摘要:

This article investigates data on recurrent events that arise from sources such as warranty claims, where the observation period for a unit is unknown until it experiences at least one event. This creates a type of truncation in the data. We consider nonparametric estimation of means and rates of the event occurrences with such “zero-truncated” data and examine the case where the population size and the distribution of observation times across units are at least approximately known. We study the behaviors of the proposed estimators by simulation. We examine some car warranty data by applying the methodology developed here and considering the underlying assumptions.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476689

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

One commonly observed response pattern in a one-factor design with ordered treatment levels is the umbrella or unimodal ordering, in which the response variable increases with an increase in the treatment level up to a point, then decreases with further increase in the treatment level. The turning point is called the peak of an umbrella ordering. In many practical settings, there are two or more different populations with umbrella orderings, and it is of interest to compare these populations. In this article, likelihood ratio tests are developed for testing whether two groups with umbrella orderings have the same peaks. Three cases are considered: variances known, variances unknown and different for each group, and variances unknown and the same for both groups. Extensions to randomized block designs and to a more general class of testing problems are discussed.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476690

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

Exact simultaneous one-sided confidence intervals for contrasts inmnormal means are discussed. The setKof contrast vectors considered is of one of two forms: Either it is a cone whose coordinates are monotone for a partial ordering defined on the coordinate index set {1, …,m} or it is the polar of such a cone. It is shown that the intervals obtained are inverted from test statistics that may be used for testing the null hypothesis that the mean vector μ lies in the dual (or negative polar) cone ofK, against the alternative that μ is not in the dual ofK. Corresponding conservative two-sided intervals are also discussed. The structure of such cones is considered and results concerning dual norms for such cones are obtained. Illustrations for simple ordering, simple-tree, and umbrella orderings are discussed.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476691

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

We present a procedure for finding simultaneous confidence intervals for the expectations μ = (μj)nj=1of a set of independent random variables, identically distributed up to their location parameters, that yields intervals less likely to contain zero than the standard simultaneous confidence intervals for many μ ≠ 0. The procedure is defined implicitly by inverting a nonequivariant hypothesis test with a hyperrectangular acceptance region whose orientation depends on the unsigned ranks of the components of μ, then projecting the convex hull of the resulting confidence region onto the coordinate axes. The projection to obtain simultaneous confidence intervals implicitly involves solvingn! sets of linear inequalities innvariables, but the optima are attained among a set of at mostn2such sets and can be found by a simple algorithm. The procedure also works when the statistics are exchangeable but not independent and can be extended to cases where the inference is based on statistics for μ that are independent but not necessarily identically distributed, provided that there are known functions of μ that are location parameters for the statistics. In the general case, however, it appears that alln! sets of linear inequalities must be examined to find the confidence intervals.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476692

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

A pilot study is often done prior to a more thorough study, to determine whether a larger-scale effort is likely to yield useful results. In one sense, the pilot study can discourage or encourage further investigation. This is true in many situations in auditing. For example, an auditor seeks to determine that amount an insurance provider overpays. Often the provider makes few mistakes and overpays little. On the other hand, occasionally a provider overpays a lot. Because the cost of auditing is expensive and the procedure is somewhat disruptive, a pilot study can prove very useful. When overpayment activity is present, the auditor would like a more precise estimate of overpayment, and then a second sample is called for. Pilot studies generally have small or moderate sample sizes. Nevertheless, the data from these samples should be used in two ways: first, to determine whether further sampling should be done, and second, to be used along with second samples for inference purposes. In this article we consider a model in which the population is normal with unknown mean and unknown variance. A pilot sample is taken and the null hypothesis that the mean is zero is tested against the alternative that the mean is positive. If null hypothesis is rejected, then a second sample is taken. Based on the data from both samples, an exact conditional lower confidence bound is obtained for the mean. The conditioning set consists of those sample points in the first sample that lead to rejection of the null hypothesis. In addition, a bias-corrected asymptotic lower confidence bound is obtained. Generalizations to models other than the normal are indicated.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476693

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

Establishment surveys based on list frames often use stratified random sampling with a small number of strata,H, and relatively large sample sizes,nh, within strata. For such surveys, a grouped balanced half-sample (GBHS) method is often used for variance estimation and for construction of confidence intervals on population parameters of interest. In this method the sample in each stratum is first randomly divided into two groups, and then the balanced half-sample (BHS) method is applied to the groups. We show that the GBHS method leads to asymptotically incorrect inferences as the strata sample sizesnh→ ∞ withHfixed. To overcome this difficulty, we propose a repeatedly grouped balanced half-sample (RGBHS) method, which essentially involves independently repeating the groupingTtimes and then taking the average of the resultingTGBHS variance estimators. This method retains the simplicity of the GBHS method. We establish its asymptotic validity as minnh→ ∞ andT→ ∞. We also study an alternative method by forming substrata within each stratum, consisting of a pair of sampling units, and then applying the BHS method on the total set of substrata, treating them as strata. We establish its asymptotic validity as minnh→ ∞. We provide simulation results on the finite-sample properties of the GBHS, RGBHS, the jackknife, and the alternative BHS method. Our results indicate that the proposed RGBHS method performs well forTas small as 15, thus providing flexibility in terms of the number of half-samples used. The alternative BHS method has also performed well in the simulation study.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476694

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

In a dual frame survey, samples are drawn independently from two overlapping frames that are assumed to cover the population of interest. This article considers the case when at least one of the samples is selected by a complex design involving, e.g., multistage sampling. A “pseudo”—maximum likelihood estimator of a population total or a mean for such dual frame surveys is proposed. An advantage of the proposed estimator is that the same weights are used for all the variables, unlike the estimators of Hartley and Fuller and Burmeister. Asymptotic properties of the estimator are studied, including its efficiency. An alternative “single frame” estimator, based on the design induced by the two separate designs, is also studied. Results of a limited simulation study indicate that our estimator is essentially as efficient as those of Hartley and Fuller and Burmeister and can lead to significant efficiency gains over the single frame estimator.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476695

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

A general theorem is given showing that an optimal stopping problem with independent random horizon is essentially equivalent to a “discounted” fixed horizon optimal stopping problem derived from it. The result is used to treat the “full information” secretary problem, where a known number of applicants for a job are potentially available. Applicants are interviewed sequentially with no recall, and theirXi-values are observed, where theXiare iid random variables from a known continuous distribution. The goal is to pick the applicant with the highestXivalue. The “payoff” for this applicant is 1, and for any other applicant is zero. A random “freeze-time” variableM, with known distribution independent of theXi's makes it impossible to pick an applicant after timeM. The optimal rule is described and necessary and sufficient conditions for it to have a “monotone structure” are given. Uniform and geometric freeze variables are discussed, and some asymptotic results are given.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476696

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

The problem of estimating the node-to-node traffic intensity from repeated measurements of traffic on the links of a network is formulated and discussed under Poisson assumptions and two types of traffic-routing regimens: deterministic (a fixed known path between each directed pair of nodes) and Markovian (a random path between each directed pair of nodes, determined according to a known Markov chain fixed for that pair). Maximum likelihood estimation and related approximations are discussed, and computational difficulties are pointed out. A detailed methodology is presented for estimates based on the method of moments. The estimates are derived algorithmically, taking advantage of the fact that the first and second moment equations give rise to a linear inverse problem with positivity restrictions that can be approached by an EM algorithm, resulting in a particularly simple solution to a hard problem. A small simulation study is carried out.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476697

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

A classification scheme for probability laws by tail behavior is proposed. It circumvents the smoothness conditions usually imposed on the probability laws by current classification schemes and yields a complete characterization of the probability distributions belonging to each category. That is, a distribution functionFhas a long, medium, or short tail, depending on whetherF(lnx) is slowly varying, regularly varying, or rapidly varying. A clear and concise connection with the limiting behavior of extreme spacings is also established and the connection with the existence of moments and moment generating functions is noted. Closure properties of the classification scheme under reliability operations are also considered.

ISSN:0162-1459    

DOI:10.1080/01621459.1996.10476698

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor