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。     

On the efficiency property of the linear estimators in the bivariate pearson type vii distribution

In this paper the efficiency property of the estimators of the parameters of the bivariate Pearson type VII distribution is studied inside the family of linear estimators, assuming that the sample is constituted by dependent random vectors. It is proven that, although there are not efficient linear estimators, the sample mean and the sample covariance matrix (affected by an unbiasedness weighting) are unbiased linear estimators of minimum distance to the Cramér-Rao lower bound. Finally, a numerical simulation example shows that the proposed estimators are computationally feasible.     

New modified moment estimators for the two-parameter weighted Lindley distribution

We propose a modification of the moment estimators for the two-parameter weighted Lindley distribution. The modification replaces the second sample moment (or equivalently the sample variance) by a certain sample average which is bounded on the unit interval for all values in the sample space. In this method, the estimates always exist uniquely over the entire parameter space and have consistency and asymptotic normality over the entire parameter space. The bias and mean squared error of the estimators are also examined by means of a Monte Carlo simulation study, and the empirical results show the small-sample superiority in addition to the desirable large sample properties. Monte Carlo simulation study showed that the proposed modified moment estimators have smaller biases and smaller mean-square errors than the existing moment estimators and are compared favourably with the maximum likelihood estimators in terms of bias and mean-square error. Three illustrative examples are finally presented.     

Small sample confidence intervals for survival functions under the proportional hazards model

We develop a saddlepoint-based method for generating small sample confidence bands for the population surviival function from the Kaplan-Meier (KM), the product limit (PL), and Abdushukurov-Cheng-Lin (ACL) survival function estimators, under the proportional hazards model. In the process we derive the exact distribution of these estimators and developed mid-ppopulation tolerance bands for said estimators. Our saddlepoint method depends upon the Mellin transform of the zero-truncated survival estimator which we derive for the KM, PL, and ACL estimators. These transforms are inverted via saddlepoint approximations to yield highly accurate approximations to the cumulative distribution functions of the respective cumulative hazard function estimators and these distribution functions are then inverted to produce our saddlepoint confidence bands. For the KM, PL and ACL estimators we compare our saddlepoint confidence bands with those obtained from competing large sample methods as well as those obtained from the exact distribution. In our simulation studies we found that the saddlepoint confidence bands are very close to the confidence bands derived from the exact distribution, while being much easier to compute, and outperform the competing large sample methods in terms of coverage probability.     

Finite sample correction factors for several simple robust estimators of normal standard deviation

Estimation of the standard deviation of a normal population is an important practical problem that in industrial practice must often be done from small and possibly contaminated data sets. Using multiple estimators is useful, as differences in the estimates may indicate whether the data set is contaminated and the form of the contamination. In this paper, finite sample correction factors have been estimated by simulation for several simple robust estimators of the standard deviation of a normal population. The estimators are the median absolute deviation, interquartile range, shortest half interval (Shorth), and median moving range. Finite sample correction factors have also been estimated for the commonly used non-robust estimators: mean absolute deviation and mean moving range. The simulation has been benchmarked against finite sample correction factors for the sample standard deviation and the sample range.     

Marshall–Olkin distribution: parameter estimation and application to cancer data

In this study, as alternatives to the maximum likelihood (ML) and the frequency estimators, we propose robust estimators for the parameters of Zipf and Marshall–Olkin Zipf distributions. A small simulation study is given to illustrate the performance of the proposed estimators. We apply the proposed estimators to a real data set from cancer research to illustrate the performance of the proposed estimators over the ML, moments and frequency estimators. We observe that the robust estimators have superiority over the frequency estimators based on classical sample mean.     

Estimating the population mean in the case of missing data using simple random sampling

In this paper, we suggest three new ratio estimators of the population mean using quartiles of the auxiliary variable when there are missing data from the sample units. The suggested estimators are investigated under the simple random sampling method. We obtain the mean square errors equations for these estimators. The suggested estimators are compared with the sample mean and ratio estimators in the case of missing data. Also, they are compared with estimators in Singh and Horn [Compromised imputation in survey sampling, Metrika 51 (2000), pp. 267–276], Singh and Deo [Imputation by power transformation, Statist. Papers 45 (2003), pp. 555–579], and Kadilar and Cingi [Estimators for the population mean in the case of missing data, Commun. Stat.-Theory Methods, 37 (2008), pp. 2226–2236] and present under which conditions the proposed estimators are more efficient than other estimators. In terms of accuracy and of the coverage of the bootstrap confidence intervals, the suggested estimators performed better than other estimators.     

Unbiased estimators for restricted adaptive cluster sampling

In adaptive cluster sampling the size of the final sample is random, thus creating design problems. To get round this, Brown (1994) and Brown & Manly (1998) proposed a modification of the method, placing a restriction on the size of the sample, and using standard but biased estimators for estimating the population mean. But in this paper a new unbiased estimator and an unbiased variance estimator are proposed, based on estimators proposed by Murthy (1957) and extended to sequential and adaptive sampling designs by Salehi & Seber (2001). The paper also considers a restricted version of the adaptive scheme of Salehi & Seber (1997a) in which the networks are selected without replacement, and obtains unbiased estimators. The method is demonstrated by a simple example. Using simulation from this example, the new estimators are shown to compare very favourably with the standard biased estimators.     

An evaluation by simulation of alternative estimators for the marginal Fisher distribution

The Fisher distribution is a standard model for directional data (or spherical data). In some cases though, only the co-latitudes can be observed, resulting in a sample of observations from the corresponding marginal distribution. This paper reports on an extensive simulation to compare and evaluate the robustness of 11 test-statistics corresponding to various estimators of the parameters of this distribution. The estimators include Maximum Likelihood and Moment-type estimators, as well as sample means and variances based on approximations to the marginal Fisher distribution. Of the test-statistics considered, the Likelihood-Ratio statistic was the only one whose sampling distribution remained close to its asymptotic distribution for all parameter values and sample sizes considered. In general, the other statistics were close to their approximate distributions only when ksin2?0, was fairly large. The paper includes details on the computational methods for finding the Maximum Likelihood and Moment estimators, and concludes with some practical advice on the choice of estimation procedure.     

Weighting for unequal selection probabilities in multilevel models

When multilevel models are estimated from survey data derived using multistage sampling, unequal selection probabilities at any stage of sampling may induce bias in standard estimators, unless the sources of the unequal probabilities are fully controlled for in the covariates. This paper proposes alternative ways of weighting the estimation of a two-level model by using the reciprocals of the selection probabilities at each stage of sampling. Consistent estimators are obtained when both the sample number of level 2 units and the sample number of level 1 units within sampled level 2 units increase. Scaling of the weights is proposed to improve the properties of the estimators and to simplify computation. Variance estimators are also proposed. In a limited simulation study the scaled weighted estimators are found to perform well, although non-negligible bias starts to arise for informative designs when the sample number of level 1 units becomes small. The variance estimators perform extremely well. The procedures are illustrated using data from the survey of psychiatric morbidity.     

Parametric inference based on judgment post stratified samples

In this paper, we consider a judgment post stratified (JPS) sample of set size $H$ from a location and scale family of distributions. In a JPS sample, ranks of measured units are random variables. By conditioning on these ranks, we derive the maximum likelihood (MLEs) and best linear unbiased estimators (BLUEs) of the location and scale parameters. Since ranks are random variables, by considering the conditional distributions of ranks given the measured observations we construct Rao-Blackwellized version of MLEs and BLUEs. We show that Rao-Blackwellized estimators always have smaller mean squared errors than MLEs and BLUEs in a JPS sample. In addition, the paper provides empirical evidence for the efficiency of the proposed estimators through a series of Monte Carlo simulations.     

Improved inference for MCP-Mod approach using time-to-event endpoints with small sample sizes

The Multiple Comparison Procedures with Modeling Techniques (MCP-Mod) framework has been recently approved by the U.S. Food, Administration, and European Medicines Agency as fit-for-purpose for phase II studies. Nonetheless, this approach relies on the asymptotic properties of Maximum Likelihood (ML) estimators, which might not be reasonable for small sample sizes. In this paper, we derived improved ML estimators and correction for their covariance matrices in the censored Weibull regression model based on the corrective and preventive approaches. We performed two simulation studies to evaluate ML and improved ML estimators with their covariance matrices in (i) a regression framework (ii) the Multiple Comparison Procedures with Modeling Techniques framework. We have shown that improved ML estimators are less biased than ML estimators yielding Wald-type statistics that controls type I error without loss of power in both frameworks. Therefore, we recommend the use of improved ML estimators in the MCP-Mod approach to control type I error at nominal value for sample sizes ranging from 5 to 25 subjects per dose.     

Two-stage estimation of inequality-constrained marginal linear models with longitudinal data

Inequality-constrained regression models have received increased attention in longitudinal analysis during recent years. Regression parameters are usually obtained from iteration algorithms. An analytical formulae of the estimators cannot be provided. Therefore, the asymptotic behavior of estimators has not been fully clarified yet. This paper presents a TS estimation (TS for short) and the asymptotic distribution of the estimators. Simulations are conducted to compare constrained TS estimation, constrained ordinary least squares (OLS) estimation and TS estimation in terms of sample bias, sample mean-square error (MSE) and sample variance of the estimators.     

Power series estimator for binary data

There are several commonly used measures of association between treatment and control event rates in the population, including odds ratios, relative risk and number needed to treat. Conventionally those parameters are estimated by the sample proportion estimators. In this paper, we show that the sample proportional estimators tend to overestimate. Fortunately, those measurements are estimable by the power series estimators and they converge to UMVUE with a speed of convergency depending on big-O. For instance, it converges slowly for the number needed to treat if the difference between two sample proportions is close to zero.     

Efficient M-estimators with auxiliary information

This paper introduces a new class of M-estimators based on generalised empirical likelihood (GEL) estimation with some auxiliary information available in the sample. The resulting class of estimators is efficient in the sense that it achieves the same asymptotic lower bound as that of the efficient generalised method of moment (GMM) estimator with the same auxiliary information. The paper also shows that in case of smooth estimating equations the proposed estimators enjoy a small second order bias property compared to both efficient GMM and full GEL estimators. Analytical formulae to obtain bias corrected estimators are also provided. Simulations show that with correctly specified auxiliary information the proposed estimators and in particular those based on empirical likelihood outperform standard M and efficient GMM estimators both in terms of finite sample bias and efficiency. On the other hand with moderately misspecified auxiliary information estimators based on the nonparametric tilting method are typically characterised by the best finite sample properties.     

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.     

Stabilizing the Performance of Kurtosis Estimator of Multivariate Data

The estimation of the kurtosis parameter of the underlying distribution plays a central role in many statistical applications. The central theme of the article is to improve the estimation of the kurtosis parameter using a priori information. More specifically, we consider the problem of estimating kurtosis parameter of a multivariate population when some prior information regarding the the parameter is available. The rationale is that the sample estimator of the kurtosis parameter has a large estimation error. In this situation we consider shrinkage and pretest estimation methodologies and reappraise their statistical properties. The estimation based on these strategies yield relatively smaller estimation error in comparison with the sample estimator in the candidate subspace. A large sample theory of the suggested estimators are developed and compared. The results demonstrate that suggested estimators outperform the estimator based on the sample data only in the candidate subspace. In an effort to appreciate the relative behavior of the estimators in a finite sample scenario, a Monte-carlo simulation study is planned and performed. The result of simulation study strongly corroborates the asymptotic result. To illustrate the application of the estimators, some example are showcased based on recently published data.     

A New Estimation Method Based on Order Statistics in the Families of Symmetric Location-scale Distributions

In this study, new unbiased and nonlinear estimators based on order statistics are proposed for the family of symmetric location-scale distributions and these estimators can be computed from both uncensored and symmetric doubly Type II censored samples. In addition, other relevant unbiased estimators are proposed to estimate standard deviations of these new estimators. A simulation study has been performed to evaluate the performance of the new estimators compared to BLU estimators for small sample sizes. As a result of the simulation study, the new estimators proposed for the location-scale family in general performed nearly as good as BLU estimators. Furthermore, the computational advantage of the proposed estimators over BLU and ML estimators are worthy of notice. In addition, these new estimators have been applied to real data, and the estimation results obtained have been compatible with those of BLUE methods.     

On concomitants of order statistics arising from the extended Farlie–Gumbel–Morgenstern bivariate logistic distribution and its application in estimation

In this paper, we consider concomitants of order statistics arising from the extended Farlie–Gumbel–Morgenstern bivariate logistic distribution and develop its distribution theory. Using ranked set sample obtained from the above distribution, unbiased estimators of the parameters associated with the study variate involved in it are generated. The best linear unbiased estimators (BLUEs) based on observations in the ranked set sample of those parameters as well have been derived. The efficiencies of the BLUEs relative to the respective unbiased estimators generated also have been evaluated.     

Estimating the fundamental frequency of a periodic function

In this paper we consider the problem of estimation of the fundamental frequency of a periodic function, which has several applications in Speech Signal Processing. The problem was originally proposed by Hannan (1974) and later on Quinn and Thomson (1991) provided an estimation procedure of the unknown parameters. It is observed that the estimation procedure of Quinn and Thomson (1991) is quite involved numerically. In this paper we propose to use two simple estimators and it is observed that their performance are quite satisfactory. Asymptotic properties of the proposed estimators are obtained. The large sample properties of the estimators are compared theoretically. We present some simulation results to compare their small sample performance. One speech data is analyzed using this particular model.