Predicting Insurance Losses Under Cross-Classification: A Comparison of Alternative Approaches

Various mathematical and statistical models for estimation of automobile insurance pricing are reviewed. The methods are compared on their predictive ability based on two sets of automobile insurance data for two different states collected over two different periods. The issue of model complexity versus data availability is resolved through a comparison of the accuracy of prediction. The models reviewed range from the use of simple cell means to various multiplicative-additive schemes to the empirical-Bayes approach. The empirical-Bayes approach, with prediction based on both model-based and individual cell estimates, seems to yield the best forecast.     

简单平均组合预测有效性的应用分析

通过实例分析,说明了当序列模式变动较大时,简单平均组合预测模型相对于其他组合预测模型的优越性,并且基于样本段的拟合精度不足以说明组合预测模型的外推预测精度。文中的分析对于组合预测模型的选择和应用具有实际参考价值。     

A sequential conditional probability ratio test procedure for comparing diagnostic tests

In this paper, we derive sequential conditional probability ratio tests to compare diagnostic tests without distributional assumptions on test results. The test statistics in our method are nonparametric weighted areas under the receiver-operating characteristic curves. By using the new method, the decision of stopping the diagnostic trial early is unlikely to be reversed should the trials continue to the planned end. The conservatism reflected in this approach to have more conservative stopping boundaries during the course of the trial is especially appealing for diagnostic trials since the end point is not death. In addition, the maximum sample size of our method is not greater than a fixed sample test with similar power functions. Simulation studies are performed to evaluate the properties of the proposed sequential procedure. We illustrate the method using data from a thoracic aorta imaging study.     

A permutation test approach to the choice of size k for the nearest neighbors classifier

The k nearest neighbors (k-NN) classifier is one of the most popular methods for statistical pattern recognition and machine learning. In practice, the size k, the number of neighbors used for classification, is usually arbitrarily set to one or some other small numbers, or based on the cross-validation procedure. In this study, we propose a novel alternative approach to decide the size k. Based on a k-NN-based multivariate multi-sample test, we assign each k a permutation test based Z-score. The number of NN is set to the k with the highest Z-score. This approach is computationally efficient since we have derived the formulas for the mean and variance of the test statistic under permutation distribution for multiple sample groups. Several simulation and real-world data sets are analyzed to investigate the performance of our approach. The usefulness of our approach is demonstrated through the evaluation of prediction accuracies using Z-score as a criterion to select the size k. We also compare our approach to the widely used cross-validation approaches. The results show that the size k selected by our approach yields high prediction accuracies when informative features are used for classification, whereas the cross-validation approach may fail in some cases.     

词义关系与英语写作

英语写作学习中,学习者写出的短文经常是词不达意,错误百出,缺乏生动与准确。究其原因,学习者词汇量有限,词义知之甚少是造成这些问题的主要障碍。但如果英语学习者能借助词义关系来扩大词汇量、正确掌握词义,他们驾驭词汇的能力必将提高,制约英语写作能力的词汇问题会迎刃而解,并使英语写作的表达更为生动与准确。     

Multiperiod Forecasts of Interest Rates

The accuracy of forecasts of interest rates over different forecast horizons and time periods is examined. The results indicate a deterioration in “absolute” forecast accuracy measured by the mean absolute error and the root mean squared error but no decrease in “relative” accuracy measured by the Theil coefficient with an increase in the forecast span. The results also indicate a decline in accuracy in periods of volatile interest rates. Support is found for the hypothesis that the ratio of the variability of predicted changes to that of actual changes falls with an increase in the forecast horizon.     

A comparison of test statistics for the recovery of rapid growth‐based enumeration tests

This paper considers five test statistics for comparing the recovery of a rapid growth‐based enumeration test with respect to the compendial microbiological method using a specific nonserial dilution experiment. The finite sample distributions of these test statistics are unknown, because they are functions of correlated count data. A simulation study is conducted to investigate the type I and type II error rates. For a balanced experimental design, the likelihood ratio test and the main effects analysis of variance (ANOVA) test for microbiological methods demonstrated nominal values for the type I error rate and provided the highest power compared with a test on weighted averages and two other ANOVA tests. The likelihood ratio test is preferred because it can also be used for unbalanced designs. It is demonstrated that an increase in power can only be achieved by an increase in the spiked number of organisms used in the experiment. The power is surprisingly not affected by the number of dilutions or the number of test samples. A real case study is provided to illustrate the theory. Copyright © 2013 John Wiley & Sons, Ltd.     

The neyman accuracy and the wolfowitz accuracy of the stein type confidence interval for the disturbance variance

In this paper we consider the Neyman accuracy and the Wolfowitz accuracy of the Stein type improved confidence interval I?_S for the disturbance variance in a linear regression model. The Neyman accuracy is a measure related to the unbiasedness of a confidence interval, and the Wolfowitz accuracy is related to the closeness of the endpoints to the true parameter. We show that I?_S is not unbiased and give some numerical results for the Neyman accuracy. As for the Wolfowitz accuracy we derive the sufficient condition for I?_S to improve on the usual confidence interval under this criterion and show numerically that a large degree of improvement can be obtainted.     

An approximation for the hotelling-lawley trace in the noncentral case

A procedure for estimating power in conjunction with the Hotelling-Lawley trace is developed. By approximating a non-central Wishart distribution with a central Wishart, and using McKeon's (1974) F-type approximation, a relatively simple procedure for obtaining power estimates is obtained. The accuracy of the approximation is investigated by comparing the approximate results with those for a wide range of conditions given in Olson's (1973) extensive Monte Carlo study. Siotani's (1971) asymptotic expansion is used to provide further comparative assessments. It is demonstrated that the approximation is of sufficient accuracy to be used in practical applications.     

Kernel Density Estimation with Generalized Binning

We propose kernel density estimators based on prebinned data. We use generalized binning schemes based on the quantiles points of a certain auxiliary distribution function. Therein the uniform distribution corresponds to usual binning. The statistical accuracy of the resulting kernel estimators is studied, i.e. we derive mean squared error results for the closeness of these estimators to both the true function and the kernel estimator based on the original data set. Our results show the influence of the choice of the auxiliary density on the binned kernel estimators and they reveal that non-uniform binning can be worthwhile.