unbiased estimator for estimating the proportion of a potentially sensitive attribute in survey sampling. The suggested randomization device makes use of the means, variances of scrambling variables, and the two scalars lie between “zero” and “one.” Thus, the same amount of information has been used at the estimation stage. The variance formula of the suggested estimator has been obtained. We have compared the proposed unbiased estimator with that of Kuk (1990 Kuk, A.Y.C. (1990). Asking sensitive questions inderectely. Biometrika 77:436438.[Crossref], [Web of Science ®] [Google Scholar]) and Franklin (1989 Franklin, L.A. (1989). A comparision of estimators for randomized response sampling with continuous distribution s from a dichotomous population. Commun. Stat. Theor. Methods 18:489505.[Taylor &; Francis Online], [Web of Science ®] [Google Scholar]), and Singh and Chen (2009 Singh, S., Chen, C.C. (2009). Utilization of higher order moments of scrambling variables in randomized response sampling. J. Stat. Plann. Inference. 139:33773380.[Crossref], [Web of Science ®] [Google Scholar]) estimators. Relevant conditions are obtained in which the proposed estimator is more efficient than Kuk (1990 Kuk, A.Y.C. (1990). Asking sensitive questions inderectely. Biometrika 77:436438.[Crossref], [Web of Science ®] [Google Scholar]) and Franklin (1989 Franklin, L.A. (1989). A comparision of estimators for randomized response sampling with continuous distribution s from a dichotomous population. Commun. Stat. Theor. Methods 18:489505.[Taylor &; Francis Online], [Web of Science ®] [Google Scholar]) and Singh and Chen (2009 Singh, S., Chen, C.C. (2009). Utilization of higher order moments of scrambling variables in randomized response sampling. J. Stat. Plann. Inference. 139:33773380.[Crossref], [Web of Science ®] [Google Scholar]) estimators. The optimum estimator (OE) in the proposed class of estimators has been identified which finally depends on moments ratios of the scrambling variables. The variance of the optimum estimator has been obtained and compared with that of the Kuk (1990 Kuk, A.Y.C. (1990). Asking sensitive questions inderectely. Biometrika 77:436438.[Crossref], [Web of Science ®] [Google Scholar]) and Franklin (1989 Franklin, L.A. (1989). A comparision of estimators for randomized response sampling with continuous distribution s from a dichotomous population. Commun. Stat. Theor. Methods 18:489505.[Taylor &; Francis Online], [Web of Science ®] [Google Scholar]) estimator and Singh and Chen (2009 Singh, S., Chen, C.C. (2009). Utilization of higher order moments of scrambling variables in randomized response sampling. J. Stat. Plann. Inference. 139:33773380.[Crossref], [Web of Science ®] [Google Scholar]) estimator. It is interesting to mention that the “optimum estimator” of the class of estimators due to Singh and Chen (2009 Singh, S., Chen, C.C. (2009). Utilization of higher order moments of scrambling variables in randomized response sampling. J. Stat. Plann. Inference. 139:33773380.[Crossref], [Web of Science ®] [Google Scholar]) depends on the parameter π under investigation which limits the use of Singh and Chen (2009 Singh, S., Chen, C.C. (2009). Utilization of higher order moments of scrambling variables in randomized response sampling. J. Stat. Plann. Inference. 139:33773380.[Crossref], [Web of Science ®] [Google Scholar]) OE in practice while the proposed OE in this paper is free from such a constraint. The proposed OE depends only on the moments ratios of scrambling variables. This is an advantage over the Singh and Chen (2009 Singh, S., Chen, C.C. (2009). Utilization of higher order moments of scrambling variables in randomized response sampling. J. Stat. Plann. Inference. 139:33773380.[Crossref], [Web of Science ®] [Google Scholar]) estimator. Numerical illustrations are given in the support of the present study when the scrambling variables follow normal distribution. Theoretical and empirical results are very sound and quite illuminating in the favor of the present study.  相似文献   

11.
This paper is based on the application of a Bayesian model to a clinical trial study to determine a more effective treatment to lower mortality rates and consequently to increase survival times among patients with lung cancer. In this study, Qian et al. [13 J. Qian, D.K. Stangl, and S. George, A Weibull model for survival data: Using prediction to decide when to stop a clinical trial, in Bayesian Biostatistics, D. Berry and D. Stangl, eds., Marcel Dekker, New York, 1996, pp. 187205. [Google Scholar]] strived to determine if a Weibull survival model can be used to decide whether to stop a clinical trial. The traditional Gibbs sampler was used to estimate the model parameters. This paper proposes to use the independent steady-state Gibbs sampling (ISSGS) approach, introduced by Dunbar et al. [3 M. Dunbar, H.M. Samawi, R. Vogel, and L. Yu, A more efficient Gibbs sampler estimation using steady state simulation: Application to public health studies, J. Stat. Simul. Comput. 10.1080/00949655.2013.770857.[Taylor &; Francis Online] [Google Scholar]], to improve the original Gibbs sampler in multidimensional problems. It is demonstrated that ISSGS provides accuracy with unbiased estimation and improves the performance and convergence of the Gibbs sampler in this application.  相似文献   

12.
ABSTRACT

In this article, we propose a generalized ratio-cum-product type exponential estimator for estimating population mean in stratified random sampling. Asymptotic expression of the bias and mean squared error of the proposed estimator are obtained. Asymptotic optimum estimator in the proposed estimator has been obtained with its mean squared error formula. Conditions under which the proposed estimator is more efficient than usual unbiased estimator, combined ratio and product type estimators, Singh et al. (2008 Singh, R., Kumar, M., Singh, R.D., Chaudhary, M.K. (2008). Exponential ratio type estimators in stratified random sampling. Presented in International Symposium on Optimisation and Statistics (I.S.O.S) at A.M.U., Dec. 2008, 2931, Aligarh, India. [Google Scholar]) estimators and Tailor and Chouhan (2014 Tailor, R., Chouhan, S. (2014). Ratio-cum-product type exponential estimator of finite population mean in stratified random sampling. Commun. Statist. Theor. Meth. 43:343354.[Taylor & Francis Online], [Web of Science ®] [Google Scholar]) estimator are obtained. An empirical study has also been carried out.  相似文献   

13.
ABSTRACT

For a trivariate distribution, an efficient family of estimators of median of study variable using the known information on the auxiliary variables has been proposed under two-phase sampling design. The expressions for bias and its mean square error have been obtained up to first order of approximation. It has been shown that the proposed estimator has smaller bias as compared to estimator defined by Singh et al. (2006 Singh, S., Singh, H.P., Upadhyaya, L.N. (2006). Chain ratio and regression type estimators for median estimation in survey sampling. Statist. Pap. 48:2346.[Crossref], [Web of Science ®] [Google Scholar]) with the same efficiency. The results have also been illustrated numerically by taking data from different populations considered in literature.  相似文献   

14.
Calibration estimation improves the precision of the estimates of population parameters by incorporating specified auxiliary information. A class of calibration estimators has been proposed for estimating the population mean by making use of a set of calibration constraints in stratified sampling. The estimator of variance of the proposed calibration estimator of the mean is derived using a lower level calibration approach. The idea is extended for stratified double sampling. A simulation study is used to evaluate the performances of the proposed estimators by comparing them with the similar estimators developed by Tracy, Singh and Arnab (2003 Tracy, D.S., Singh, S., Arnab, R. (2003). Note on calibration in stratified and double sampling. Surv. Methodol. 29(1): 99104. [Google Scholar]) based on different sets of calibration constraints.  相似文献   

15.
Singh et al. (1986 Singh, B., Chaubey, Y.P., Dwivedi, T.D. (1986). An almost unbiased ridge estimator. Sankhya B48: 34236. [Google Scholar]) proposed an almost unbiased ridge estimator using Jackknife method that required transformation of the regression parameters. This article shows that the same method can be used to derive the Jackknifed ridge estimator of the original (untransformed) parameter without transformation. This method also leads in deriving easily the second-order Jackknifed ridge that may reduce the bias further. We further investigate the performance of these estimators along with a recent method by Batah et al. (2008 Batah, F. S.M., Ramanathan, T.V., Gore, S.D. (2008). The efficiency of modified Jack-knife and ridge type regression estimators: a comparison. Surv. Math. Applic. 3:111122. [Google Scholar]) called modified Jackknifed ridge theoretically as well as numerically.  相似文献   

16.
This article further investigates the allocation of coverage limits and deductibles to multiple independent risks from the viewpoint of policyholders with increasing utility functions. In a more general setup, we develop the usual stochastic orders on the retained loss, which either generalize or supplement the corresponding results due to Lu and Meng (2011 Lu, Z., Meng, L. (2011). Stochastic comparisons for allocations of policy limits and deductibles with applications. Insur. Math. Econ. 48:338343. [Google Scholar]) and Hu and Wang (2014 Hu, S., Wang, R. (2014). Stochastic comparisons and optimal allocation for policy limits and deductibles. Commun. Stat. Theory Methods 43:151164. [Google Scholar]). Also, the most unfavorable and favorable allocations of coverage limits and deductibles are developed for multiple risks with dominated reversed hazard rates and hazard rates, respectively.  相似文献   

17.
Sanaullah et al. (2014 Sanaullah, A., Ali, H.M., Noor ul Amin, M., Hanif, M. (2014). Generalized exponential chain ratio estimators under stratified two-phase random sampling. Appl. Math. Comput. 226:541547.[Crossref], [Web of Science ®] [Google Scholar]) have suggested generalized exponential chain ratio estimators under stratified two-phase sampling scheme for estimating the finite population mean. However, the bias and mean square error (MSE) expressions presented in that work need some corrections, and consequently the study based on efficiency comparison also requires corrections. In this article, we revisit Sanaullah et al. (2014 Sanaullah, A., Ali, H.M., Noor ul Amin, M., Hanif, M. (2014). Generalized exponential chain ratio estimators under stratified two-phase random sampling. Appl. Math. Comput. 226:541547.[Crossref], [Web of Science ®] [Google Scholar]) estimator and provide the correct bias and MSE expressions of their estimator. We also propose an estimator which is more efficient than several competing estimators including the classes of estimators in Sanaullah et al. (2014 Sanaullah, A., Ali, H.M., Noor ul Amin, M., Hanif, M. (2014). Generalized exponential chain ratio estimators under stratified two-phase random sampling. Appl. Math. Comput. 226:541547.[Crossref], [Web of Science ®] [Google Scholar]). Three real datasets are used for efficiency comparisons.  相似文献   

18.
We propose a class of estimators for the population mean when there are missing data in the data set. Obtaining the mean square error equations of the proposed estimators, we show the conditions where the proposed estimators are more efficient than the sample mean, ratio-type estimators, and the estimators in Singh and Horn (2000 Singh , S. , Horn , S. ( 2000 ). Compromised imputation in survey sampling . Metrika 51 : 267276 .[Crossref], [Web of Science ®] [Google Scholar]) and Singh and Deo (2003 Singh , S. , Deo , B. (2003). Imputation by power transformation. Statist. Pap. 44:555579.[Crossref], [Web of Science ®] [Google Scholar]) in the case of missing data. These conditions are also supported by a numerical example.  相似文献   

19.
ABSTRACT

In this article, the problem of estimation of the several proportions of two inter-dependent sensitive characteristics prevailing in a given population is considered. A new two-stage randomized response model has been proposed by extending Lee et al.’s (2013 Lee, C., Sedory, S., Singh, S (2013). Estimation at least seven measures of qualitative variables from a single sample using randomized response technique. Stat. Probab. Lett. 83(1):399409.[Crossref], [Web of Science ®] [Google Scholar]) model. The expressions for biases, variances, and mean square errors of different estimators have been provided. The relative efficiency comparisons of the proposed estimators has been made, numerically by considering the different practicable choices of the design parameters. It was observed that the proposed extended version performs efficiently than simple and crossed models of Lee et al. (2013 Lee, C., Sedory, S., Singh, S (2013). Estimation at least seven measures of qualitative variables from a single sample using randomized response technique. Stat. Probab. Lett. 83(1):399409.[Crossref], [Web of Science ®] [Google Scholar]).  相似文献   

20.
Salient features of a family of short-tailed symmetric distributions, introduced recently by Tiku and Vaughan [1] Tiku, M. L. and Vaughan, D. C. 1999. “A family of short-tailed symmetric distributions”. In Technical Report Canada: McMaster University.  [Google Scholar], are enunciated. Assuming the error distribution to be one of this family, the methodology of modified likelihood is used to derive MML estimators of parameters in a linear regression model. The estimators are shown to be efficient, and robust to inliers. This paper is essentially the first to achieve robustness to inliers. The methodology is extended to long-tailed symmetric distributions and the resulting estimators are shown to be efficient, and robust to outliers. This paper should be read in conjunction with Islam et al. [2] Islam, Q., Tiku, M. L. and Yildirim, F. 2001. Nonnormal regression, Part I: Skew distributions. Commun. Stat.—Theory Meth., to appear [Google Scholar]who develop modified likelihood methodology for skew distributions in the context of linear regression.  相似文献   

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