A modified estimator of population mean using power transformation

Summary In this paper we have suggested two modified estimators of population mean using power transformation. It has been shown that the modified estimators are more efficient than the sample mean estimator, usual ratio estimator, Sisodia and Dwivedi’s (1981) estimator and Upadhyaya and Singh’s (1999) estimator at their optimum conditions. Empirical illustrations are also given for examining the merits of the proposed estimators. Following Kadilar and Cingi (2003) the work has been extended to stratified random sampling, and the same data set has been studied to examine the performance in stratified random sampling.     

Estimation of the SURE model

The paper presents the essentials of the SURE model and the estimation of its parameters β and ω. Two alternative compact representations of the model are being used. The parameter β is estimated by least squares (LS), generalized least squares (GLS) and maximum likelihood (ML) (under normality). For ω two estimators are being considered, viz an LS-related estimator and a maximum likelihood estimator (under normality). Attention is being given to the study of asymptotic properties of all estimators examined. It turns out that the LS-related and ML estimators of ω follow the same asymptotic (normal) distribution. Efficiency comparisons for the various estimators of β conclude the paper.     

A comparison of estimation techniques for the three parameter pareto distribution

This paper compares minimum distance estimation with best linear unbiased estimation to determine which technique provides the most accurate estimates for location and scale parameters as applied to the three parameter Pareto distribution. Two minimum distance estimators are developed for each of the three distance measures used (Kolmogorov, Cramer‐von Mises, and Anderson‐Darling) resulting in six new estimators. For a given sample size 6 or 18 and shape parameter 1(1)4, the location and scale parameters are estimated. A Monte Carlo technique is used to generate the sample sets. The best linear unbiased estimator and the six minimum distance estimators provide parameter estimates based on each sample set. These estimates are compared using mean square error as the evaluation tool. Results show that the best linear unbaised estimator provided more accurate estimates of location and scale than did the minimum estimators tested.     

Nonparametric estimation with left-truncated and right-censored data when the sample size before truncation is known

In this article, we consider nonparametric estimation of the survival function when the data are subject to left-truncation and right-censoring and the sample size before truncation is known. We propose two estimators. The first estimator is derived based on a self-consistent estimating equation. The second estimator is obtained by using the constrained expectation-maximization algorithm. Simulation results indicate that both estimators are more efficient than the product-limit estimator. When there is no censoring, the performance of the proposed estimators is compared with that of the estimator proposed by Li and Qin [Semiparametric likelihood-based inference for biased and truncated data when total sample size is known, J. R. Stat. Soc. B 60 (1998), pp. 243–254] via simulation study.     

Comparative Study of Blu and ML Estimators of Location and Scale Parameters of an Extreme Value Distribution for Small Samples and Type I Censorship

The Maximum Likelihood (ML) and Best Linear Unbiased (BLU) estimators of the location and scale parameters of an extreme value distribution (Lawless [1982]) are compared under conditions of small sample sizes and Type I censorship. The comparisons were made in terms of the mean square error criterion. According to this criterion, the ML estimator of σ in the case of very small sample sizes (n < 10) and heavy censorship (low censoring time) proved to be more efficient than the corresponding BLU estimator. However, the BLU estimator for σ attains parity with the corresponding ML estimator when the censoring time increases even for sample sizes as low as 10. The BLU estimator of σ attains equivalence with the ML estimator when the sample size increases above 10, particularly when the censoring time is also increased. The situation is reversed when it came to estimating the location parameter μ, as the BLU estimator was found to be consistently more efficient than the ML estimator despite the improved performance of the ML estimator when the sample size increases. However, computational ease and convenience favor the ML estimators.     

Estimators Based on Data‐Driven Generalized Weighted Cramér‐von Mises Distances under Censoring – with Applications to Mixture Models

Abstract. Estimators based on data‐driven generalized weighted Cramér‐von Mises distances are defined for data that are subject to a possible right censorship. The function used to measure the distance between the data, summarized by the Kaplan–Meier estimator, and the target model is allowed to depend on the sample size and, for example, on the number of censored items. It is shown that the estimators are consistent and asymptotically multivariate normal for every p dimensional parametric family fulfiling some mild regularity conditions. The results are applied to finite mixtures. Simulation results for finite mixtures indicate that the estimators are useful for moderate sample sizes. Furthermore, the simulation results reveal the usefulness of sample size dependent and censoring sensitive distance functions for moderate sample sizes. Moreover, the estimators for the mixing proportion seem to be fairly robust against a ‘symmetric’ contamination model even when censoring is present.     

Minimum local distance density estimation

We present a local density estimator based on first-order statistics. To estimate the density at a point, x, the original sample is divided into subsets and the average minimum sample distance to x over all such subsets is used to define the density estimate at x. The tuning parameter is thus the number of subsets instead of the typical bandwidth of kernel or histogram-based density estimators. The proposed method is similar to nearest-neighbor density estimators but it provides smoother estimates. We derive the asymptotic distribution of this minimum sample distance statistic to study globally optimal values for the number and size of the subsets. Simulations are used to illustrate and compare the convergence properties of the estimator. The results show that the method provides good estimates of a wide variety of densities without changes of the tuning parameter, and that it offers competitive convergence performance.     

Estimating principal points of univariate distributions

SUMMARY The term 'principal points' originated in a problem of determining 'typical' heads for the design of protection masks, as described by Flury. Two principal points in the mask example correspond to a small and a large size. Principal points are cluster means for theoretical distributions, and sample cluster means from a k -means algorithm are non-parametric estimators of principal points. This paper demonstrates that maximum likelihood estimators and semi-parametric estimators based on symmetry constraints typically perform much better than the k -means estimators. Asymptotic results on the efficiency of these estimators of two principal points for four symmetric univariate distributions are given. Simulation results are provided to examine the performance of the estimators for finite sample sizes. Finally, the different estimators of two principal points are compared using the head dimension data for the design of protection masks.     

Estimation of the variance when kurtosis is known

The unbiased estimator of a population variance σ², S ² has traditionally been overemphasized, regardless of sample size. In this paper, alternative estimators of population variance are developed. These estimators are biased and have the minimum possible mean-squared error [and we define them as the “minimum mean-squared error biased estimators” (MBBE)]. The comparative merit of these estimators over the unbiased estimator is explored using relative efficiency (RE) (a ratio of mean-squared error values). It is found that, across all population distributions investigated, the RE of the MBBE is much higher for small samples and progressively diminishes to 1 with increasing sample size. The paper gives two applications involving the normal and exponential distributions.     

Efficient estimators for adaptive stratified sequential sampling

In stratified sampling, methods for the allocation of effort among strata usually rely on some measure of within-stratum variance. If we do not have enough information about these variances, adaptive allocation can be used. In adaptive allocation designs, surveys are conducted in two phases. Information from the first phase is used to allocate the remaining units among the strata in the second phase. Brown et al. [Adaptive two-stage sequential sampling, Popul. Ecol. 50 (2008), pp. 239–245] introduced an adaptive allocation sampling design – where the final sample size was random – and an unbiased estimator. Here, we derive an unbiased variance estimator for the design, and consider a related design where the final sample size is fixed. Having a fixed final sample size can make survey-planning easier. We introduce a biased Horvitz–Thompson type estimator and a biased sample mean type estimator for the sampling designs. We conduct two simulation studies on honey producers in Kurdistan and synthetic zirconium distribution in a region on the moon. Results show that the introduced estimators are more efficient than the available estimators for both variable and fixed sample size designs, and the conventional unbiased estimator of stratified simple random sampling design. In order to evaluate efficiencies of the introduced designs and their estimator furthermore, we first review some well-known adaptive allocation designs and compare their estimator with the introduced estimators. Simulation results show that the introduced estimators are more efficient than available estimators of these well-known adaptive allocation designs.     

Developing a restricted two-parameter Liu-type estimator: A comparison of restricted estimators in the binary logistic regression model

In the context of estimating regression coefficients of an ill-conditioned binary logistic regression model, we develop a new biased estimator having two parameters for estimating the regression vector parameter β when it is subjected to lie in the linear subspace restriction Hβ = h. The matrix mean squared error and mean squared error (MSE) functions of these newly defined estimators are derived. Moreover, a method to choose the two parameters is proposed. Then, the performance of the proposed estimator is compared to that of the restricted maximum likelihood estimator and some other existing estimators in the sense of MSE via a Monte Carlo simulation study. According to the simulation results, the performance of the estimators depends on the sample size, number of explanatory variables, and degree of correlation. The superiority region of our proposed estimator is identified based on the biasing parameters, numerically. It is concluded that the new estimator is superior to the others in most of the situations considered and it is recommended to the researchers.     

A comparison of some robust,adaptive, and partially adaptive estimators of regression models

Numerous estimation techniques for regression models have been proposed. These procedures differ in how sample information is used in the estimation procedure. The efficiency of least squares (OLS) estimators implicity assumes normally distributed residuals and is very sensitive to departures from normality, particularly to "outliers" and thick-tailed distributions. Lead absolute deviation (LAD) estimators are less sensitive to outliers and are optimal for laplace random disturbances, but not for normal errors. This paper reports monte carlo comparisons of OLS,LAD, two robust estimators discussed by huber, three partially adaptiveestimators, newey's generalized method of moments estimator, and an adaptive maximum likelihood estimator based on a normal kernal studied by manski. This paper is the first to compare the relative performance of some adaptive robust estimators (partially adaptive and adaptive procedures) with some common nonadaptive robust estimators. The partially adaptive estimators are based on three flxible parametric distributions for the errors. These include the power exponential (Box-Tiao) and generalized t distributions, as well as a distribution for the errors, which is not necessarily symmetric. The adaptive procedures are "fully iterative" rather than one step estimators. The adaptive estimators have desirable large sample properties, but these properties do not necessarily carry over to the small sample case.

The monte carlo comparisons of the alternative estimators are based on four different specifications for the error distribution: a normal, a mixture of normals (or variance-contaminated normal), a bimodal mixture of normals, and a lognormal. Five hundred samples of 50 are used. The adaptive and partially adaptive estimators perform very well relative to the other estimation procedures considered, and preliminary results suggest that in some important cases they can perform much better than OLS with 50 to 80% reductions in standard errors.

     

Comment on specification of household engel curves by nonparamftric regression

ABSTRACT

This paper first derives an adaptive estimator when heteroskedasticity is present in the individual specific error in an error component model and then compares the finite sample performance of the proposed estimator with various other estimators. While the Monte Carlo results show that the proposed estimator performs adequately in terms of relative efficiency, its performance on the basis of empirical size is quite similar to the other estimators considered.     

Reliability estimation for the exponential distribution

This paper is concerned with classical statistical estimation of the reliability function for the exponential density with unknown mean failure time θ, and with a known and fixed mission time τ. The minimum variance unbiased (MVU) estimator and the maximum likelihood (ML) estimator are reviewed and their mean square errors compared for different sample sizes. These comparisons serve also to extend previous work, and reinforce further the nonexistence of a uniformly best estimator. A class of shrunken estimators is then defined, and it produces a shrunken quasi-estimator and a shrunken estimator. The mean square errors for both these estimators are compared to the mean square errors of the MVU and ML estimators, and the new estimators are found to perform very well. Unfortunately, these estimators are difficult to compute for practical applications. A second class of estimators, which is easy to compute is also developed. Its mean square error properties are compared to the other estimators, and it outperforms all the contending estimators over the high and low reliability parameter space. Since, for all the estimators, analytical mean square error comparisons are not tractable, extensive numerical analyses are done in obtaining both the exact small sample and large sample results.     

On intra-class correlation coefficient estimation

Consider the problem of estimating the intra-class correlation coefficient of a symmetric normal distribution. In a recent article (Pal and Lim (1999)) it has been shown that the three popular estimators, namely—the maximum likelihood estimator (MLE), the method of moments estimator (MME) and the unique minimum variance unbiased estimator (UMVUE), are second order admissible under the squared error loss function. In this paper we study the performance of the above mentioned estimators in terms of Pitman Nearness Criterion (PNC) as well as Stochastic Domination Criterion (SDC). We then apply the aforementioned estimators to two real life data sets with moderate to large sample sizes, and bootstrap bias as well as mean squared errors are computed to compare the estimators. In terms of overall performance the MME seems most appealing among the three estimators considered here and this is the main contribution of our paper. Formerly University of Southewestern Louisisna     

IS ADAPTIVE ESTIMATION USEFUL FOR PANEL MODELS WITH HETEROSKEDASTICITY IN THE INDIVIDUAL SPECIFIC ERROR COMPONENT? SOME MONTE CARLO EVIDENCE

This paper first derives an adaptive estimator when heteroskedasticity is present in the individual specific error in an error component model and then compares the finite sample performance of the proposed estimator with various other estimators. While the Monte Carlo results show that the proposed estimator performs adequately in terms of relative efficiency, its performance on the basis of empirical size is quite similar to the other estimators considered.     

Comment

Abstract

A semiparametric estimator for evaluating the parameters of data generated under a sample selection process is developed. This estimator is based on the generalized maximum entropy estimator and performs well for small and ill-posed samples. Theoretical and sampling comparisons with parametric and semiparametric estimators are given. This method and standard ones are applied to three small-sample empirical applications of the wage-participation model for female teenage heads of households, immigrants, and Native Americans.     

随机效应空间滞后单指数面板模型

对随机效应空间滞后单指数面板模型,本文构建了该模型的截面极大似然估计方法,从理论证明和数值模拟两方面分别考察了其估计量的大样本性质和小样本表现。研究结果表明:(1)在大样本条件下,估计量均具有一致性,并且参数估计量具有渐近正态性。(2)在小样本条件下,各估计量依然具有良好的表现,其精度随着样本容量的增加而提高;空间权重矩阵结构的复杂性对空间相关系数的估计量影响较大,但对其他估计量的影响较小。     

Estimating the variance in nonparametric regression—what is a reasonable choice?

The exact mean-squared error (MSE) of estimators of the variance in nonparametric regression based on quadratic forms is investigated. In particular, two classes of estimators are compared: Hall, Kay and Titterington's optimal difference-based estimators and a class of ordinary difference-based estimators which generalize methods proposed by Rice and Gasser, Sroka and Jennen-Steinmetz. For small sample sizes the MSE of the first estimator is essentially increased by the magnitude of the integrated first two squared derivatives of the regression function. It is shown that in many situations ordinary difference-based estimators are more appropriate for estimating the variance, because they control the bias much better and hence have a much better overall performance. It is also demonstrated that Rice's estimator does not always behave well. Data-driven guidelines are given to select the estimator with the smallest MSE.     

Robust estimation methods for exponential data: a monte-carlo comparison

We compare the performance of seven robust estimators for the parameter of an exponential distribution. These include the debiased median and two optimally-weighted one-sided trimmed means. We also introduce four new estimators: the Transform, Bayes, Scaled and Bicube estimators. We make the Monte Carlo comparisons for three sample sizes and six situations. We evaluate the comparisons in terms of a new performance measure, Mean Absolute Differential Error (MADE), and a premium/protection interpretation of MADE. We organize the comparisons to enhance statistical power by making maximal use of common random deviates. The Transform estimator provides the best performance as judged by MADE. The singly-trimmed mean and Transform method define the efficient frontier of premium/protection.