Estimation of the inverse of mean

For the inverse of mean, a class of estimators with finite moments is considered and its properties are analyzed in the context of normal and non-normal populations.     

Autocorrelation and tolerance limits

Tolerance limits are limits that include a specified proportion of the population at a given confidence level. They are used to make sure that the production will not be outside specifications. Tolerance limits are either designed based on the normality assumption, or nonparametric tolerance limits are established. In either case, no provision for autocorrelated processes is made in the available design tables of tolerance limits. It is shown how to construct tolerance limits to cover a specified proportion of the population when autocorrelation is present in the process. A comparison of four different tolerance limits is provided, and recommendations are given for choosing the "best" estimator of the process variability for the construction of tolerance limits.     

农民工参与就业培训的决定因素及对收入影响的实证分析

笔者利用在7个省市的调研数据,利用离散选择模型分析农民工参与就业培训的影响因素;同时,运用平均处理效应估计方法,考察参与就业培训对农民工收入水平的影响。分析结果说明,就业培训有助于提高农民工在就业市场的竞争力,提高农民工的收入水平。但这需要增加资金投入,加大宣传力度,正确引导营利性培训机构的发展。     

Estimation of sample selection bias models

Econometric models with sample selection biases are widely used in various fields of economics, such as labor economics. The Maximum Likelihood Estimator (MLE) is seldom used to estimate models because of computational difficulty, while Heckman's two-step estimator is widely used to estimate these models. However, Heckman's two-step estimator sometimes performs poorly. In this paper, methods of calculating the MLE are analysed, and finite sample properties of the MLE and Heckman's two-step estimator are compared using Monte Carlo experiments and empirical examples.     

Estimating the error variance in nonparametric regression by a covariate-matched u-statistic

For nonparametric regression models with fixed and random design, two classes of estimators for the error variance have been introduced: second sample moments based on residuals from a nonparametric fit, and difference-based estimators. The former are asymptotically optimal but require estimating the regression function; the latter are simple but have larger asymptotic variance. For nonparametric regression models with random covariates, we introduce a class of estimators for the error variance that are related to difference-based estimators: covariate-matched U-statistics. We give conditions on the random weights involved that lead to asymptotically optimal estimators of the error variance. Our explicit construction of the weights uses a kernel estimator for the covariate density.     

A comparison of species diversity estimators

Although having been much criticized, diversity indices are still widely used in animal and plant ecology to evaluate, survey, and conserve ecosystems. It is possible to quantify biodiversity by using estimators for which statistical characteristics and performance are, as yet, poorly defined. In the present study, four of the most frequently used diversity indices were compared: the Shannon index, the Simpson index, the Camargo eveness index, and the Pielou regularity index. Comparisons were performed by simulating the Zipf–Mandelbrot parametric model and estimating three statistics of these indices, i.e., the relative bias, the coefficient of variation, and the relative root-mean-squared error. Analysis of variance was used to determine which of the factors contributed most to the observed variation in the four diversity estimators: abundance distribution model or sample size. The results have revealed that the Camargo eveness index tends to demonstrate a high bias and a large relative root-mean-squared error whereas the Simpson index is least biased and the Shannon index shows a smaller relative root-mean-squared error, regardless of the abundance distribution model used and even when sample size is small. Shannon and Pielou estimators are sensitive to changes in species abundance pattern and present a nonnegligible bias for small sample sizes (<1000 individuals). Received: May 8, 1998 / Accepted: May 6, 1999     

On the mvue for the distribution in the multivariate normal regression

In the multivariate normal regression setting, the estimability of a distribution is studied generalizing earlier results for the univariate case. The MVUE of an estimable distribution is obtained.     

Estimation of the mean of an exponential distribution in the presence of an outlier

Kale and Sinha (1971) have found an estimator of the mean of an exponential distribution in the présence of an outlying observation with higher expected value. Here an alternative estimator of the mean is proposed and it is compared with the estimator of Kale and Sinha (1971) and the maximum likelihood estimator given by Kale (1975). The proposed estimator is found to be more efficient than the latter two estimators in some cases.     

Analysis of Linear Models with One Factor Having Both Fixed and Random Levels

ABSTRACT

A general theory for a case where a factor has both fixed and random effect levels is developed under one-way treatment structure model. Estimation procedures for the fixed effects and variance components are consider for the model. The testing of fixed effects is considered when the variance–covariance matrix is known and unknown. Confidence intervals for estimable functions and prediction intervals for predictable functions are constructed. The computational procedures are illustrated using data from an on-farm trial.     

Trace of the Variance-Covariance Matrix in Natural Exponential Families

In this article, we introduce the notion of trace variance function which is the trace of the variance-covariance matrix. Under some conditions, we prove that this trace variance function characterizes the Natural Exponential Family (NEF). We apply this characterization in order to estimate the distribution which belongs to some NEFs. Therefore, we introduce the estimator of this trace variance function. We give the asymptotic properties of this estimator. Finally, we illustrate our results using a simulation study.