Record-breaking data: a parametric comparison of the inverse-sampling and the random-sampling schemes

In many industrial quality control experiments and destructive stress testing, the only available data are successive minima (or maxima)i.e., record-breaking data. There are two sampling schemes used to collect record-breaking data: random sampling and inverse sampling. For random sampling, the total sample size is predetermined and the number of records is a random variable while in inverse-sampling the number of records to be observed is predetermined; thus the sample size is a random variable. The purpose of this papper is to determinevia simulations, which of the two schemes, if any, is more efficient. Since the two schemes are equivalent asymptotically, the simulations were carried out for small to moderate sized record-breaking samples. Simulated biases and mean square errors of the maximum likelihood estimators of the parameters using the two sampling schemes were compared. In general, it was found that if the estimators were well behaved, then there was no significant difference between the mean square errors of the estimates for the two schemes. However, for certain distributions described by both a shape and a scale parameter, random sampling led to estimators that were inconsistent. On the other hand, the estimated obtained from inverse sampling were always consistent. Moreover, for moderated sized record-breaking samples, the total sample size that needs to be observed is smaller for inverse sampling than for random sampling.     

On the sample characterization criterion for normal distributions

Conventionally, it was shown that the underlying distribution is normal if and only if the sample mean and sample variance from a random sample are independent. This paper focusses on the normal population characterization theorem by showing that, if the joint distribution of a skew normal sample follows certain multivariate skew normal distribution, the sample mean and sample variance are still independent.     

Computing optimal adjustment schemes for the general tool-wear problem

An important problem in process adjustment using feedback is how often to sample the process and when and by how much to apply an adjustment. Minimum cost feedback schemes based on simple, but practically interesting, models for disturbances and dynamics have been discussed in several particular cases. The more general situation in which there may be measurement and adjustment errors, deterministic process drift, and costs of taking an observation, of making an adjustment, and of being off target, is considered in this article. Assuming all these costs to be known, a numerical method to minimize the overall expected cost is presented. This numerical method provides the optimal sampling interval, action limits, and amount of adjustment; and the resulting average adjustment interval, mean squared deviation from target, and minimum overall expected cost. When the costs of taking an observation, of making an adjustment, and of being off target are not known, the method can be used to choose a particular scheme by judging the advantages and disadvantages of alternative options considering the mean squared deviation they produce, the frequency with which they require observations to be made, and the resulting overall length of time between adjustments. Computer codes that perform the required computations are provided in the appendices and applied to find optimal adjustment schemes in three real examples of application.     

On cumulative entropies

In analogy with the cumulative residual entropy recently proposed by Wang et al. [2003a. A new and robust information theoretic measure and its application to image alignment. In: Information Processing in Medical Imaging. Lecture Notes in Computer Science, vol. 2732, Springer, Heidelberg, pp. 388–400; 2003b. Cumulative residual entropy, a new measure of information and its application to image alignment. In: Proceedings on the Ninth IEEE International Conference on Computer Vision (ICCV’03), vol. 1, IEEE Computer Society Press, Silver Spring, MD, pp. 548–553], we introduce and study the cumulative entropy, which is a new measure of information alternative to the classical differential entropy. We show that the cumulative entropy of a random lifetime X can be expressed as the expectation of its mean inactivity time evaluated at X. Hence, our measure is particularly suitable to describe the information in problems related to ageing properties of reliability theory based on the past and on the inactivity times. Our results include various bounds to the cumulative entropy, its connection to the proportional reversed hazards model, and the study of its dynamic version that is shown to be increasing if the mean inactivity time is increasing. The empirical cumulative entropy is finally proposed to estimate the new information measure.     

A comparison of classification models to identify the Fragile X Syndrome

The main models of machine learning are briefly reviewed and considered for building a classifier to identify the Fragile X Syndrome (FXS). We have analyzed 172 patients potentially affected by FXS in Andalusia (Spain) and, by means of a DNA test, each member of the data set is known to belong to one of two classes: affected, not affected. The whole predictor set, formed by 40 variables, and a reduced set with only nine predictors significantly associated with the response are considered. Four alternative base classification models have been investigated: logistic regression, classification trees, multilayer perceptron and support vector machines. For both predictor sets, the best accuracy, considering both the mean and the standard deviation of the test error rate, is achieved by the support vector machines, confirming the increasing importance of this learning algorithm. Three ensemble methods - bagging, random forests and boosting - were also considered, amongst which the bagged versions of support vector machines stand out, especially when they are constructed with the reduced set of predictor variables. The analysis of the sensitivity, the specificity and the area under the ROC curve agrees with the main conclusions extracted from the accuracy results. All of these models can be fitted by free R programs.     

女性人口文化程度对其婚育状况的影响探析

本文以1995年全国1％人口抽样调查资料为基础,对女性人口文化程度与其早婚状况、平均初婚年龄．以及女性初婚年龄与其平均活产子女数间的相关关系进行了深入的定量分析．     

Ridge estimation of restricted parameters in production techniques

The problem of determining ridge estimates of the regression parameters in a two-input production function model,constrained to be non-negative,has been formulated as an exercise in quadratic programming. Relevant Kuhn-Tucker conditions have been derived and a small simulation studv has been carried out.     

Chain ratio type estimator for ratio of two population m3ans using auxiliary characters

In this paper we have proposed chain ratio type estimators for ratio of two population means using two auxiliary characters. The expressions for bias and mean square error of these estimators have been derived. A comparison of the proposed estimator with that of double sampling estimator has been made in terms of mean square error. An emperical study has also been made.     

Comparison of estimators of the location parameter using pitman's closeness criterion

Necessary and sufficient conditions for a linear estimator to dominate another linear estimator of a location parameter under the Pitman's criterion of comparison are discussed. Consequently it is demonstrated that a linear biased estimator can not dominate a linear unbiased estimator under Pitman's criterion and that the sample mean is the Closest Linear Unbiased Estimator (CLUE). It is also shown that the ridge regression estimator with a known biasing constant can not dominate the ordinary least squares estimator. If an estimator δdominates an estimator δin the average loss sense then sufficient conditions are obtained under which δis also preferred over δunder Pitman's criterion. Further we obtain sufficient conditions under which preference under the Pitman's criterion will lead to preference under the mean squared error sense.