Jackknife evaluation of uncertainty judgments aggregated by the Kullback-Leibler distance

One feasible approach to aggregating uncertainty judgments in risk assessments is to use calibration variables (or seed questions) and the Kullback-Leibler (K-L) distance to evaluate experts’ substantive or normative expertise and assign weights based on the corresponding scores. However, the reliability of this aggregation model and the effects of the number of seed questions or experts on the stability of the aggregated results are still at issue. To assess the stability of the aggregation model, this study applies the jackknife re-sampling technique to a large data set of real-world expert opinions. We also use a nonlinear regression model to analyze and interpret the resulting jackknife estimates. Our statistical model indicates that the stability of Cooke’s classical model, in which the components of the scoring rule are determined by the K-L distance, increases exponentially as the number of seed questions increases. Considering the difficulty and importance of creating and choosing appropriate seed variables, the results of this study justify the use of the K-L distance to determine and aggregate better probability interval or distribution estimates.     

Resampling time series using missing values techniques

Several techniques for resampling dependent data have already been proposed. In this paper we use missing values techniques to modify the moving blocks jackknife and bootstrap. More specifically, we consider the blocks of deleted observations in the blockwise jackknife as missing data which are recovered by missing values estimates incorporating the observation dependence structure. Thus, we estimate the variance of a statistic as a weighted sample variance of the statistic evaluated in a “complete” series. Consistency of the variance and the distribution estimators of the sample mean are established. Also, we apply the missing values approach to the blockwise bootstrap by including some missing observations among two consecutive blocks and we demonstrate the consistency of the variance and the distribution estimators of the sample mean. Finally, we present the results of an extensive Monte Carlo study to evaluate the performance of these methods for finite sample sizes, showing that our proposal provides variance estimates for several time series statistics with smaller mean squared error than previous procedures.     

Confidence intervals for quantile estimation using Jackknife techniques

We consider the inference on quantiles, Q _y (β), with jackknife techniques, in finite populations of a variable, Y, using the quantile information on an auxiliary variable, X. Jackknife techniques are applied to estimate quantiles and the behaviour of these estimators is analyzed. Their properties are studied for simple random sampling. We also examine the confidence intervals obtained with jackknife variances.     

Problems arising from jackknifing the estimate of a Kaplan-Meier integral

Stute and Wang (1994) considered the problem of estimating the integral S^θ = ∫ θ dF, based on a possibly censored sample from a distribution F, where θ is an F-integrable function. They proposed a Kaplan-Meier integral to approximate S^θ and derived an explicit formula for the delete-1 jackknife estimate . differs from only when the largest observation, X_(n), is not censored (δ_(n) = 1 and next-to-the-largest observation, X_(n-1), is censored (δ_(n-1) = 0). In this note, it will pointed out that when X_(n) is censored is based on a defective distribution, and therefore can badly underestimate . We derive an explicit formula for the delete-2 jackknife estimate . However, on comparing the expressions of and , their difference is negligible. To improve the performance of and , we propose a modified estimator according to Efron (1980). Simulation results demonstrate that is much less biased than and and .     

偏最小二乘建模在R软件中的实现及实证分析

通过介绍偏最小二乘（PLS）的建模和显著性检验原理,解决了小样本多变量且变量间存在多重共线性的回归问题,建立了多变量对多变量的回归模型,并使用R软件（版本为Ri3862．15．1）实现了PLS建模;最后基于葡萄和葡萄酒理化指标数据进行了实证分析．     

Using AdaBoost for the prediction of subcellular location of prokaryotic and eukaryotic proteins

In this paper, AdaBoost algorithm, a popular and effective prediction method, is applied to predict the subcellular locations of Prokaryotic and Eukaryotic Proteins-a dataset derived from SWISSPROT 33.0. Its prediction ability was evaluated by re-substitution test, Leave-One-Out Cross validation (LOOCV) and jackknife test. By comparing its results with some most popular predictors such as Discriminant Function, neural networks, and SVM, we demonstrated that the AdaBoost predictor outperformed these predictors. As a result, we arrive at the conclusion that AdaBoost algorithm could be employed as a robust method to predict subcellular location. An online web server for predicting subcellular location of prokaryotic and eukaryotic proteins is available at http://chemdata.shu.edu.cn/subcell/ .     

Aqueous iodic acid: Conductance and thermodynamics

Precision conductance measurements are reported on aqueous solutions of iodic acid for 16 concentrations between 17 and 0.7 mM and for 20 temperatures between 5° and 100°C. RlnK _a (m) and _o were calculated at each temperature and the data expressed by suitable temperature functions. From RlnK _a (m) as a function of temperature changes in standard enthalpy, entropy, and heat capacity were calculated. C _p proved to be independent of temperature so that H⁰ was a linear function of temperature. Comparisons have been made with other published data for iodic acid. The pattern of variation of Walden products with temperature was similar to that found earlier for substituted benzoic acids.     

Support Vector Machines for predicting HIV protease cleavage sites in protein

Knowledge of the polyprotein cleavage sites by HIV protease will refine our understanding of its specificity, and the information thus acquired is useful for designing specific and efficient HIV protease inhibitors. The pace in searching for the proper inhibitors of HIV protease will be greatly expedited if one can find an accurate, robust, and rapid method for predicting the cleavage sites in proteins by HIV protease. In this article, a Support Vector Machine is applied to predict the cleavability of oligopeptides by proteases with multiple and extended specificity subsites. We selected HIV-1 protease as the subject of the study. Two hundred ninety-nine oligopeptides were chosen for the training set, while the other 63 oligopeptides were taken as a test set. Because of its high rate of self-consistency (299/299 = 100%), a good result in the jackknife test (286/299 = 95%) and correct prediction rate (55/63 = 87%), it is expected that the Support Vector Machine method can be referred to as a useful assistant technique for finding effective inhibitors of HIV protease, which is one of the targets in designing potential drugs against AIDS. The principle of the Support Vector Machine method can also be applied to analyzing the specificity of other multisubsite enzymes.     

Assessing the Effect of Individual Data Points on Inference From Empirical Likelihood

An oft-cited advantage of empirical likelihood is that the confidence intervals that are produced by this nonparametric technique are not necessarily symmetric. Rather, they reflect the nature of the underlying data and hence give a more representative way of reaching inferences about the functional of interest. However, this advantage can easily become a disadvantage if the resultant intervals are unduly influenced by one of the data points. This article proposes simple methods for evaluating the effect of single points on empirical likelihood confidence intervals. In addition to suggesting diagnostics for detecting important observations, we examine the use of bootstrap and of jackknife influence functions to assess the extremity of suspect points.