摘要:

Various methods have been suggested in the literature to handle a missing covariate in the presence of surrogate covariates. These methods belong to one of two paradigms. In the imputation paradigm, Pepe and Fleming (1991) and Reilly and Pepe (1995) suggested filling in missing covariates using the empirical distribution of the covariate obtained from the observed data. We can proceed one step further by imputing the missing covariate using nonparametric maximum likelihood estimates (NPMLE) of the density of the covariate. Recently Murphy and Van der Vaart (1998a) showed that such an approach yields a consistent, asymptotically normal, and semiparametric efficient estimate for the logistic regression coefficient. In the weighting paradigm, Zhao and Lipsitz (1992) suggested an estimating function using completely observed records after weighting inversely by the probability of observation. An extension of this weighting approach designed to achieve semiparametric efficient bound is considered by Robins, Hsieh and Newey (RHN) (1995). The two ends of each paradigm (NPMLE and RHN) attain the efficiency bound and are asymptotically equivalent. However, both require a substantial amount of computation. A question arises whether and when, in practical situations, this extensive computation is worthwhile. In this paper we investigate the performance of single and multiple imputation estimates, weighting estimates, semiparametric efficient estimates, and two new imputation estimates. Simulation studies suggest that the sample size should be substantially large (e.g. n=2000) for NPMLE and RHN to be more efficient than simpler imputation estimates. When the sample size is moderately large (n≤ 1500), simpler imputation estimates have as small a variance as semiparametric efficient estimates.

ISSN:0361-0918    

DOI:10.1080/03610910008813598

出版商:Marcel Dekker, Inc.    

年代:2000

数据来源: Taylor

摘要:

We describe a class of rank test procedures for the two-sample problem with right censored survival data. The class of tests is directly generalized from the linear rank tests by assigning each observation a rank according to its corresponding Wilcoxon scores. It allows a flexible choice of score functions, in particular, those powerful against scale differences between the two survival distributions. Monte Carlo simulations have shown that some members of this class have great power in detecting crossing-curve alternatives (alternatives where underlying survival curves cross over). The class also contains tests essentially equivalent to the Gehan-Wilcoxon and the logrank tests.

ISSN:0361-0918    

DOI:10.1080/03610910008813599

出版商:Marcel Dekker, Inc.    

年代:2000

数据来源: Taylor

摘要:

A procedure for selecting a Poisson population with smallest mean is considered using an indifference zone approach. The objective is to determine the smallest sample sizenrequired fromk≥ 2 populations in order to attain the desired probability of correct selection. Since the means procedure is not consistent with respect to the difference or ratio alone, two distance measures are used simultaneously to overcome the difficulty in obtaining the smallest probability of correct selection that is greater than some specified limit. The constants required to determinenare computed and tabulated. The asymptotic results are derived using a normal approximation. A comparison with the exact results indicates that the proposed approximation works well. Only in the extreme cases small increases innare observed. An example of industrial accident data is used to illustrate this procedure.

ISSN:0361-0918    

DOI:10.1080/03610910008813600

出版商:Marcel Dekker, Inc.    

年代:2000

数据来源: Taylor

摘要:

A fixed-point method is proposed for calculating quantiles of the sample mean for a saddlepoint approximation. We show that this method has fast convergence rate and can be extended to more general statistics. Examples are given to show the accuracy of the approximation.

ISSN:0361-0918    

DOI:10.1080/03610910008813601

出版商:Marcel Dekker, Inc.    

年代:2000

数据来源: Taylor

摘要:

The effects of estimation of the control limits on the performance of the popular Shewhart X-bar chart are examined via the average run length and the probability of a false alarm, when one or both of the process mean and variance are unknown. Exact expressions for the run length, the average run length (ARL) and the false alarm rate are obtained, in each case, using expectation by conditioning. Applying Jensen's inequality, together with expectation by conditioning, a simple lower bound to the ARL is obtained. This could be useful in designing the charts. The expressions for the exact ARL and the exact probabilities of false alarm are evaluated, using simulations, for various numbers of subgroups and shift sizes. The calculations throw new light on the performance of the Shewhart X-bar chart. Some recommendations are given.

ISSN:0361-0918    

DOI:10.1080/03610910008813602

出版商:Marcel Dekker, Inc.    

年代:2000

数据来源: Taylor

摘要:

A simple multiplicative noise model with a constant signal has become a basic mathematical model in processing synthetic aperture radar images. The purpose of this paper is to examine a general multiplicative noise model with linear signals represented by a number of unknown parameters. The ordinary least squares (LS) and weighted LS methods are used to estimate the model parameters. The biases of the weighted LS estimates of the parameters are derived. The biases are then corrected to obtain a second-order unbiased estimator, which is shown to be exactly equivalent to the maximum log quasi-likelihood estimation, though the quasi-likelihood function is founded on a completely different theoretical consideration and is known, at the present time, to be a uniquely acceptable theory for multiplicative noise models. Synthetic simulations are carried out to confirm theoretical results and to illustrate problems in processing data contaminated by multiplicative noises. The sensitivity of the LS and weighted LS methods to extremely noisy data is analysed through the simulated examples.

ISSN:0361-0918    

DOI:10.1080/03610910008813603

出版商:Marcel Dekker, Inc.    

年代:2000

数据来源: Taylor

摘要:

The Monte Carlo method gives some estimators to evaluate the expectation [ILM0001] based on samples from either the true densityfor from some instrumental density. In this paper, we show that the Riemann estimators introduced by Philippe (1997) can be improved by using the importance sampling method. This approach produces a class of Monte Carlo estimators such that the variance is of orderO(n−2). The choice of an optimal estimator among this class is discussed. Some simulations illustrate the improvement brought by this method. Moreover, we give a criterion to assess the convergence of our optimal estimator to the integral of interest.

ISSN:0361-0918    

DOI:10.1080/03610910008813604

出版商:Marcel Dekker, Inc.    

年代:2000

数据来源: Taylor

摘要:

Most of the research effort concerning the development and statistical study of capability indices has been devoted to normal processes. In this paper a statistical study of a capability index for non-normal processes proposed by Clements (1989) is developed. An approximate distribution for the natural estimator of the index is obtained from a distribution free point of view and a simulation study is used to compare it with its empirical distribution. An approximate conservative lower confidence limit for the index is also constructed.

ISSN:0361-0918    

DOI:10.1080/03610910008813605

出版商:Marcel Dekker, Inc.    

年代:2000

数据来源: Taylor

摘要:

The robust principal components analysis (RPCA) introduced by Campbell (Applied Statistics1980,29,231–237) provides in addition to robust versions of the usual output of a principal components analysis, weights for the contribution of each point to the robust estimation of each component. Low weights may thus be used to indicate outliers. The present simulation study provides critical values for testing the kth smallest weight in the RPCA of a sample of n p-dimensional vectors, under the null hypothesis of a multivariate normal distribution. The cases p=2(2)10, 15, 20 for n=20, 30, 40, 50, 75, 100 subject to n≥p/2, are examined, with k≤√n.

ISSN:0361-0918    

DOI:10.1080/03610910008813606

出版商:Marcel Dekker, Inc.    

年代:2000

数据来源: Taylor

摘要:

Changes in the process mean (μ) or in the process standard deviation (σ) ought to be regarded as an indication that a production process is out of control.

ISSN:0361-0918    

DOI:10.1080/03610910008813607

出版商:Marcel Dekker, Inc.    

年代:2000

数据来源: Taylor