Generalized ratio-type and ratio-exponential-type estimators for population mean under modified Horvitz-Thompson estimator in adaptive cluster sampling

In the present article, we propose the generalized ratio-type and generalized ratio-exponential-type estimators for population mean in adaptive cluster sampling (ACS) under modified Horvitz-Thompson estimator. The proposed estimators utilize the auxiliary information in combination of conventional measures (coefficient of skewness, coefficient of variation, correlation coefficient, covariance, coefficient of kurtosis) and robust measures (tri-mean, Hodges-Lehmann, mid-range) to increase the efficiency of the estimators. Properties of the proposed estimators are discussed using the first order of approximation. The simulation study is conducted to evaluate the performances of the estimators. The results reveal that the proposed estimators are more efficient than competing estimators for population mean in ACS under both modified Hansen-Hurwitz and Horvitz-Thompson estimators.     

Componentwise B-spline estimation for varying coefficient models with longitudinal data

A componentwise B-spline method is proposed for estimating the unknown functions in the varying-coefficient models with longitudinal data. Different amounts of smoothing are used for different individual coefficient functions and the estimators of different coefficient functions are obtained by different minimization operations. The local asymptotic bias and variance of the estimators are derived. It is shown that our estimators achieve the local and global optimal convergence rates even if the coefficient functions belong to different smoothness families. The asymptotic distributions of the estimators are also established and are used to construct approximate pointwise confidence intervals for coefficient functions. Finite sample properties of our procedures are studied through Monte Carlo simulations.     

Estimation of Population Mean Using Known Coefficient of Variation of the Study Character in the Presence of Non Response

Using the known coefficient of variation of the study character, generalized and regression-type estimators for the population mean using two phase sampling in the presence of non response were proposed and their properties have been studied. The conditions under which the proposed estimators are more efficient than the relevant estimators have been obtained. The empirical studies were given in the support of the problems in the case of positive and negative correlation between the study and the auxiliary characters which show the increase in the efficiency of the proposed estimators using known coefficient of variation of the study character with respect to the relevant estimators.     

Pairwise-Difference Rank Estimation of the Transformation Model

This article considers pairwise-difference rank estimators of the coefficient vector in a transformation model. These estimators, like other existing rank estimators, require no subjective bandwidth choice. Monte Carlo simulations, numerical asymptotic efficiency comparisons, and two empirical applications suggest that the proposed estimators perform well in comparison with existing semiparametric estimators.     

Estimation of Bowley's Coefficient of Skewness in the Presence of Auxiliary Information

In this paper, we suggest regression-type estimators for estimating the Bowley's coefficient of skewness using auxiliary information. To the first degree of approximation, the bias and mean-squared error expressions of the regression-type estimators are obtained, and the regions under which these estimators are more efficient than the conventional estimator are also determined. Further, a general class of estimators of the Bowley's coefficient of skewness is defined along with its properties. A class of estimators based on estimated optimum values is also defined. It is shown to the first degree of approximations that the variance of the class of estimators based on estimated optimum values is the same as that of the minimum variance of the proposed class of estimators. A simulation study is carried out to demonstrate the performance of the proposed difference estimator over the usual estimator.     

Modeling of censored bivariate extremal events

In this paper we consider the estimation of the coefficient of tail dependence and of small tail probability under a bivariate randomly censoring mechanism. A new class of generalized moment estimators of the coefficient of tail dependence and the estimator of small tail probability are proposed, respectively. Under the bivariate Hall-type conditions, the asymptotic distributions of these estimators are established. Monte Carlo simulations are performed and the new estimators are applied to an insurance data-set.     

Comparative Study of Robust Estimators Based on a Sensitivity Coefficient in Principal Component Analysis

This work is devoted to robust principal component analysis (PCA). We give a comparison between some multivariate estimators of location and scatter by computing the influence functions of the sensitivity coefficient ρ corresponding to these estimators, and the mean squared error (MSE) of estimators of ρ. The coefficient ρ measures the closeness between the subspaces spanned by the initial eigenvectors and their corresponding version derived from an infinitesimal perturbation of the data distribution.     

A sufficient condition for the MSE dominance of the positive-part shrinkage estimator when each individual regression coefficient is estimated in a misspecified linear regression model

In this paper, assuming that there exist omitted explanatory variables in the specified model, we derive the exact formula for the mean squared error (MSE) of a general family of shrinkage estimators for each individual regression coefficient. It is shown analytically that when our concern is to estimate each individual regression coefficient, the positive-part shrinkage estimators have smaller MSE than the original shrinkage estimators under some conditions even when the relevant regressors are omitted. Also, by numerical evaluations, we showed the effects of our theorem for several specific cases. It is shown that the positive-part shrinkage estimators have smaller MSE than the original shrinkage estimators for wide region of parameter space even when there exist omitted variables in the specified model.     

Estimation of coefficient of dispersion using auxiliary information

In this note, we consider the problem of estimation of coefficient of dispersion of a study variable by making use of known value of the coefficient of dispersion of an auxiliary variable. We propose ratio and regression-type estimators. We derive expressions of bias and variance of the proposed estimators to the first order of approximation. The relative efficiencies of the ratio and regression-type estimators with respect to the naïve estimator are investigated through a simulation study.     

Linearly admissible estimators of stochastic regression coefficient under balanced loss function

The admissibility of linear estimators in a linear model with stochastic regression coefficient is investigated under a balanced loss function. The sufficient and necessary conditions for linear estimators to be admissible in classes of homogeneous and non-homogeneous linear estimators are obtained, respectively.     

Interval estimation of the mean in a two-stage nested model

The problem of constructing confidence intervals to estimate the mean in a two-stage nested model is considered. Several approximate intervals, which are based on both linear and nonlinear estimators of the mean are investigated. In particular, the method of bootstrap is used to correct the bias in the ‘usual’ variance of the nonlinear estimators. It is found that the intervals based on the nonlinear estimators did not achieve the nominal confidence coefficient for designs involving a small number of groups. Further, it turns out that the intervals are generally conservative, especially at small values of the intraclass correlation coefficient, and that the intervals based on the nonlinear estimators are more conservative than those based on the linear estimators. Compared with the others, the intervals based on the unweighted mean of the group means performed well in terms of coverage and length. For small values of the intraclass correlation coefficient, the ANOVA estimators of the variance components are recommended, otherwise the unweighted means estimator of the between groups variance component should be used. If one is fortunate enough to have control over the design, he is advised to increase the number of groups, as opposed to increasing group sizes, while avoiding groups of size one or two.     

Reducing component estimation for varying coefficient models

The estimation problem for varying coefficient models has been studied by many authors. We consider the problem in the case that the unknown functions admit different degrees of smoothness. In this paper we propose a reducing component local polynomial method to estimate the unknown functions. It is shown that all of our estimators achieve the optimal convergence rates. The asymptotic distributions of our estimators are also derived. The established asymptotic results and the simulation results show that our estimators outperform the the existing two-step estimators when the coefficient functions admit different degrees of smoothness. We also develop methods to speed up the estimation of the model and the selection of the bandwidths.     

SECOND ORDER ASYMPTOTIC COMPARISON OF ESTIMATORS UNDER UNIVERSAL DOMINATION CRITERION

The main purpose of this paper is to formulate theories of universal optimality, in the sense that some criteria for performances of estimators are considered over a class of loss functions. It is shown that the difference of the second order terms between two estimators in any risk functions is expressed as a form which is characterized by a peculiar value associated with the loss functions, which is referred to as the loss coefficient. This means that the second order optimal problem is completely characterized by the value of the loss coefficient. Furthermore, from the viewpoint of change of the loss coefficient, the relationship between two estimators is classified into six types. On the basis of this classification, the concept of universal second order admissibility is introduced. Some sufficient conditions are given to determine whether any estimators are universally admissible or not.     

Minimum phi-divergence estimators for multinomial logistic regression with complex sample design

This article develops the theoretical framework needed to study the multinomial regression model for complex sample design with pseudo-minimum phi-divergence estimators. The numerical example and the simulation study propose new estimators for the parameter of the logistic regression with overdispersed multinomial distributions for the response variables, the pseudo-minimum Cressie–Read divergence estimators, as well as new estimators for the intra-cluster correlation coefficient. The simulation study shows that the Binder’s method for the intra-cluster correlation coefficient exhibits an excellent performance when the pseudo-minimum Cressie–Read divergence estimator, with \(\lambda =\frac{2}{3}\), is plugged.     

Improved two phase sampling exponential ratio and product type estimators for population mean of study character in the presence of non response

Improved two phase sampling exponential ratio and product type estimators for population mean using known coefficient of variation of study character in the presence of non response have been proposed and their properties are studied under large sample approximation. The proposed estimators are compared with the other existing estimators by using the MSE criterion and the conditions under which the proposed estimators perform better are obtained. An empirical study is also given to judge the performance of the proposed estimators. At the end, simulation studies have been carried out to verify the superiority to the proposed estimators.     

Immaculating the inconsistent estimator of slope parameter in measurement error model with replicated data

ABSTRACT

The measurement error model with replicated data on study as well as explanatory variables is considered. The measurement error variance associated with the explanatory variable is estimated using the complete data and the grouped data which is used for the construction of the consistent estimators of regression coefficient. These estimators are further used in constructing an almost unbiased estimator of regression coefficient. The large sample properties of these estimators are derived without assuming any distributional form of the measurement errors and the random error component under the setup of an ultrastructural model.     

Variance Estimators of the Gini Coefficient—Probability Sampling

An estimator of the Gini coefficient (the well-known income inequality measure) of a finite population is defined for an arbitrary probability sampling design, taking the sampling design into consideration. Alternative estimators of the variance of the estimated Gini coefficient are introduced. The sampling performance of the Gini coefficient estimator and its variance estimators is studied by means of a Monte Carlo study, using stratified sampling from a miniature population of Swedish households with authentic income data.     

Equivariant estimation of a normal mean using a normal concomitant variable for covariance adjustment

Equivariant point estimators of one component of a bivariate normal mean vector are considered when the second component is known. Equivariant point estimators are characterized and compared in terms of their risk functions with respect to a normalized squared-error loss function. Specific point estimators that dominate the usual estimator when the squared correlation coefficient is sufficiently large are provided.     

An estimator of population total in multiple characteristics and its robustness to product moment correlation coefficient

We developed an alternative estimator for the probability proportional to size with replacement sampling scheme when certain characteristics under study have low correlation with the size measured used for sample selection. The performance of the proposed estimator has been studied with other related alternative estimators by comparing biases and the variances of respective alternative estimators. Most of the alternative estimators assume the knowledge of the product moment correlation coefficient. Therefore an empirical study, with the help of wide variety of populations, has been carried out to study their respective efficiency when correlation coefficient is departed from its true value.     

The non-optimality of interval restricted and pre-test estimators under squared error loss

We consider the linear regression model with an interval restriction imposed on the coefficients, and examine the sampling performance of a family of Stein interval restricted and pre-test estimators Tor the coefficient vector. The risk, under squared error loss, of these Stein-like estimators are derived, and the inadmissibility of the maximum likelihood interval restricted and pre-test estimators is demonstrated.