Confidence bands for quantile function under random censorship

Some new confidence bands are established for the quantile function from randomly censored data. The method does not require estimation of the density function. As an application, we construct bands for the quantile function of the length of fractures in the granitic plutons near Lac du Bonnet, Manitoba, where an Underground Research Laboratory is being built for the nuclear waste disposal program in Canada.Geological Survey of Canada Contribution Number 10386.Research partially supported by an NSERC Canada Grant.Research done while at Carieton University, supported by NSERC Canada and EMR Canada Grants of M. Csörg.     

Response surface methodology for the optimization of the ultrasonic-assisted rhamnolipid treatment of oily sludge

This study investigates the recovery of oily sludge using ultrasound-assisted rhamnolipids and uses oil recovery yield as an evaluation index. The Box–Behnken response surface method was employed to investigate the individual and interactive effects of four different operating factors: frequency, dosage, liquid–solid ratio, and stirring speed. The model optimization results showed that the order of degree of influence of these four factors is frequency > liquid–solid ratio > dosage > stirring speed. The mathematical model predicted the highest oil recovery yield as 92.27%, which was highly accurate (in the 95% confidence interval) as from the experimental results, the highest oil recovery yield was 89.95% under optimal reaction conditions (frequency = 25.58 kHz, dosage = 150.45 mg/L, liquid–solid ratio = 4.1:1 mL/g, and stirring speed = 407 rpm). Thus, the deviation from the prediction model was only 2.32%, indicating that this method provides a theoretical basis for the treatment of oily sludge and can be implemented for practical application in Huaidong in the Xinjiang Province.     

A smoothed bootstrap estimator for a studentized sample quantile

If the underlying distribution functionF is smooth it is known that the convergence rate of the standard bootstrap quantile estimator can be improved fromn ^–1/4 ton ^–1/2+, for arbitrary >0, by using a smoothed bootstrap. We show that a further significant improvement of this rate is achieved by studentizing by means of a kernel density estimate. As a consequence, it turns out that the smoothed bootstrap percentile-t method produces confidence intervals with critical points being second-order correct and having smaller length than competitors based on hybrid or on backwards critical points. Moreover, the percentile-t method for constructing one-sided or two-sided confidence intervals leads to coverage accuracies of ordern ^–1+, for arbitrary >0, in the case of analytic distribution functions.     

Assessing process capability based on the lower confidence bound of Cpk for asymmetric tolerances

It has been proved that process capability indices provide very efficient measures of the capability of processes from many different perspectives. At the present time, the C_pk index is used more than any other index for measuring process capability. However, most existing research works for capability testing have focused on processes with symmetric tolerances, but not for asymmetric tolerances. A lower confidence bound estimates the minimum process capability, conveying critical information regarding product quality, which is essential to quality assurance. The sample size determination, which provides the sample sizes necessary to achieve a desired lower confidence bound, is directly related to the cost of the data collection plan. This paper provides explicit formulas with efficient algorithms to obtain the lower confidence bounds and sample sizes required for specified precision of the estimation on C_pk for processes with asymmetric tolerances. A Matlab computer program using a binary search method is developed. For the practitioners to use in their in-plant applications, we tabulate lower confidence bounds for some commonly used capability requirement and the sampling accuracy of C_pk for sample sizes determination. A realistic example of forging process is presented to illustrate the applicability of the proposed method.     

出现保障延误时间的可修系统稳态可用度的评定

考虑可修的单元产品在出现故障时,由于种种原因,故障不能得到及时维修,形成了一段保障延误时间.于是这一更新过程为:正常工作(直到出现故障)-保障延误-故障维修-正常工作…….假设工作时间、保障延误时间均服从指数分布,故障维修时间服从对数正态分布,用经典方法和广义p值方法给出了可用度的置信下限.     

Joint empirical likelihood confidence regions for a finite number of quantiles under strong mixing samples

In this paper, we obtain the joint empirical likelihood confidence regions for a finite number of quantiles under strong mixing samples. As an application of this result, the empirical likelihood confidence intervals for the difference of any two quantiles are also obtained.     

Stochastic monotonicity of the MLE of exponential mean under different censoring schemes

In this paper, we present a general method which can be used in order to show that the maximum likelihood estimator (MLE) of an exponential mean θ is stochastically increasing with respect to θ under different censored sampling schemes. This propery is essential for the construction of exact confidence intervals for θ via “pivoting the cdf” as well as for the tests of hypotheses about θ. The method is shown for Type-I censoring, hybrid censoring and generalized hybrid censoring schemes. We also establish the result for the exponential competing risks model with censoring.     

Empirical likelihood for balanced ranked-set sampled data

Ranked-set sampling (RSS) often provides more efficient inference than simple random sampling (SRS). In this article, we propose a systematic nonparametric technique, RSS-EL, for hypothesis testing and interval estimation with balanced RSS data using empirical likelihood (EL). We detail the approach for interval estimation and hypothesis testing in one-sample and two-sample problems and general estimating equations. In all three cases, RSS is shown to provide more efficient inference than SRS of the same size. Moreover, the RSS-EL method does not require any easily violated assumptions needed by existing rank-based nonparametric methods for RSS data, such as perfect ranking, identical ranking scheme in two groups, and location shift between two population distributions. The merit of the RSS-EL method is also demonstrated through simulation studies. This work was supported by National Natural Science Foundation of China (Grant No. 10871037)     

Weibull分布定时截尾试验数据情形下可靠度的置信限

本文针对Weibull分布定时截尾型试验数据提出了一种计算可靠度置信限的方法。通过采用数据填充的方式将不完全数据虚拟成完全数据,利用完全数据情形下可靠度置信限的计算方法得到删失数据情形下可靠度的置信限。模拟研究表明本文提出的算法具有较好的计算稳定性和可操作性。     

On Conservative Confidence Intervals

The subject of the paper – (conservative) confidence intervals – originates in applications to auditing. Auditors are interested in upper confidence bounds for an unknown mean for all sample sizes n. The samples are drawn from populations such that often only a few observations are nonzero. The conditional distribution of an observation given that it is nonzero usually has a very irregular shape. However, it can be assumed that observations are bounded. We propose a way to reduce the problem to inequalities for tail probabilities of certain relevant statistics. Note that a traditional approach involving limit theorems forces to impose additional conditions on regularity of samples and leads to approximate or asymptotic bounds. In the case of , as a statistic we can use sample mean, say , and we have to use Hoeffding [7] inequalities, since currently they are the best available. This leads to upper confidence bounds for which are of (asymptotic) size at most in the case of risk =0.05, where is the unknown standard deviation. We have , where is the bound in a model with normally distributed observations. It seems that the bound is very robust and can be improved replacing Hoeffding's inequalities by more refined ones. The commonly used Stringer bound (it is still not known whether it is an upper confidence bound) is of asymptotic size c with equality only for Bernoulli distributions, and the ratio c / can be arbitrary large already for rather simple distributions. Our bounds can involve a priori information (professional judgment of an auditor) of type ₀ or/and ₀, which leads to improvements. Most of the results also hold for sampling without replacement from finite populations. The i.i.d. condition can be replaced by a martingale-type dependence assumption. Finally, the results can be extended to the noni.i.d. case and for settings with several samples.