Percentile Bootstrap Confidence Interval Research Articles

Comparative analysis of availability for a redundant repairable system

We consider the steady-state availability, denoted A, of a repairable system consisted of one operating unit and one spare. This paper we are interested in computational comparisons of confidence intervals for A based on four feasible and efficient approaches. The natural estimator A ^ of A, defined as the ratio of the sample mean lifetime of the operating unit to the sum of the sample mean lifetime of the operating unit and the sample mean downtime of system, is strongly consistent and asymptotically normal. The interval estimations for A are constructed through four bootstrap approaches; standard bootstrap confidence interval, percentile bootstrap confidence interval, bias-corrected percentile bootstrap confidence interval as well as bias-corrected and accelerated confidence interval. Finally, by calculating the coverage percentage and the average length of intervals, some numerical simulation comparisons are conducted in order to illustrate the performances of A ^ on various interval estimations.

Mean response time for a G/ G/1 queueing system: Simulated computation

Mean response time, denoted by r, plays an important role of system characteristics in queueing models. In this paper we developed a data-based recursion relation to compute a sequence of response times, and the sample mean from these response times, denoted by r ˆ , was used to estimate mean response time r of an FCFS G/ G/1 queueing system. We further construct new confidence intervals of r for a G/ G/1 queueing system, which are based on four bootstrap methods; standard bootstrap (SB) confidence interval, percentile bootstrap (PB) confidence interval, bias-corrected percentile bootstrap (BCPB) confidence interval, and bias-corrected and accelerated (BCa) confidence interval. A numerical simulation study is conducted in order to demonstrate performance of the proposed estimator r ˆ and bootstrap confidence intervals of r. From the simulation results, we show that r ˆ is a consistent estimator of r. In addition, we also investigate the accuracy of the four bootstrap confidence intervals by calculating the coverage percentage, the average length, and the relative average length of confidence intervals. Detailed discussions of simulation results for seven various queueing models are presented.

Confidence intervals of mean response time for an M/G/1 queueing system: Bootstrap simulation

Mean response time plays an important role of system performance measures in queueing model. In this paper, we construct new confidence intervals of mean response time for an M/G/1 FCFS queueing system, which are based on four bootstrap methods: standard bootstrap confidence interval, percentile bootstrap confidence interval, bootstrap- t confidence interval, and bias-corrected and accelerated confidence interval. We also perform the accuracy of these bootstrap confidence intervals through calculating the coverage probability and the average length of confidence intervals. Detailed discussions of the simulation results for three various models of an M/G/1 FCFS queueing system are presented and some conclusions are provided.

Comparison of family-based association tests in chromosome regions selected by linkage-based confidence intervals

We use the Genetic Analysis Workshop 14 simulated data to explore the effectiveness of a two-stage strategy for mapping complex disease loci consisting of an initial genome scan with confidence interval construction for gene location, followed by fine mapping with family-based tests of association on a dense set of single-nucleotide polymorphisms. We considered four types of intervals: the 1-LOD interval, a basic percentile bootstrap confidence interval based on the position of the maximum Zlr score, and asymptotic and bootstrap confidence intervals based on a generalized estimating equations method. For fine mapping we considered two family-based tests of association: a test based on a likelihood ratio statistic and a transmission-disequilibrium-type test implemented in the software FBAT. In two of the simulation replicates, we found that the bootstrap confidence intervals based on the peak Zlr and the 1-LOD support interval always contained the true disease loci and that the likelihood ratio test provided further strong confirmatory evidence of the presence of disease loci in these regions.

An Alternative to Cohen's Standardized Mean Difference Effect Size: A Robust Parameter and Confidence Interval in the Two Independent Groups Case.

The authors argue that a robust version of Cohen's effect size constructed by replacing population means with 20% trimmed means and the population standard deviation with the square root of a 20% Winsorized variance is a better measure of population separation than is Cohen's effect size. The authors investigated coverage probability for confidence intervals for the new effect size measure. The confidence intervals were constructed by using the noncentral t distribution and the percentile bootstrap. Over the range of distributions and effect sizes investigated in the study, coverage probability was better for the percentile bootstrap confidence interval.

Efficiently measuring recognition performance with sparse data

We examine methods for measuring performance in signal-detection-like tasks when each participant provides only a few observations. Monte Carlo simulations demonstrate that standard statistical techniques applied to a d' analysis can lead to large numbers of Type I errors (incorrectly rejecting a hypothesis of no difference). Various statistical methods were compared in terms of their Type I and Type II error (incorrectly accepting a hypothesis of no difference) rates. Our conclusions are the same whether these two types of errors are weighted equally or Type I errors are weighted more heavily. The most promising method is to combine an aggregate d' measure with a percentile bootstrap confidence interval, a computer-intensive nonparametric method of statistical inference. Researchers who prefer statistical techniques more commonly used in psychology, such as a repeated measures t test, should use gamma (Goodman & Kruskal, 1954), since it performs slightly better than or nearly as well as d'. In general, when repeated measures t tests are used, gamma is more conservative than d': It makes more Type II errors, but its Type I error rate tends to be much closer to that of the traditional .05 alpha level. It is somewhat surprising that gamma performs as well as it does, given that the simulations that generated the hypothetical data conformed completely to the d' model. Analyses in which H--FA was used had the highest Type I error rates. Detailed simulation results can be downloaded from www.psychonomic.org/archive/Schooler-BRM-2004.zip.

BOOTSTRAP CONFIDENCE INTERVALS FOR STEADY-STATE AVAILABILITY

Steady-state availability, denoted by A, has been widely used as a measure to evaluate the reliability of a repairable system. In this paper, we develop new confidence intervals for steady-state availability based on four bootstrap methods; standard bootstrap confidence interval, percentile bootstrap confidence interval, bootstrap-t confidence interval, and bias-corrected and accelerated confidence interval. We also investigate the accuracy of these bootstrap confidence intervals by calculating the coverage probability and the average length of intervals.

Bootstrap Confidence Interval of the Difference Between Two Process Capability Indices

1 - C pk 2 , cannot be inferred statistically because of the complexity of the sampling probability theory. This study proposes a bootstrap resampling simulation method to construct the biased corrected percentile bootstrap (BCPB) confidence interval of (C pk 1 - C pk 2 ), which can be used to select the better of two suppliers. The various simulation results indicate that the bootstrap confidence interval of (C pk 1 - C pk 2 ) can be employed to evaluate effectively the difference between the performance of two suppliers.

A Semi-Parametric Quantile Function Estimator for Use in Bootstrap Estimation Procedures

In this note we develop a new quantile function estimator called the tail extrapolation quantile function estimator. The estimator behaves asymptotically exactly the same as the standard linear interpolation estimator. For finite samples there is small correction towards estimating the extreme quantiles. We illustrate that by employing this new estimator we can greatly improve the coverage probabilities of the standard bootstrap percentile confidence intervals. The method does not reqiure complicated calculations and hence it should appeal to the statistical practitioner.

Bandwidth selection for the smoothed bootstrap percentile method

Some applications of the bootstrap involve smoothing the estimated distribution that is resampled, a method known as the smoothed bootstrap. Recently, the effect of resampling a kernel smoothed distribution was evaluated through expansions for the coverage of bootstrap percentile confidence intervals. It was shown that under a smooth function model, a bandwidth of order n −1/4 can accomplish a first-order correction for the one-sided percentile method. This paper proposes and investigates the performance of some data-based methods for selecting this bandwidth. The methods are studied through asymptotic comparisons and the resulting intervals are compared in the finite sample case to other well-known bootstrap confidence interval methods through a simulation study.

Intervalo de confiança "bootstrap" como ferramenta para classificar raças do nematóide de cisto da soja

Estimativas "bootstrap" da média aritmética dos genótipos de soja 'Pickett', 'Peking', PI88788 e PI90763 e os intervalos de confiança obtidos pela teoria normal e através da distribuição "bootstrap" deste estimador, como o percentil "bootstrap" e o BCa, correção para o viés e aceleração, do parâmetro de diferenciação da cultivar padrão de suscetibilidade Lee são utilizados para classificar raças do nematóide de cisto da soja. Os intervalos de confiança obtidos a partir da distribuição "bootstrap" apresentaram menor amplitude e foram muito similares, dessa forma, o limite inferior do intervalo de confiança percentil "bootstrap" foi tomado como nível de referência nas distribuições "bootstrap" do estimador da média aritmética dos genótipos diferenciadores, permitindo estimar a probabilidade empírica de uma reação positiva ou negativa, e, conseqüentemente, identificar a raça mais provável sob determinado teste.

Problems with interval estimates of the incremental cost-effectiveness ratio.

The defining feature of a confidence interval is that it has a fixed minimum probability of covering the true value of the parameter being estimated, whatever the value of the parameter. The authors demonstrate by simulation that some recently proposed methods for interval estimation of the incremental cost-effectiveness ratio (ICER) either do not satisfy this definition or have other problems that limit their usefulness in applications. The problems are most prominent when the ICER is large and the true effectiveness difference is small relative to its standard error. A modification of the percentile bootstrap confidence interval that involves a reordering of the sample space provides a partial solution of the problem.

Kernel Smoothing to Improve Bootstrap Confidence Intervals

Summary Some studies of the bootstrap have assessed the effect of smoothing the estimated distribution that is resampled, a process usually known as the smoothed bootstrap. Generally, the smoothed distribution for resampling is a kernel estimate and is often rescaled to retain certain characteristics of the empirical distribution. Typically the effect of such smoothing has been measured in terms of the mean-squared error of bootstrap point estimates. The reports of these previous investigations have not been encouraging about the efficacy of smoothing. In this paper the effect of resampling a kernel-smoothed distribution is evaluated through expansions for the coverage of bootstrap percentile confidence intervals. It is shown that, under the smooth function model, proper bandwidth selection can accomplish a first-order correction for the one-sided percentile method. With the objective of reducing the coverage error the appropriate bandwidth for one-sided intervals converges at a rate of n −1/4, rather than the familiar n −1/5 for kernel density estimation. Applications of this same approach to bootstrap t and two-sided intervals yield optimal bandwidths of order n −1/2. These bandwidths depend on moments of the smooth function model and not on derivatives of the underlying density of the data. The relationship of this smoothing method to both the accelerated bias correction and the bootstrap t methods provides some insight into the connections between three quite distinct approximate confidence intervals.

Pulling cost-effectiveness analysis up by its bootstraps: a non-parametric approach to confidence interval estimation.

The statistic of interest in the economic evaluation of health care interventions is the incremental cost effectiveness ratio (ICER), which is defined as the difference in cost between two treatment interventions over the difference in their effect. Where patient-specific data on costs and health outcomes are available, it is natural to attempt to quantify uncertainty in the estimated ICER using confidence intervals. Recent articles have focused on parametric methods for constructing confidence intervals. In this paper, we describe the construction of non-parametric bootstrap confidence intervals. The advantage of such intervals is that they do not depend on parametric assumptions of the sampling distribution of the ICER. We present a detailed description of the non-parametric bootstrap applied to data from a clinical trial, in order to demonstrate the strengths and weaknesses of the approach. By examining the bootstrap confidence limits successively as the number of bootstrap replications increases, we conclude that percentile bootstrap confidence interval methods provide a promising approach to estimating the uncertainty of ICER point estimates. However, successive bootstrap estimates of bias and standard error suggests that these may be unstable; accordingly, we strongly recommend a cautious interpretation of such estimates.

Estimation of a process capability index for inverse gaussian distribution

In this article, interval estimates of Clements' process capability index are studied through bootstrapping when the underlying distribution is Inverse Gaussian. The standard bootstrap, the percentile bootstrap, and the bias-corrected percentile bootstrap confidence intervals are compared.

Richardson Extrapolation and the Bootstrap

Abstract Simulation methods [particularly Efron's (1979) bootstrap] are being applied more and more frequently in statistical inference. Given data (X 1 …, Xn ) distributed according to P, which belongs to a hypothesized model P, the basic goal is to estimate the distribution L P of a function Tn (X 1, …, Xn, P). The bootstrap presupposes the existence of an estimate and involves estimating L P by the distribution L* n of ), where (X 1*, …, Xn *) is distributed according to The method is of particular interest when Ln *, though known in principle, can realistically only be computed by simulation. Such computation can be expensive if n is large and Tn is complex (e.g., see the multivariate goodness-of-fit tests of Beran and Millar 1986). Even when bootstrap application to a single data set is not excessively expensive, Monte Carlo studies of the bootstrap are another matter. We propose a method based on the classical ideas of Richardson extrapolation for reducing the computational cost inherent in bootstrap simulations and Monte Carlo studies of the bootstrap, by performing simulations for statistics based on two smaller sample sizes. We study theoretically which ratio of the two small sample sizes is apt to give best results. We show how our method works for approximating the χ2, t, and smoothed binomial distributions, and for setting bootstrap percentile confidence intervals for the variance of a normal distribution with a mean of 0.