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101.
Let X1X2,.be i.i.d. random variables and let Un= (n r)-1S?(n,r) h (Xi1,., Xir,) be a U-statistic with EUn= v, v unknown. Assume that g(X1) =E[h(X1,.,Xr) - v |X1]has a strictly positive variance s?2. Further, let a be such that φ(a) - φ(-a) =α for fixed α, 0 < α < 1, where φ is the standard normal d.f., and let S2n be the Jackknife estimator of n Var Un. Consider the stopping times N(d)= min {n: S2n: + n-1≤2a-2},d > 0, and a confidence interval for v of length 2d,of the form In,d= [Un,-d, Un + d]. We assume that Var Un is unknown, and hence, no fixed sample size method is available for finding a confidence interval for v of prescribed width 2d and prescribed coverage probability α Turning to a sequential procedure, let IN(d),d be a sequence of sequential confidence intervals for v. The asymptotic consistency of this procedure, i.e. limd → 0P(v ∈ IN(d),d)=α follows from Sproule (1969). In this paper, the rate at which |P(v ∈ IN(d),d) converges to α is investigated. We obtain that |P(v ∈ IN(d),d) - α| = 0 (d1/2-(1+k)/2(1+m)), d → 0, where K = max {0,4 - m}, under the condition that E|h(X1, Xr)|m < ∞m > 2. This improves and extends recent results of Ghosh & DasGupta (1980) and Mukhopadhyay (1981). 相似文献
102.
Using the data from the AIDS Link to Intravenous Experiences cohort study as an example, an informative censoring model was
used to characterize the repeated hospitalization process of a group of patients. Under the informative censoring assumption,
the estimators of the baseline rate function and the regression parameters were shown to be related to a latent variable.
Hence, it becomes impractical to directly estimate the unknown quantities in the moments of the estimators for the bandwidth
selection of a smoothing estimator and the construction of confidence intervals, which are respectively based on the asymptotic
mean squared errors and the asymptotic distributions of the estimators. To overcome these difficulties, we develop a random
weighted bootstrap procedure to select appropriate bandwidths and to construct approximated confidence intervals. One can
see that our method is simple and faster to implement from a practical point of view, and is at least as accurate as other
bootstrap methods. In this article, it is shown that the proposed method is useful through the performance of a Monte Carlo
simulation. An application of our procedure is also illustrated by a recurrent event sample of intravenous drug users for
inpatient cares over time. 相似文献
103.
Danny Dyer 《Revue canadienne de statistique》1981,9(1):71-77
By using the structural density function (Fraser 1979, Ch. 7) of the parameters of a Pareto distribution, the structural distribution function of the strong Pareto law is derived. Its fractiles have been evaluated numerically for special cases, and the results are displayed through graphs from which structural one-sided probability bounds may be found. It is shown that these graphs may also be used to find structural tolerance bounds for the Pareto distribution. 相似文献
104.
物资调运时间为区间数的最短路问题研究 总被引:3,自引:0,他引:3
郭瑞鹏 《北京理工大学学报(社会科学版)》2006,8(6):29-30
针对紧急状态下物资调配时间为区间数问题,在经典的Dijkstra算法基础上,通过定义一个算子,把区间数序关系转换成实数序关系,对区间数进行排序,给出了区间数的最短路算法。 相似文献
105.
The academic performance of over 38,000 Texas students who failed the state’s 1994 reading test was examined through their sophomore year in high school. Propensity score matching resulted in strata with retained and promoted students of comparable observed characteristics. Reading scores were analyzed using a two-level hierarchical linear model. Same grade comparisons show that third graders failing the state-mandated reading test who repeated the grade consistently outperformed in later grades the socially promoted children who also failed the third grade test. Additional analyses indicate that alternative explanations for the findings such as omitted variables, regression to the mean, differential panel attrition and cohort effects are not supported. The results are consistent with findings from other recent studies which suggest that grade retention in third grade may help increase student achievement. 相似文献
106.
In this article, we consider the progressive Type II right censored sample from Pareto distribution. We introduce a new approach for constructing the simultaneous confidence interval of the unknown parameters of this distribution under progressive censoring. A Monte Carlo study is also presented for illustration. It is shown that this confidence region has a smaller area than that introduced by Ku? and Kaya (2007). 相似文献
107.
Environmental variables have an important effect on the reliability of many products such as coatings and polymeric composites. Long-term prediction of the performance or service life of such products must take into account the probabilistic/stochastic nature of the outdoor weather. In this article, we propose a time series modeling procedure to model the time series data of daily accumulated degradation. Daily accumulated degradation is the total amount of degradation accrued within one day and can be obtained by using a degradation rate model for the product and the weather data. The fitted model of the time series can then be used to estimate the future distribution of cumulative degradation over a period of time, and to compute reliability measures such as the probability of failure. The modeling technique and estimation method are illustrated using the degradation of a solar reflector material. We also provide a method to construct approximate confidence intervals for the probability of failure. 相似文献
108.
Despite the simplicity of the Bernoulli process, developing good confidence interval procedures for its parameter—the probability of success p—is deceptively difficult. The binary data yield a discrete number of successes from a discrete number of trials, n. This discreteness results in actual coverage probabilities that oscillate with the n for fixed values of p (and with p for fixed n). Moreover, this oscillation necessitates a large sample size to guarantee a good coverage probability when p is close to 0 or 1. It is well known that the Wilson procedure is superior to many existing procedures because it is less sensitive to p than any other procedures, therefore it is less costly. The procedures proposed in this article work as well as the Wilson procedure when 0.1 ≤p ≤ 0.9, and are even less sensitive (i.e., more robust) than the Wilson procedure when p is close to 0 or 1. Specifically, when the nominal coverage probability is 0.95, the Wilson procedure requires a sample size 1, 021 to guarantee that the coverage probabilities stay above 0.92 for any 0.001 ≤ min {p, 1 ?p} <0.01. By contrast, our procedures guarantee the same coverage probabilities but only need a sample size 177 without increasing either the expected interval width or the standard deviation of the interval width. 相似文献
109.
In addition to the distribution function, the mean residual life (MRL) function is the other important function which can be used to characterize a lifetime in survival analysis and reliability. For inference on the MRL function, some procedures have been proposed in the literature. However, the coverage accuracy of such procedures may be low when the sample size is small. In this article, an empirical likelihood (EL) inference procedure of MRL function is proposed and the limiting distribution of the EL ratio for MRL function is derived. Based on the result, we obtain confidence interval/band for the MRL function. The proposed method is compared with the normal approximation based method through simulation study in terms of coverage probability. 相似文献
110.
The problems of constructing tolerance intervals for the binomial and Poisson distributions are considered. Closed-form approximate equal-tailed tolerance intervals (that control percentages in both tails) are proposed for both distributions. Exact coverage probabilities and expected widths are evaluated for the proposed equal-tailed tolerance intervals and the existing intervals. Furthermore, an adjustment to the nominal confidence level is suggested so that an equal-tailed tolerance interval can be used as a tolerance interval which includes a specified proportion of the population, but does not necessarily control percentages in both tails. Comparison of such coverage-adjusted tolerance intervals with respect to coverage probabilities and expected widths indicates that the closed-form approximate tolerance intervals are comparable with others, and less conservative, with minimum coverage probabilities close to the nominal level in most cases. The approximate tolerance intervals are simple and easy to compute using a calculator, and they can be recommended for practical applications. The methods are illustrated using two practical examples. 相似文献