Semiparametric Efficient Distribution Free Estimation of Panel Models

This article generalizes results from Park et al. (1998 Park , B. U. , Sickles , R. C. , Simar , L. ( 1998 ). Stochastic frontiers: a semiparametric approach . J. Econometrics 84 : 273 – 301 .[Crossref], [Web of Science ®] , [Google Scholar]) and Adams et al. (1999 Adams , R. M. , Berger , A. N. , Sickles , R. C. ( 1999 ). Semiparametric approaches to stochastic panel frontiers with applications in the banking industry . J. Bus. Econ. Statist. 17 : 349 – 358 .[Taylor & Francis Online] , [Google Scholar]) on semiparametric efficient estimation of panel models. The form of semiparametric efficient estimators depends on the statistical assumptions imposed. Normality assumptions on the transitory error are sometimes inappropriate. We relax the normality assumption used in the articles above to derive more general semiparametric efficient estimators. These estimators are illustrated in a Monte Carlo simulation and an analysis of banking productivity.     

Asymptotics of the Lp-Norms of Density Estimators in the Nonlinear Autoregressive Models

This article investigates the asymptotic behavior of the error density function in nonlinear autoregressive stationary time series regression models. For any 1 ? p < ∞, the kernel density estimator of residuals is shown to be consistent for the error estimator concerning the L_p-distance, which extends the result developed by Cheng and Sun (2008 Cheng, F. X. (2005). Asymptotic distributions of error density estimators in first-order autoregression models. Sankhy Ind. J. Statist. 67:553–567. [Google Scholar]) in L₂-norm. Moreover, the result developed in this article is extended the results of Horváth and Zitikis (2003 Horváth, L., Zitikis, R. (2003). Asymptotics of the L_p-norms of density estimators in the first-order autoregressive models. Statist. Probab. Lett. 65:331342.[Crossref], [Web of Science ®] , [Google Scholar]) to nonlinear autoregressive models.     

Measures of predictor sensitivity for order-insensitive partitioning of multiple correlation

Lindeman et al. [12 Lindeman, R. H., Merenda, P. F. and Gold, R. Z. 1980. Introduction to Bivariate and Multivariate Analysis, Glenview, IL: Scott Foresman.  [Google Scholar]] provide a unique solution to the relative importance of correlated predictors in multiple regression by averaging squared semi-partial correlations obtained for each predictor across all p! orderings. In this paper, we propose a series of predictor sensitivity statistics that complement the variance decomposition procedure advanced by Lindeman et al. [12 Lindeman, R. H., Merenda, P. F. and Gold, R. Z. 1980. Introduction to Bivariate and Multivariate Analysis, Glenview, IL: Scott Foresman.  [Google Scholar]]. First, we detail the logic of averaging over orderings as a technique of variance partitioning. Second, we assess predictors by conditional dominance analysis, a qualitative procedure designed to overcome defects in the Lindeman et al. [12 Lindeman, R. H., Merenda, P. F. and Gold, R. Z. 1980. Introduction to Bivariate and Multivariate Analysis, Glenview, IL: Scott Foresman.  [Google Scholar]] variance decomposition solution. Third, we introduce a suite of indices to assess the sensitivity of a predictor to model specification, advancing a series of sensitivity-adjusted contribution statistics that allow for more definite quantification of predictor relevance. Fourth, we describe the analytic efficiency of our proposed technique against the Budescu conditional dominance solution to the uneven contribution of predictors across all p! orderings.     

Efficient separate class of estimators of population mean in stratified random sampling

In this paper, efficient class of estimators for population mean using two auxiliary variates is suggested. It has been shown that the suggested estimator is more efficient than usual unbiased estimator in stratified random sampling, usual ratio and product-type estimators, Tailor and Lone (2012 Tailor, R. and Lone, H. A. (2012). Separate ratio-cum- product estimators of finite population mean using auxiliary information. J. Rajasthan Stat. Assoc. 1(2):94–102. [Google Scholar], 2014) estimators, and other considered estimators. The bias and mean-squared error of the suggested estimator are obtained up to the first degree of approximation. Conditions under which the suggested estimator is more efficient than other considered estimators are obtained. An empirical study has been carried out to demonstrate the performances of the suggested estimator.     

Some new results on allocation of coverage limits and deductibles to mutually independent risks

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. 48:338–343. [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 43:151–164. [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.     

Improved Exponential Type Estimators of the Mean of a Sensitive Variable in the Presence of Nonsensitive Auxiliary Information

Recently, Koyuncu et al. (2013 Koyuncu, N., Gupta, S., Sousa, R. (2014). Exponential type estimators of the mean of a sensitive variable in the presence of non-sensitive auxiliary information. Communications in Statistics- Simulation and Computation[PubMed], [Web of Science ®] , [Google Scholar]) proposed an exponential type estimator to improve the efficiency of mean estimator based on randomized response technique. In this article, we propose an improved exponential type estimator which is more efficient than the Koyuncu et al. (2013 Koyuncu, N., Gupta, S., Sousa, R. (2014). Exponential type estimators of the mean of a sensitive variable in the presence of non-sensitive auxiliary information. Communications in Statistics- Simulation and Computation[PubMed], [Web of Science ®] , [Google Scholar]) estimator, which in turn was shown to be more efficient than the usual mean estimator, ratio estimator, regression estimator, and the Gupta et al. (2012 Gupta, S., Shabbir, J., Sousa, R., Corte-Real, P. (2012). Regression estimation of the mean of a sensitive variable in the presence of auxiliary information. Communications in Statistics – Theory and Methods 41:2394–2404.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) estimator. Under simple random sampling without replacement (SRSWOR) scheme, bias and mean square error expressions for the proposed estimator are obtained up to first order of approximation and comparisons are made with the Koyuncu et al. (2013 Koyuncu, N., Gupta, S., Sousa, R. (2014). Exponential type estimators of the mean of a sensitive variable in the presence of non-sensitive auxiliary information. Communications in Statistics- Simulation and Computation[PubMed], [Web of Science ®] , [Google Scholar]) estimator. A simulation study is used to observe the performances of these two estimators. Theoretical findings are also supported by a numerical example with real data. We also show how to, extend the proposed estimator to the case when more than one auxiliary variable is available.     

On Asymptotic Normality of the Local Polynomial Regression Estimator with Stochastic Bandwidths

Nonparametric density and regression estimators commonly depend on a bandwidth. The asymptotic properties of these estimators have been widely studied when bandwidths are non stochastic. In practice, however, in order to improve finite sample performance of these estimators, bandwidths are selected by data driven methods, such as cross-validation or plug-in procedures. As a result, nonparametric estimators are usually constructed using stochastic bandwidths. In this article, we establish the asymptotic equivalence in probability of local polynomial regression estimators under stochastic and nonstochastic bandwidths. Our result extends previous work by Boente and Fraiman (1995 Boente , G. , Fraiman , R. ( 1995 ). Asymptotic distribution of data-driven smoothers in density and regression estimation under dependence . Can. J. Statist. 23 : 383 – 397 .[Crossref], [Web of Science ®] , [Google Scholar]) and Ziegler (2004 Ziegler , K. ( 2004 ). Adaptive kernel estimation of the mode in nonparametric random design regression model . Probab. Mathemat. Statist. 24 : 213 – 235 . [Google Scholar]).     

A Similarity Measure Based on Species Proportions

ABSTRACT

There are several indices for measuring the similarity of two populations, including the ratio of the number of shared species to the number of distinct species (Jaccard's index) and the conditional probability of observing a shared species (Smith et al., 1996 Smith , W. , Solow , A. R. , Preston , P. E. ( 1996 ). An estimator of species overlap using a modified beta-binomial model. Biometrics 52 : 1472 – 1477 . [CSA] [CROSSREF] [Crossref], [Web of Science ®] , [Google Scholar]). However, these indices only take into account the number of species and species proportions of shared species. In this article, we propose a new similarity index which includes the species proportions of both the shared and non shared species in each population, and also propose a Nonparametric Maximum Likelihood Estimator (NPMLE) for this index. Bootstrap and delta methods are used to evaluate the standard errors of the NPMLE. Based on a loss function, we also compare a class of nonparametric estimators for the proposed index in various situations.     

Some Classes of Estimators for the Population Median Using Auxiliary Information

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 : 261 – 269 . [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 ): 57 – 63 . [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.     

Minimum Divergence,Generalized Empirical Likelihoods,and Higher Order Expansions

This article studies the minimum divergence (MD) class of estimators for econometric models specified through moment restrictions. We show that MD estimators can be obtained as solutions to a tractable lower dimensional optimization problem. This problem is similar to the one solved by the generalized empirical likelihood estimators of Newey and Smith (2004 Newey , W. K. , Smith , R. J. ( 2004 ). Higher order properties of GMM and Generalized Empirical Likelihood estimators . Econometrica 72 : 219 – 255 .[Crossref], [Web of Science ®] , [Google Scholar]), but it is equivalent to it only for a subclass of divergences. The MD framework provides a coherent testing theory: tests for overidentification and parametric restrictions in this framework can be interpreted as semiparametric versions of Pearson-type goodness of fit tests. The higher order properties of MD estimators are also studied and it is shown that MD estimators that have the same higher order bias as the empirical likelihood (EL) estimator also share the same higher order mean square error and are all higher order efficient. We identify members of the MD class that are not only higher order efficient, but also, unlike the EL estimator, well behaved when the moment restrictions are misspecified.     

An Asymmetric Kernel Estimator of Density Function for Stationary Associated Sequences

Here, we apply the smoothing technique proposed by Chaubey et al. (2007 Chaubey , Y. P. , Sen , A. , Sen , P. K. ( 2007 ). A new smooth density estimator for non-negative random variables. Technical Report No. 1/07. Department of Mathematics and Statistics, Concordia University, Montreal, Canada . [Google Scholar]) for the empirical survival function studied in Bagai and Prakasa Rao (1991 Bagai , I. , Prakasa Rao , B. L. S. ( 1991 ). Estimation of the survival function for stationary associated processes . Statist. Probab. Lett. 12 : 385 – 391 .[Crossref], [Web of Science ®] , [Google Scholar]) for a sequence of stationary non-negative associated random variables.The derivative of this estimator in turn is used to propose a nonparametric density estimator. The asymptotic properties of the resulting estimators are studied and contrasted with some other competing estimators. A simulation study is carried out comparing the recent estimator based on the Poisson weights (Chaubey et al., 2011 Chaubey , Y. P. , Dewan , I. , Li , J. ( 2011 ). Smooth estimation of survival and density functions for a stationary associated process using poisson weights . Statist. Probab. Lett. 81 : 267 – 276 .[Crossref], [Web of Science ®] , [Google Scholar]) showing that the two estimators have comparable finite sample global as well as local behavior.     

Ratio-Cum-Product Type Exponential Estimator of Finite Population Mean in Stratified Random Sampling

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 : 34 – 42 .[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 ): 159 – 163 .[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.     

On generalized exponential chain ratio estimators under stratified two-phase random sampling

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. 226:541–547.[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. 226:541–547.[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. 226:541–547.[Crossref], [Web of Science ®] , [Google Scholar]). Three real datasets are used for efficiency comparisons.     

An Improved Class of Estimators in Two-Phase Sampling Using Two Auxiliary Variables

This article suggests an improved class of estimators under the general framework of two-phase sampling scheme in presence of two auxiliary variables. This class includes a large number of estimators (Chand, 1975 Chand , L. ( 1975 ). Some Ratio-Type Estimator Based on Two or More Auxiliary Variables. Unpublished Ph.D. dissertation, Iowa State University, Iowa . [Google Scholar]; Kiregyera, 1980 Kiregyera , B. ( 1980 ). A chain ratio-type estimator in finite population double sampling using two auxiliary variables . Metrika 27 : 217 – 223 .[Crossref] , [Google Scholar], 3; Mukharjee et al., 1987 Mukharjee , R. , Rao , T. J. , Vijayan , K. ( 1987 ). Regression-type estimators using multiple auxiliary information . Aust. J. Statist. 29 : 244 – 254 . [Google Scholar]) and also the class of estimators suggested by Sahoo et al. (1993 Sahoo , J. , Sahoo , L. N. , Mohanty , S. ( 1993 ). A regression approach to estimation in two phase sampling using two auxiliary variables . Curr. Sci. 65 ( 1 ): 73 – 75 . [Google Scholar]).     

Generalized ratio-cum-product type exponential estimator in stratified random sampling

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, 29–31, 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. 43:343–354.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) estimator are obtained. An empirical study has also been carried out.     

Asymptotic normality of the local linear estimation of the conditional density for functional time-series data

This article focuses on the conditional density of a scalar response variable given a random variable taking values in a semimetric space. The local linear estimators of the conditional density and its derivative are considered. It is assumed that the observations form a stationary α-mixing sequence. Under some regularity conditions, the joint asymptotic normality of the estimators of the conditional density and its derivative is established. The result confirms the prospect in Rachdi et al. (2014 Rachdi, M., A. Laksaci, J. Demongeot, A. Abdali, and F. Madani. 2014. Theoretical and practical aspects of the quadratic error in the local linear estimation of the conditional density for functional data. Computational Statistics and Data Analysis 73 :53–68.[Crossref], [Web of Science ®] , [Google Scholar]) and can be applied in time-series analysis to make predictions and build confidence intervals. The finite-sample behavior of the estimator is investigated by simulations as well.     

Random Effects,Fixed Effects and Hausman's Test for the Generalized Mixed Regressive Spatial Autoregressive Panel Data Model

This article suggests random and fixed effects spatial two-stage least squares estimators for the generalized mixed regressive spatial autoregressive panel data model. This extends the generalized spatial panel model of Baltagi et al. (2013 Baltagi, B. H., Egger, P., Pfaffermayr, M. (2013). A generalized spatial panel data model with random effects. Econometric Reviews 32:650–685.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) by the inclusion of a spatial lag term. The estimation method utilizes the Generalized Moments method suggested by Kapoor et al. (2007 Kapoor, M., Kelejian, H. H., Prucha, I. R. (2007). Panel data models with spatially correlated error components. Journal of Econometrics 127(1):97–130.[Crossref], [Web of Science ®] , [Google Scholar]) for a spatial autoregressive panel data model. We derive the asymptotic distributions of these estimators and suggest a Hausman test a la Mutl and Pfaffermayr (2011 Mutl, J., Pfaffermayr, M. (2011). The Hausman test in a Cliff and Ord panel model. Econometrics Journal 14:48–76.[Crossref], [Web of Science ®] , [Google Scholar]) based on the difference between these estimators. Monte Carlo experiments are performed to investigate the performance of these estimators as well as the corresponding Hausman test.     

Hartley-Ross Type Estimators for Population Mean Using Known Parameters of Auxiliary Variate

This article proposes Hartley-Ross type unbiased estimators of finite population mean using information on known parameters of auxiliary variate when the study variate and auxiliary variate are positively correlated. The variances of the proposed unbiased estimators are obtained. It has been shown that the proposed estimators are more efficient than the simple mean estimator, usual ratio estimator and estimators proposed by Sisodia and Dwivedi (1981 Sisodia , B. V. S. , Dwivedi , V. K. ( 1981 ). A modified ratio estimator using coefficient of variation of auxiliary variable . J. Indian Soc. Agricultural Statist. 33 ( 1 ): 13 – 18 . [Google Scholar]), Kadilar and Cingi (2006 Kadilar , C. , Cingi , H. ( 2006 ). A new ratio estimator using correlation coefficient . Int. Statist. 1 – 11 . [Google Scholar]), and Kadilar et al. (2007 Kadilar , C. , Candan , M. , Cingi , H. ( 2007 ). Ratio estimators using robust regression . Hacet. J. Math. Statist. 36 ( 2 ): 181 – 188 .[Web of Science ®] , [Google Scholar]) under certain realistic conditions. Empirical studies are also carried out to demonstrate the merits of the proposed unbiased estimators over other estimators considered in this article.     

Optimal allocations of coverage limits for two independent random losses of insurance policy

This article recasts the optimal allocations of coverage limits for two independent random losses. Under some regularity conditions on the two concerned probability density functions, we build the sufficient and necessary condition for the existence of the optimal allocation of coverage limits, and derive the optimal allocation whenever they do exist. The results supplement Lu and Meng (2011 Lu, Z.Y., Meng, L.L. (2011). Stochastic comparisons for allocations of upper limits and deductibles with applications. Insur.: Math. Econ. 48:338–343.[Crossref], [Web of Science ®] , [Google Scholar], Proposition 5.2) and Hu and Wang (2014 Hu, S., Wang, R. (2014). Stochastic comparisons and optimal allocation for policy limits and deductibles. Commun. Stat. – Theory Methods 43:151–164.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar], Theorem 5.1).     

Estimation of finite population mean using two auxiliary variables in stratified two-phase sampling

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 12:159–163. [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 2012:1–15, 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 41:247–256. [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, 3:74–78. [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 227:171–175. [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 226:541–547. [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):1–14. [Google Scholar]).