摘要:

In this paper we propose a robust simple linear regression method, namely the smooth adaptwe line (SAL), which divides the data set into three equal groups on the basis of the ordered values of the explanatory variable. The estimators of the slope and intercept are obtained by using the smooth adaptive estimators (SA) (Han and Hawkins 1994) of thc threc groups. The estimators are compared with the least squares (LS) estimators and two other three-group estimators, the resistant line (RL) method (Tukey 1970) and the Bartlett's line (BL) method (Bartlett 1949). A Monte Carlo study is used to study their biases and relative efficiencies for the cases with and without outliers under either normality or non-normality assumption. When there is no outlier or one outlier or small outliers, SAL dominates RL for distributions with tails lighter than t3. Also, SAL dominates BL except for small sample size, say n = 10. To compareSALwith LS, it is known that under normality assumption and no outlier,LSis the best. However, when there are outliers, SAL dominatesLSwhen the outliers are in the x-direction or there are large outliers in the y-direction.

ISSN:0361-0918    

DOI:10.1080/03610919708813364

出版商:Marcel Dekker, Inc.    

年代:1997

数据来源: Taylor

摘要:

Harris (Biometrika, 1989) suggests a predictive distribution based on bootstrapping using the maximum likelihood estimator of an unknown parameter. Basu and Harris (Biometrika, 1994) introduce robust estimative and bootstrap predictive distributions for discrete models by using the minimum Hellinger distance estimator of the unknown parameter instead of the maximum likelihood estimator. Generalizing the results of Basu and Harris, the present paper considers parametric predictive distributions using the minimumpenalized blended weight Hellinger distanceestimator for discrete models. Monte Carlo siniulations suggest that the proposed predictive distributions are attractive robust substitutes for the usual predictive distributions based on the maximum likelihood estimator under data contamination, and perform favorably compared to the predictive distributions suggested by Basu and Harris

ISSN:0361-0918    

DOI:10.1080/03610919708813365

出版商:Marcel Dekker, Inc.    

年代:1997

数据来源: Taylor

摘要:

Combining information from several independent normal populations to estimate a common parameter has applications in meta-analysis and is an important statistical problem. For this application a Bayesian technique via the Gibbs sampler is adopted. Given several normal independent populations with a common mean and different variances, it is possible to perform a complete Bayesian analysis that determines the posterior distribution of the important parameter, the common mean, by using the Gibbs sampler. The methodology is illustrated using two examples. Characteristics such as the mean and the 95% Credible Region are presented. In example 2 a hypotheses test is performed.

ISSN:0361-0918    

DOI:10.1080/03610919708813366

出版商:Marcel Dekker, Inc.    

年代:1997

数据来源: Taylor

摘要:

We consider the estimation of the scale parameter of the shifted exponential distribution and the variance of the normal distribution when the locations of these distributions are unknown and when loss is measured by invariant asymmetric loss functions. Stein type and Bayesian estimators are derived and compared in terms of risk improvements over the best affine equivariant estimator (BAEE). It is demonstrated that, under asymmetric loss, Bayes estimators provide a much larger degree of improvement over the BAEE than Stein estimators.

ISSN:0361-0918    

DOI:10.1080/03610919708813367

出版商:Marcel Dekker, Inc.    

年代:1997

数据来源: Taylor

摘要:

The 2-CUSUM procedure which is a simple modification or the standard CUSUM chart is described and evaluated asymptotically and in a small average run lengths setting. A Markov chain representation to determine approximate expressions for the run length distribution, its moments and its percentage points is given for thts procedure. A simple design of three 2-CUSUM procedures for detecting small, moderate and large shifts in the mean of a normal distribution is proposed. A comparative analysis with the CUSUM envelope and standard CUSUM charts is given showing Lhat quick detection is attainable simultaneously for a wide range of deviations from the targct mean.

ISSN:0361-0918    

DOI:10.1080/03610919708813368

出版商:Marcel Dekker, Inc.    

年代:1997

数据来源: Taylor

摘要:

Shewhartcontrol charts are designed to be used with independent observations. Actualdataare, however, often positively autocorrelated. This simulation study compares the performance of the traditional fixed interval Shewhartcontrol chart with the variable interval technique when the data are autocorrelated. Samples of size 1 are ernployedintheinvestigationwhichisconductedbyvarying the interval length, autocorrelation parameter, and shift in the process mean. Adjustments for false alarms caused by the presence of autocorrelation are implemented. The results suggest that the average time to signal depends on the shift magnitude and the amount of autocorrelation in the process. We show that, in general, when monitoring an autocorrelated process it is advantageous to use the variable interval technique over the fixed interval approach and that this advantage increases in proportion to the shifi in the process mean.

ISSN:0361-0918    

DOI:10.1080/03610919708813369

出版商:Marcel Dekker, Inc.    

年代:1997

数据来源: Taylor

摘要:

In this paper some modifications to the traditional “V-mask” CUSUM control chart, here denoted V-CUSUM, are discussed. In particular, substitution of the linear decision boundary of the V-CUSUM by a parabolic shaped decision boundary is studied. The performance, in terms of average run length,ARL, of the thus defined parabolic CUSUM control chart, P-CUSUM, is explored in a simulation study. The results for the P-CUSUM are compared with some other versions of CUSUM charts and with the Shewhart-chart. The results show that the P-CUSUM provides good detection for a wider range of shift sizes than the other charts under study. Another advantage of the P-CUSUM is its relative simplicity compared to other CUSUM charts, in the respect that the control limits are given by one parameter only. The P-CUSUM has the disadvantage that it cannot be handled recurrently and requires the storage of previous observations. It is argued that the P-CUSUM is better suited to provide estimates of the current process mean. and may so be preferred to other CUSUM charts in applications where deviations fiom target are counteracted by adjustments to the process.

ISSN:0361-0918    

DOI:10.1080/03610919708813370

出版商:Marcel Dekker, Inc.    

年代:1997

数据来源: Taylor

摘要:

In this paper we examine the use of Efron's (1992) jackknife-after-bootstrap to assess the accuracy of the bootstrap. We consider the possibility of using the bootstrap to estimate the finite sample variability of some simple linear statistical models and feasible generalized least squares estimator applied to the seemingly unrelated regressions model. We find that the jackknife-after-bootstrap usually overestimates the variability of the bootstrap standard error by a substantial amount, but that the amount of error declines with increasing numbers of bootstrap samples. Thus the jackknife-after-bootstrap can serve to estimate a comfortable upper bound for the bootstrap standard-error.

ISSN:0361-0918    

DOI:10.1080/03610919708813371

出版商:Marcel Dekker, Inc.    

年代:1997

数据来源: Taylor

摘要:

Survival data subject to left truncation and right censoring are encountered in many follow–up studies. One such situation is follow–up data collected under a cross–sectional sampling scheme. Efron (1981) described two different methods for bootstrapping right censored survival data, which he termed the “obvious” and the “simple” methods, and demonstrated that these two methods are equivalent. Using the nonparametric estimate of the joint distribution of the truncation and censoring times and the nonparametric maximum likelihood estima.te for the sur viva1 curve we generalize the “obvious” method of bootstrapping to the current data. A simulation study examining the large sample behavior of the extensions of both methods is presented. The methods are applied to obtain confidence bands for the nonparametric maximum likelihood estimate of the survival curve, confidence bands for the nonparametric maximum likelihood estimate of tlie truncation distribution, and confidence intervals for the proportion of truncated data. The simulation study shows that, for the specific non-trivial case illustrated, the two methods yield similar large sample results. However. the validity of the extension of the simple method, in general, remains unclear. The authors, therefore, recommend use of the obvious nethod. Real data applications are presented with AIDS Prevalent Cohort Data and the CDC Blood Transfusion Data.

ISSN:0361-0918    

DOI:10.1080/03610919708813372

出版商:Marcel Dekker, Inc.    

年代:1997

数据来源: Taylor

摘要:

This paper proposes a simple numerical procedure for evaluating the asymptotic covariance matrix of the conditional Gaussian maximum likelihood estimator of the parameters for vector autoregressive moving average models when such models are in their appropriate echelon canonical forms. Furthermore, in the process of evaluating the covariance matrix, closed form expressions for the gradient vector are derived in relatively simple terms. Evidence is presented to illustrate the practical application of the technique. Suggestions as to the numerical implementation of the technique in finite sample situations are also made.

ISSN:0361-0918    

DOI:10.1080/03610919708813373

出版商:Marcel Dekker, Inc.    

年代:1997

数据来源: Taylor