Rank regression in order restricted randomised designs

This paper uses order restricted randomised design (ORRD) to create a judgment ranked blocking factor based on available subjective information in a small set of experimental units (EUs). The design then performs a carefully designed randomisation scheme with certain restriction to assign the treatment levels to EUs across these subjective judgment blocks. Such an assignment induces positive dependence among within-set units, and the restrictions on the randomisation translate this positive dependence into a variance reduction technique. We provide a unified theory to analyse the data sets collected from an ORRD. The analysis uses the general framework of rank regression methodology in linear models, with some modification to our randomisation scheme, to estimate regression parameter and to test general linear hypotheses. It is shown that the estimators and test statistics have limiting normal and chi-square distributions regardless the quality of ranking information. A simulation study shows that the asymptotic results remain valid even for relatively small sample sizes. The proposed tests are applied to a clinical trial data set.     

Biostatistical genetics and genetic epidemiology

It is well-known that when ranked set sampling (RSS) scheme is employed to estimate the mean of a population, it is more efficient than simple random sampling (SRS) with the same sample size. One can use a RSS analog of SRS regression estimator to estimate the population mean of Y using its concomitant variable X when they are linearly related. Unfortunately, the variance of this estimate cannot be evaluated unless the distribution of X is known. We investigate the use of resampling methods to establish confidence intervals for the regression estimation of the population mean. Simulation studies show that the proposed methods perform well in a variety of situations when the assumption of linearity holds, and decently well under mild non-linearity.     

Parametric Estimation Procedures in Multivariate Generalized Pareto Models

Abstract.  Modelling the tails of a multivariate distribution can be reasonably done by multivariate generalized Pareto distributions (GPDs). We present several methods of parametric estimation in these models, which use decompositions of the corresponding random vectors with the help of different versions of Pickands coordinates. The estimators are compared to each other with simulated data sets. To show the practical value of the methods, they are applied to a real hydrological data set.     

On stratified bivariate ranked set sampling for regression estimators

We investigate the relative performance of stratified bivariate ranked set sampling (SBVRSS), with respect to stratified simple random sampling (SSRS) for estimating the population mean with regression methods. The mean and variance of the proposed estimators are derived with the mean being shown to be unbiased. We perform a simulation study to compare the relative efficiency of SBVRSS to SSRS under various data-generating scenarios. We also compare the two sampling schemes on a real data set from trauma victims in a hospital setting. The results of our simulation study and the real data illustration indicate that using SBVRSS for regression estimation provides more efficiency than SSRS in most cases.     

On concomitants of order statistics arising from the extended Farlie–Gumbel–Morgenstern bivariate logistic distribution and its application in estimation

In this paper, we consider concomitants of order statistics arising from the extended Farlie–Gumbel–Morgenstern bivariate logistic distribution and develop its distribution theory. Using ranked set sample obtained from the above distribution, unbiased estimators of the parameters associated with the study variate involved in it are generated. The best linear unbiased estimators (BLUEs) based on observations in the ranked set sample of those parameters as well have been derived. The efficiencies of the BLUEs relative to the respective unbiased estimators generated also have been evaluated.     

Selection of the best well control system by using fuzzy multiple-attribute decision-making methods

There are numerous difficulties involved in drilling operations of an oil well, one of the most important of them being well control. Well control systems are applied when we have irruption of liquids or unwanted intrusion of the reservoir's liquid (oil, gas or brine) into the well, during drilling when the pressure of well fluid column is less than formation pressure, and the permeability of the reservoir has a value that is able to pass the liquid through. For this purpose, a variety of methods including Driller, wait and weight, and the concurrent methods were used to control the well at different drilling sites. In this study, we investigate the optimum method for well control using a fussy method based on many parameters, including technical factors (mud weight, drilling rate, blockage of pipes, sensitivity to drilling network changes, etc.) and security factors (existence of effervescent mud, drilling circuit control, etc.), and cost of selection, which is one of the most important decisions that are made under critical conditions such as irruption. Till now, these methods were selected based on the experience of field personnel in drilling sites. The technical criteria and standards were influenced by experience, so the soft computerizing system (fuzzy method) was used. Thus, both these criteria and standards would be of greater importance and indicate whether the optimum numerical method is the same one that is expressed by human experience. The concurrent method was selected as the best for well control, using the fuzzy method at the end of the evaluation, while field personnel experience suggests the Driller method.     

Efficiency of ranked set sampling in entropy estimation and goodness-of-fit testing for the inverse Gaussian law

When measuring units are expensive or time consuming, while ranking them is relatively easy and inexpensive, it is known that ranked set sampling (RSS) is preferable to simple random sampling (SRS). Many authors have suggested several extensions of RSS. As a variation, Al-Saleh and Al-Kadiri [Double ranked set sampling, Statist. Probab. Lett. 48 (2000), pp. 205–212] introduced double ranked set sampling (DRSS) and it was extended by Al-Saleh and Al-Omari [Multistage ranked set sampling, J. Statist. Plann. Inference 102 (2002), pp. 273–286] to multistage ranked set sampling (MSRSS). The entropy of a random variable (r.v.) is a measure of its uncertainty. It is a measure of the amount of information required on the average to determine the value of a (discrete) r.v.. In this work, we discuss entropy estimation in RSS design and aforementioned extensions and compare the results with those in SRS design in terms of bias and root mean square error (RMSE). Motivated by the above observed efficiency, we continue to investigate entropy-based goodness-of-fit test for the inverse Gaussian distribution using RSS. Critical values for some sample sizes determined by means of Monte Carlo simulations are presented for each design. A Monte Carlo power analysis is performed under various alternative hypotheses in order to compare the proposed testing procedure with the existing methods. The results indicate that tests based on RSS and its extensions are superior alternatives to the entropy test based on SRS.     

An extended association rule mining strategy for gene relationship discovery from microarray data

DNA microarrays allow for measuring expression levels of a large number of genes between different experimental conditions and/or samples. Association rule mining (ARM) methods are helpful in finding associational relationships between genes. However, classical association rule mining (CARM) algorithms extract only a subset of the associations that exist among different binary states; therefore can only infer part of the relationships on gene regulations. To resolve this problem, we developed an extended association rule mining (EARM) strategy along with a new way of the association rule definition. Compared with the CARM method, our new approach extracted more frequent genesets from a public microarray data set. The EARM method discovered some biologically interesting association rules that were not detected by CARM. Therefore, EARM provides an effective tool for exploring relationships among genes.     

论东汉初统治思想演化的轨迹及其原因

东汉初年统治思想经历了柔道———尚法崇刚———尊儒尚柔的发展与调整过程。在这一过程中,统治思想曲线呈现出刚柔相济,正反结合的轨迹。这一轨迹又与东汉初年豪强地主势力的兴衰强弱相一致,从根本上保证了东汉初年社会的稳步发展。     

Solving the Stochastic Growth Model by Linear-Quadratic Approximation and by Value-Function Iteration

This article describes three approximation methods I used to solve the growth model (Model 1) studied by the National Bureau of Economic Research's nonlinear rational-expectations-modeling group project, the results of which were summarized by Taylor and Uhlig (1990). The methods involve computing exact solutions to models that approximate Model 1 in different ways. The first two methods approximate Model 1 about its nonstochastic steady state. The third method works with a version of the model in which the state space has been discretized. A value function iteration method is used to solve that model.