Interval Estimation for the Two-Parameter Exponential Distribution Based on the Doubly Type II Censored Sample

The interval estimation of the scale parameter and the joint confidence region of the parameters of two-parameter exponential distribution under doubly Type II censoring is proposed. In addition, the simulation study for the performance of our methods is done in this paper. One biometrical example is also given to illustrate the proposed methods.     

逐次定数截尾下Weibull分布参数的逆矩估计

基于逐次定数截尾样本下,讨论了两参数Weibull分布的参数估计,得到了两参数的逆矩估计.并利用模拟方法与极大似然估计作比较,模拟结果表明逆矩估计优于极大似然估计。     

On estimating the reliability after sequentially estimating the mean: The exponential case

Sequential estimation problems for the mean parameter of an exponential distribution has received much attention over the years. Purely sequential and accelerated sequential estimators and their asymptotic second-order characteristics have been laid out in the existing literature, both for minimum risk point as well as bounded length confidence interval estimation of the mean parameter. Having obtained a data set from such sequentially designed experiments, the paper investigates estimation problems for the associatedreliability function. Second-order approximations are provided for the bias and mean squared error of the proposed estimator of the reliability function, first under a general setup. An ad hoc bias-corrected version is also introduced. Then, the proposed estimator is investigated further under some specific sequential sampling strategies, already available in the literature. In the end, simulation results are presented for comparing the proposed estimators of the reliability function for moderate sample sizes and various sequential sampling strategies.     

Optimal Estimation of the Parameters of the Gompertz Distribution Based on the Doubly Type II Censored Sample

In this paper, we develop exact confidence intervals and exactjoint confidence regions for the parameters of the Gompertzdistribution under the doubly type II censored sample. We alsoprovide optimal criteria for finding a best exact confidenceinterval and a best exact joint confidence region among theseinterval estimations. Finally, we give a numerical example toillustrate our proposed method. Furthermore,when compared to estimation of Chen (1997), our proposedmethod can get a better parameter estimation.     

Fat tails and spurious estimation of consumption‐based asset pricing models

The standard generalized method of moments (GMM) estimation of Euler equations in heterogeneous‐agent consumption‐based asset pricing models is inconsistent under fat tails because the GMM criterion is asymptotically random. To illustrate this, we generate asset returns and consumption data from an incomplete‐market dynamic general equilibrium model that is analytically solvable and exhibits power laws in consumption. Monte Carlo experiments suggest that the standard GMM estimation is inconsistent and susceptible to Type II errors (incorrect nonrejection of false models). Estimating an overidentified model by dividing agents into age cohorts appears to mitigate Type I and II errors.     

Estimation of P[Y < X] for generalized exponential distribution

This paper deals with the estimation of P[Y < X] when X and Y are two independent generalized exponential distributions with different shape parameters but having the same scale parameters. The maximum likelihood estimator and its asymptotic distribution is obtained. The asymptotic distribution is used to construct an asymptotic confidence interval of P[Y < X]. Assuming that the common scale parameter is known, the maximum likelihood estimator, uniformly minimum variance unbiased estimator and Bayes estimator of P[Y < X] are obtained. Different confidence intervals are proposed. Monte Carlo simulations are performed to compare the different proposed methods. Analysis of a simulated data set has also been presented for illustrative purposes.Part of the work was supported by a grant from the Natural Sciences and Engineering Research Council     

Estimation of the change point of a distribution based on the number of failed test items

This paper discusses the family of life distributions with failure rate functions which decrease initially until a change point and remain constant thereafter. The paper focuses on the estimation for the change point of the failure rate function. While point estimation of the change point of the failure rate function has been discussed by some authors, one can hardly find any existing work on the interval estimation of the change point. In this paper, a method for constructing approximate confidence intervals for the change point is proposed. The proposed approximate confidence intervals are based on the number of failed test items at or before a fixed inspection time. Received: September 1999     

Nonparametric estimation in case of endogenous selection

This paper addresses the problem of estimation of a nonparametric regression function from selectively observed data when selection is endogenous. Our approach relies on independence between covariates and selection conditionally on potential outcomes. Endogeneity of regressors is also allowed for. In the exogenous and endogenous case, consistent two-step estimation procedures are proposed and their rates of convergence are derived. Pointwise asymptotic distribution of the estimators is established. In addition, bootstrap uniform confidence bands are obtained. Finite sample properties are illustrated in a Monte Carlo simulation study and an empirical illustration.     

Estimation in generalized bivariate Birnbaum–Saunders models

In this paper, we propose two moment-type estimation methods for the parameters of the generalized bivariate Birnbaum–Saunders distribution by taking advantage of some properties of the distribution. The proposed moment-type estimators are easy to compute and always exist uniquely. We derive the asymptotic distributions of these estimators and carry out a simulation study to evaluate the performance of all these estimators. The probability coverages of confidence intervals are also discussed. Finally, two examples are used to illustrate the proposed methods.     

浅谈假设检验中的两类错误及样本含量的关系

假设检验是统计推断的内容之一,统计推断在体育统计学中的地位也十分重要。在假设检验中存在两类错误。在很多时候,我们往往只注意第一类错误的控制,而对于第二类错误经常不考虑。其实,对于第二类错误的控制也是十分必要的。本文对于两类错误的成因以及如何控制第二类错误进行了探讨,希望对于第二类错误的控制提出一些解决的方法。     

自相关过程能力指数置信区间的构建与评价

过程能力指数是指过程处于控制状态下的实际加工能力,其计算方法通常要求过程是独立同分布的,而实际过程中数据往往表现出一定的自相关性。评价过程控制的能力指数是一个基于样本观测值的统计量,需要对其进行统计检验。当过程自相关时,还需要对其进行统计推断。本文提出了自相关下过程能力指数置信区间的构建方法,并从理论和模拟两个角度研究自相关对该置信区间的影响,给出了自相关情形下置信区间的计算步骤。模拟和实证均表明：正自相关会导致常规方法估计出的置信区间偏大且上移,负自相关会导致置信区间估计偏小且下移,本文提出的方法能很好地解决置信区间估计不准确的问题,能较准确地评价过程的实际生产能力。     

Modified maximum spacings method for generalized extreme value distribution and applications in real data analysis

This paper analyzes weekly closing price data of the S&P 500 stock index and electrical insulation element lifetimes data based on generalized extreme value distribution. A new estimation method, modified maximum spacings (MSP) method, is proposed and obtained by using interior penalty function algorithm. The standard error of the proposed method is calculated through Bootstrap method. The asymptotic properties of the modified MSP estimators are discussed. Some simulations are performed, which show that the proposed method is not only available for the whole shape parameter space, but is also of high efficiency. The benchmark risk index, value at risk (VaR), is evaluated according to the proposed method, and the confidence interval of VaR is also calculated through Bootstrap method. Finally, the results are compared with those derived by empirical calculation and some existing methods.     

Beyond Intermediates: The Role of Consumption and Commuting in the Construction of Local Input–Output Tables

Estimating intermediate trade using conventional non-survey methods produces biased results. This problem has led to a methodological recommendation that emphasizes the accurate estimation of intermediate trade flows. This paper argues for a qualification of the consensus view: when simulating input–output (IO) tables, analysts need also to consider spillover effects driven by wage and consumption flows. In particular, for metropolitan economies, capturing wage and consumption flows is essential to obtain accurate Type II multipliers. This is demonstrated by constructing an interregional IO table that captures the interdependence between a city and its commuter belt, nested within the wider regional economy.     

Bootstrap and Asymptotic Tests of Long-run Relationships in Cointegrated Systems

Hypothesis testing on cointegrating vectors based on the asymptotic distributions of the test statistics are known to suffer from severe small sample size distortion. In this paper an alternative bootstrap procedure is proposed and evaluated through a Monte Carlo experiment, finding that the Type I errors are close to the nominal signficance levels but power might be not entirely adequate. It is then shown that a combined test based on the outcomes of both the asymptotic and the bootstrap tests will have both correct size and low Type II error, therefore improving the currently available procedures.     

Estimation of population proportion in randomized response sampling using weighted confidence interval construction

This paper considers the problem of estimation for binomial proportions of sensitive attributes in the population of interest. Randomized response techniques are suggested for protecting the privacy of respondents and reducing the response bias while eliciting information on sensitive attributes. By applying the Wilson (J Am Stat Assoc 22:209–212, 1927) score approach for constructing confidence intervals, various probable point estimators and confidence interval estimators are suggested for the common structures of randomized response procedures. In addition, efficiency comparisons are carried out to study the performances of the proposed estimators for both the cases of direct response surveys and randomized response surveys. Circumstances under which each proposed estimators is better are also identified.     

Three-stage estimation procedures for the negative exponential distributions

Fixed-width confidence interval estimation problems for location parameters of negative exponential populations have been studied. Three-stage sampling procedures have been developed for both the one- and two-sample situations. Our discussions are primarily concerned with second-order expansions of various characteristics of the proposed procedures including those for the achieved coverage probability in either problem. Some simulated results are also presented to indicate the usefulness of our procedures for moderate sample sizes.     

Sequential estimation of means of linear processes

First the minimum risk point estimation as well as the fixed-width confidence interval problems for the mean parameter of a linear process are addressed under the framework of Fakhre-Zakeri and Lee (1992). The accelerated versions of their full sequential methodologies are introduced in order to achieve operational savings. Next, multi-sample analogs are discussed along the lines of Mukhopadhyay and Sriram (1992) both under full sequential as well as accelerated sequential sampling. In either setup, the first-order asymptotic characteristics are highlighted.     

Simultaneous optimal estimation in linear mixed models

Simultaneous optimal estimation in linear mixed models is considered. A necessary and sufficient condition is presented for the least squares estimator of the fixed effects and the analysis of variance estimator of the variance components to be of uniformly minimum variance simultaneously in a general variance components model. That is, the matrix obtained by orthogonally projecting the covariance matrix onto the orthogonal complement space of the column space of the design matrix is symmetric, each eigenvalue of the matrix is a linear combinations of the variance components and the number of all distinct eigenvalues of the matrix is equal to the the number of the variance components. Under this condition, uniformly optimal unbiased tests and uniformly most accurate unbiased confidence intervals are constructed for the parameters of interest. A necessary and sufficient condition is also given for the equivalence of several common estimators of variance components. Two examples of their application are given.     

Testing for serial correlation in simultaneous equation models: Some further results

In this paper approximate counterparts of the exact tests earlier proposed by the authors are examined. Type 1 error probabilities and test powers are estimated and compared using Monte Carlo experiments. The effect on the Type 1 error probabilities of the misspecification which results when serial correlation is present elsewhere in the system is also investigated.     

Distribution-free Approximate Methods for Constructing Confidence Intervals for Quantiles

Quantile estimation is important for a wide range of applications. While point estimates based on one or two order statistics are common, constructing confidence intervals around them, however, is a more difficult problem. This paper has two goals. First, it surveys the numerous distribution-free methods for constructing approximate confidence intervals for quantiles. These techniques can be divided roughly into four categories: using a pivotal quantity, resampling, interpolation, and empirical likelihood methods. Second, a method based on the pivotal quantity that has received limited attention in the past is extended. Comprehensive simulation studies are used to compare performance across methods. The proposed method is simple and performs similarly to linear interpolation methods and a smoothed empirical likelihood method. While the proposed method has slightly wider interval widths, it can be calculated for more extreme quantiles even when there are few observations.