Assessing Statistical Results: Magnitude,Precision, and Model Uncertainty

ABSTRACT

Evaluating the importance and the strength of empirical evidence requires asking three questions: First, what are the practical implications of the findings? Second, how precise are the estimates? Confidence intervals provide an intuitive way to communicate precision. Although nontechnical audiences often misinterpret confidence intervals (CIs), I argue that the result is less dangerous than the misunderstandings that arise from hypothesis tests. Third, is the model correctly specified? The validity of point estimates and CIs depends on the soundness of the underlying model.     

一种改进型专家模糊核聚类赋权方法研究

针对传统基于判断矩阵的专家模糊核聚类赋权方法，由于归一化条件的制约，导致离群点对聚类结果产生不良影响的问题，提出一种改进型模糊核聚类算法。该方法在聚类过程中，通过放宽归一化约束条件，削弱离群点对聚类结果的影响；并且针对传统基于信息熵与一致性系数线性耦合的聚类标准的局限性，提出一种基于偏差熵的赋权方法，依据专家对自身类别的聚类贡献度，确定专家权重，克服了传统方法的不足。算例表明，该方法可行、有效。     

Aliasing Error of Sampling Theorem

Let f∈L_p~r(R),1相似文献   

具有多元权值约束的鲁棒 LPM 积极投资组合

在用方差控制投资组合风险的同时,由于方差的对称性导致投资组合的收益也受到限制． 相比之下,下偏距 (lower partial moment: LPM) 由于具有只控制风险,而不限制收益的特点,在近年来倍受关注． 但在非正态假设下,LPM 无法获得良好的解析性质． 在对资产收益分布未知的假设下,通过使用最坏情形下的LPM来度量投资组合的损失,提出了具有多元权值约束的鲁棒积极投资组合问题,并获得了具有m( m=0,1,2) -阶 LPM 约束的鲁棒积极投资组合问题的解析解． 通过分析解的性质和比较问题的有效前沿,得到了许多有趣的和新颖的结果． 数值结果比较表明,鲁棒LPM模型比经典的均值－方差模型具有许多更好的性能．     

基于白化权函数分类区分度的变权灰色聚类

针对灰色聚类指标权重确定的问题,通过定义白化权函数的分类区分度来度量各指标对聚类对象的分类所作的贡献,并据此确定分类指标的权重。在此基础上,提出了变权灰色聚类方法。结果表明,该方法能够融合聚类对象的样本信息和专家的经验,有效确定不同聚类对象的各指标权重,且适用于聚类指标的量纲不同、数量级悬殊较大的情形。最后通过一个实例说明了变权灰色聚类的实用性和有效性。     

Optimal designs for response functions with a downturn

In many toxicological assays, interactions between primary and secondary effects may cause a downturn in mean responses at high doses. In this situation, the typical monotonicity assumption is invalid and may be quite misleading. Prior literature addresses the analysis of response functions with a downturn, but so far as we know, this paper initiates the study of experimental design for this situation. A growth model is combined with a death model to allow for the downturn in mean doses. Several different objective functions are studied. When the number of treatments equals the number of parameters, Fisher information is found to be independent of the model of the treatment means and on the magnitudes of the treatments. In general, A- and D_A-optimal weights for estimating adjacent mean differences are found analytically for a simple model and numerically for a biologically motivated model. Results on c-optimality are also obtained for estimating the peak dose and the EC₅₀ (the treatment with response half way between the control and the peak response on the increasing portion of the response function). Finally, when interest lies only in the increasing portion of the response function, we propose composite D-optimal designs.     

抽样调查中的权数问题研究

用样本数据推断总体,权数的作用十分重要。使用权数,不仅能将样本还原到总体,还能调整样本结构,使其与总体结构相一致,因此正确的使用权数是我们进行统计推断的基础。本文系统阐述了抽样调查分析中权数的获取过程,以及后期对初始权数调整过程。由于权数是把双刃剑,在提高精度的同时,有可能提高估计量的误差,本文提出了对权数进行评估的方法,研讨如何对权数进行控制,最后根据我国综合社会调查项目（CGSS）的数据进行实证分析,按照所给方法不仅能提高估计精度,而且能够降低抽样推断中的权效应。     

Importance sampling for signal extraction model in time series analysis

In time series analysis, signal extraction model (SEM) is used to estimate unobserved signal component from observed time series data. Since parameters of the components in SEM are often unknown in practice, a commonly used method is to estimate unobserved signal component using the maximum likelihood estimates (MLEs) of parameters of the components. This paper explores an alternative way to estimate unobserved signal component when parameters of the components are unknown. The suggested method makes use of importance sampling (IS) with Bayesian inference. The basic idea is to treat parameters of the components in SEM as a random vector and compute a posterior probability density function of the parameters using Bayesian inference. Then IS method is applied to integrate out the parameters and thus estimates of unobserved signal component, unconditional to the parameters, can be obtained. This method is illustrated with a real time series data. Then a Monte Carlo study with four different types of time series models is carried out to compare a performance of this method with that of a commonly used method. The study shows that IS method with Bayesian inference is computationally feasible and robust, and more efficient in terms of mean square errors (MSEs) than a commonly used method.     

Bayesian model comparison via parallel model output

Bayesian estimation via MCMC methods opens up new possibilities in estimating complex models. However, there is still considerable debate about how selection among a set of candidate models, or averaging over closely competing models, might be undertaken. This article considers simple approaches for model averaging and choice using predictive and likelihood criteria and associated model weights on the basis of output for models that run in parallel. The operation of such procedures is illustrated with real data sets and a linear regression with simulated data where the true model is known.     

Estimation of population mean and variance in flock management: a ranked set sampling approach in a finite population setting

Ranked set sampling is a sampling technique that provides substantial cost efficiency in experiments where a quick, inexpensive ranking procedure is available to rank the units prior to formal, expensive and precise measurements. Although the theoretical properties and relative efficiencies of this approach with respect to simple random sampling have been extensively studied in the literature for the infinite population setting, the use of ranked set sampling methods has not yet been explored widely for finite populations. The purpose of this study is to use sheep population data from the Research Farm at Ataturk University, Erzurum, Turkey, to demonstrate the practical benefits of ranked set sampling procedures relative to the more commonly used simple random sampling estimation of the population mean and variance in a finite population. It is shown that the ranked set sample mean remains unbiased for the population mean as is the case for the infinite population, but the variance estimators are unbiased only with use of the finite population correction factor. Both mean and variance estimators provide substantial improvement over their simple random sample counterparts.