Hypothesis testing for quantiles of two-parameter binary models

A procedure is developed to test the equality of the quantiles from k populations, assuming the responses follow a two-parameter binary model.The method utilizes the asymptotic distribution of the maximum likelihood estimators.The exact distribution of the test statistic is discussed in general.This exact distribution is generated for the logit model in order to investgate the convergence properties of the asymptotic procedure.     

Saddlepoint approximations to sensitivities of tail probabilities of random sums and comparisons with Monte Carlo estimators

This article proposes computing sensitivities of upper tail probabilities of random sums by the saddlepoint approximation. The considered sensitivity is the derivative of the upper tail probability with respect to the parameter of the summation index distribution. Random sums with Poisson or Geometric distributed summation indices and Gamma or Weibull distributed summands are considered. The score method with importance sampling is considered as an alternative approximation. Numerical studies show that the saddlepoint approximation and the method of score with importance sampling are very accurate. But the saddlepoint approximation is substantially faster than the score method with importance sampling. Thus, the suggested saddlepoint approximation can be conveniently used in various scientific problems.     

Omnitab-a simple language for statistical computations

The OMNITAB system of computer programming provides a simple, yet extremely versatile means of communicating with the computer using simple English words and phrases, It is written in FORTRAN and is available for implementation on UNIVAC 1108, IBM 360, Burroughs 5500 and CDC 6600 equipment. It is based on a worksheet, stored in the computer, which is a two dimensional array easy to visualize even by beginners. The system has particular use for students of statistics, of all ages, in that it allows them to interact with the data without requiring that they master any diffiicult and esoteric (for statisticians) computer skills. The programming system is described together with several applications to statistical problems. Full program documentation is available from the authors.     

Online monitoring with local smoothing methods and adaptive ridging

We consider online monitoring of sequentially arising data as e.g. met in clinical information systems. The general focus thereby is to detect breakpoints, i.e. timepoints where the measurement series suddenly changes the general level. The method suggested is based on local estimation. In particular, local linear smoothing is combined by ridging with local constant smoothing. The procedure is demonstrated by examples and compared with other available online monitoring routines.     

Tests for exponentiality

The idea of measuring the departure of data bu a plot of obeserved observations against their expectation has been expeetations has been exploited in this paper to develop tests for exponentiality the tests are for parameter two parameter exponential distribution with complete sample and one parameter exponential distribution with complete sample and one large sample distributions of the test statistics critical points have been computed for different levels of significance and applications of these have been computed for differents levels of significance and applications of these tests have been discussed in case of three data sets.     

The em algorithm for the quasi-likelihood regression model

The objective of this paper is to present a method which can accommodate certain types of missing data by using the quasi-likelihood function for the complete data. This method can be useful when we can make first and second moment assumptions only; in addition, it can be helpful when the EM algorithm applied to the actual likelihood becomes overly complicated. First we derive a loss function for the observed data using an exponential family density which has the same mean and variance structure of the complete data. This loss function is the counterpart of the quasi-deviance for the observed data. Then the loss function is minimized using the EM algorithm. The use of the EM algorithm guarantees a decrease in the loss function at every iteration. When the observed data can be expressed as a deterministic linear transformation of the complete data, or when data are missing completely at random, the proposed method yields consistent estimators. Examples are given for overdispersed polytomous data, linear random effects models, and linear regression with missing covariates. Simulation results for the linear regression model with missing covariates show that the proposed estimates are more efficient than estimates based on completely observed units, even when outcomes are bimodal or skewed.     

Robust estimation of the exponential mean parameter for small samples: Complete and censored data

This paper studies methods for simple estimation of the exponential mean parameter in small samples in the presence of outliers. Existing estimation methods are discussed. Adaptation of these methods to allow for Type I censoring is investigated. New robust procedures are proposed. A series of simulation experiments Indicate trimming provides significant protection against outliers while the premium is usually small when trimming uncontarninated samples. A linearly weighted mean is recommended for uncontarninated samples, both censored and complete. In larger samples, (n - 20), the proposed Huber-type estimator performs quite well in all situations of censoring and contarnination     

非正常波动统计数据修匀方法研究——以福建省消费数据为例

统计数据经常会受到定期或不定期的非正常波动因素的影响，因此而扭曲的时间序列短期的基本变动，使得我们难以深入研究和正确解释经济规律。如果利用科学的方法将这些非正常波动因素从经济时间序列中测定、分离、抵消和调整，对这些非正常波动统计数据进行修匀，则能更好地反映其基本的发展趋势。以福建省社会消费零售总额指标和相对指标为例，对其进行了修匀处理和并进行修匀前后的对比分析，发现修匀后的曲线较平滑，修匀效果比较合理。进行外推预测和模拟，得到模型的动态模拟结果以及静态预测结果，得到的环比CPI的动态模拟结果较好地反映了CPI的走势，静态预测较好地显示出短期波动情况。     

Survival models with two phases and length biased sampling

A survival model is presented in which all patients go through a first phase of disease; some then die and the remainder progress to a second phase of disease. The data observed are the path taken and the total sojourn time in the system but not the time, if ever, at which the second phase is entered. The sojourn time in each phase is assumed to be exponentially distributed with possibly different rates for the two phases. Themodel describes serious diseases that progress through one or two phases, and can be extended to multiple phases. The model is extended to account for several length-biased sampling situations. Censoring is considered in all models. Maximum like lihood estimates for the parameters involved exist, are consistent and are a symptotically normal. One of the proposed models is applied to data from the Veterans Administration involving a study of coronary arterial occlusive disease.     

A theorem on the density of the density ordinate and an alternative interpretation of the bqx-muller method

This paper obtains a theorem about the density of the density ordinate when the latter is regarded as a random variable in its own right. The theorem is used to provide an alternative interpretation of the BOX-MULLER simulation method which extends also to an alternative method for simulating from the LAPLACE density