Polynomial regression with errors in the variables

A polynomial functional relationship with errors in both variables can be consistently estimated by constructing an ordinary least squares estimator for the regression coefficients, assuming hypothetically the latent true regressor variable to be known, and then adjusting for the errors. If normality of the error variables can be assumed, the estimator can be simplified considerably. Only the variance of the errors in the regressor variable and its covariance with the errors of the response variable need to be known. If the variance of the errors in the dependent variable is also known, another estimator can be constructed.     

The construction of data to reflect the research objective,and how randomisation tests make such data usable

When comparing the central values of two independent groups, should a t-test be performed, or should the observations be transformed into their ranks and a Wilcoxon-Mann-Whitney test performed? This paper argues that neither should automatically be chosen. Instead, provided that software for conducting randomisation tests is available, the chief concern should be with obtaining data values that are a good reflection of scientific reality and appropriate to the objective of the research; if necessary, the data values should be transformed so that this is so. The subsequent use of a randomisation (permutation) test will mean that failure of the transformed data values to satisfy assumptions such as normality and equality of variances will not be of concern.     

论人口普查质量评估统计量

人口统计学家通常用人口普查误差来评估人口普查质量。然而,确切的人口普查误差是无法计算的,能够计算的仅仅是它的估计量。甚至,在有些时候所估计的,其实并不是人口普查误差,而仅仅是人口普查的平均差。详细解析这方面的基本理论和基本概念,分析人们在应用人口普查质量评估统计量时的常见误区,指出这种错误所引发的连带问题。     

Insights into the appropriate level of disaggregation for efficient time series model forecasting

This paper provides a potentially valuable insight on how to assess if the forecasts from an autoregressive moving average model based on aggregated data could be substantially improved through disaggregation. It is argued that, theoretically, the absence of moving average (MA) terms indicates that no forecasting efficiency improvements can be achieved through disaggregation. In practice, it is found that there is a strong correlation between the statistical significance of the MA component in the aggregate model and the magnitude of the forecast mean square error (MSE) decreases that can be achieved through disaggregation. That is, if a model includes significant MA terms, the forecast MSE improvements that may be gained from disaggregation could be substantial. Otherwise, they are more likely to be relatively small or non-existent.     

Split Hamiltonian Monte Carlo

We show how the Hamiltonian Monte Carlo algorithm can sometimes be speeded up by “splitting” the Hamiltonian in a way that allows much of the movement around the state space to be done at low computational cost. One context where this is possible is when the log density of the distribution of interest (the potential energy function) can be written as the log of a Gaussian density, which is a quadratic function, plus a slowly-varying function. Hamiltonian dynamics for quadratic energy functions can be analytically solved. With the splitting technique, only the slowly-varying part of the energy needs to be handled numerically, and this can be done with a larger stepsize (and hence fewer steps) than would be necessary with a direct simulation of the dynamics. Another context where splitting helps is when the most important terms of the potential energy function and its gradient can be evaluated quickly, with only a slowly-varying part requiring costly computations. With splitting, the quick portion can be handled with a small stepsize, while the costly portion uses a larger stepsize. We show that both of these splitting approaches can reduce the computational cost of sampling from the posterior distribution for a logistic regression model, using either a Gaussian approximation centered on the posterior mode, or a Hamiltonian split into a term that depends on only a small number of critical cases, and another term that involves the larger number of cases whose influence on the posterior distribution is small.     

对生产帕累托最优条件充分性的质疑与改进

现有的理论中,生产帕累托最优条件不充分,其最优状态不是唯一的,使得理论自身及随后的应用上产生了一些矛盾。确定唯一最优状态的充分条件应该是：双方都满意的交换利益分割和边际技术替代率相等。前者保证交换实现,后者保证交换产生的利益被完全穷尽。只要遵循新交换原则,交换必能实现,但不一定是帕累托最优。信息不充分时,如果信息不对称者对对方所判断的生产函数改变了其真实生产函数的技术性质,交换虽能实现,但生产并没有达到帕累托最优。     

Comparing Predictive Accuracy

We propose and evaluate explicit tests of the null hypothesis of no difference in the accuracy of two competing forecasts. In contrast to previously developed tests, a wide variety of accuracy measures can be used (in particular, the loss of function need not be quadratic and need not even be symmetric), and forecast errors can be non-Gaussian, nonzero mean, serially correlated, and contemporaneously correlated. Asymptotic and exact finite-sample tests are proposed, evaluated, and illustrated.     

统计数据预处理的理论与方法述评

统计数据预处理是提升数据质量的重要阶段,包括数据审查、数据清理、数据转换和数据验证四大步骤。根据处理对象的特点及每一步骤的不同目标,统计数据预处理可采用的方法包括描述及探索性分析、缺失值处理、异常值处理、数据变换技术、信度与效度检验、宏观数据诊断等六大类。选用恰当的方法开展统计数据预处理,有利于保证数据分析结论真实、有效。     

教学质量评估的标志设计和有效性检验

目前 ,高等院校普遍开展了制度化的教学质量评估工作 ,其中“学生评教”是教学质量考评的重要手段。从理论上讲 ,“教学”作为学校的主产品 ,学生对这一产品的质量具有最直接、最客观感受 ,从而也能作出最准确的评价。有学者对此专门研究后认为 ,学生评价教学是最受支持的评价途径之一[1 ] 。但是 ,毕竟教学评估是一项主观性较强的工作 ,评估设计上的科学性和评估数据的有效性直接关系着评估结果的客观性和公正性。本文就统计评价方法论的角度就学生评教这一教学质量评估实践中的问题和对策作一探讨。　　一、学生评教中的主要问题目前 ,各…     

Uniform robustness against nonnormality of the t and f tests

The size of the two-sample t test is generally thought to be robust against nonnormal distributions if the sample sizes are large. This belief is based on central limit theory, and asymptotic expansions of the moments of the t statistic suggest that robustness may be improved for moderate sample sizes if the variance, skewness, and kurtosis of the distributions are matched, particularly if the sample sizes are also equal.

It is shown that asymptotic arguments such as these can be misleading and that, in fact, the size of the t test can be as large as unity if the distributions are allowed to be completely arbitrary. Restricting the distributions to be identical or symmetric (but otherwise arbitrary) does not guarantee that the size can be controlled either, but controlling the tail-heaviness of the distributions does. The last result is proved more generally for the k-sample F test.     

Letters to the Editor

Letters to the editor will be confined to discussions of papers that have appeared in The American Statistician and of important issues facing the statistical community. Letters discussing papers in The American Statistician must be received within two months of publication of the paper; the author of the paper will then be given an opportunity to reply, and the letters and reply will be published together. All letters to the editor will be refereed. Corrections of errors that have been noted in papers published in The American Statistician will be listed as corrections at the end of this section.     

Estimation of the shape and scale parameters of Pareto distribution using ranked set sampling

In the current paper, the estimation of the shape and location parameters α and c, respectively, of the Pareto distribution will be considered in cases when c is known and when both are unknown. Simple random sampling (SRS) and ranked set sampling (RSS) will be used, and several traditional and ad hoc estimators will be considered. In addition, the estimators of α, when c is known using an RSS version based on the order statistic that maximizes the Fisher information for a fixed set size, will be considered. These estimators will be compared in terms of their biases and mean square errors. The estimators based on RSS can be real competitors against those based on SRS.     

Rank-Based Classification Using Robust Discriminant Functions

The Pareto distribution model assumption in the peaks over threshold method, will be tested by making using of the Kolmogorov–Smirnov goodness of fit method. Pareto distributed variables can be transformed to exponential, and the test will be for exponentiality. It was found that the statistic can be used as an indication of where to choose the threshold and to check the Pareto model assumption.     

Analogies for Helping Clinicians and Investigators Better Understand the Principles and Practice of Biostatistics

For the interaction between the biostatistician and the clinician or research investigator to be successful, it is important not only for the investigator to be able to explain biological and medical principles in a way that can be understood by the biostatistician, so, too, the biostatistician needs tools to help the investigator understand both the practice of statistics and specific statistical methods. In our practice, we have found it useful to draw analogies between statistical concepts and familiar medical or everyday ideas. These analogies help to stress a point or provide an understanding on the part of the investigator. For example, explaining the reason for using a nonparametric procedure (a general procedure used when the underlying distribution of the data is not known or cannot be assumed) by comparing it to using broad spectrum antibiotics (a general antibiotic used when the specific bacteria causing infection is unknown or cannot be assumed) can be an effective teaching tool. We present a variety of useful (and hopefully amusing) analogies that can be adopted by statisticians to help investigators at all levels of experience better understand principles and practice of statistics.     

On tests of linearity for dose response data: asymptotic, exact conditional and exact unconditional tests

The approximate chi-square statistic, X 2 Q , which is calculated as the difference between the usual chi-square statistic for heterogeneity and the Cochran-Armitage trend test statistic, has been widely applied to test the linearity assumption for dose-response data. This statistic can be shown to be asymptotically distributed as chi-square with K - 2 degrees of freedom. However, this asymptotic property could be quite questionable if the sample size is small, or if there is a high degree of sparseness or imbalance in the data. In this article, we consider how exact tests based on this X 2 Q statistic can be performed. Both the exact conditional and unconditional versions will be studied. Interesting findings include: (i) the exact conditional test is extremely sensitive to a small change in dosages, which may eventually produce a degenerate exact conditional distribution; and (ii) the exact unconditional test avoids the problem of degenerate distribution and is shown to be less sensitive to the change in dosages. A real example involving an animal carcinogenesis experiment as well as a fictitious data set will be used for illustration purposes.     

Semiparametric Estimation of a Change-point for Recurrent Events Data

One particular recurrent events data scenario involves patients experiencing events according to a common intensity rate, and then a treatment may be applied. The treatment might be effective for a limited amount of time, so that the intensity rate would be expected to change abruptly when the effect of the treatment wears out. In particular, we allow models for the intensity rate, post-treatment, to be at first decreasing and then change to increasing (and vice versa). Two estimators of the location of this change are proposed.     

Child health,breast-feeding,and survival in Malaysia: a random-effects logit approach

This study examines the possibility that estimation of the effect of breast-feeding on infant survival is affected by selection bias, in that children who are healthier at birth may be more likely to be breast-fed. Data are from the 1976 Malaysian Family Life Survey. "Ordinary logit models for breast-feeding and survival are estimated, and the results suggest that selection is indeed present. For example, children of higher birth weight appear to be more likely to be breast-fed and likely to survive. In addition, weight at birth and the duration of breast-feeding appear to be linked." Using birth weight as an indicator for the child's health, the authors conclude that "the direct influence of breast-feeding on survival remains of overwhelming importance even after corrections for selection bias are made."     

The Folded Logistic Distribution

ABSTRACT

Physical measurements like dimensions, including time, and angles in scientific experiments are frequently recorded without their algebraic sign. The directions of those physical quantities measured with respect to a frame of reference in most practical applications are considered to be unimportant and are ignored. As a consequence, the underlying distribution of measurements is replaced by a distribution of absolute measurements. When the underlying distribution is logistic, the resulting distribution is called the “folded logistic distribution”. Here, the properties of the folded logistic distribution will be presented and the techniques for estimating parameters will be given. The advantages of using this folded logistic distribution over the folded normal distribution will be discussed and some examples will be cited.