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.     

Noninformative priors for the between-group variance in the unbalanced one-way random effects model with heterogeneous error variances

For the unbalanced one-way random effects model with heterogeneous error variances, we propose the non-informative priors for the between-group variance and develop the first- and second-order matching priors. It turns out that the second-order matching priors do not exist and the reference prior and Jeffreys prior do not satisfy a first-order matching criterion. We also show that the first-order matching prior meets the frequentist target coverage probabilities much better than the Jeffreys prior and reference prior through simulation study, and the Bayesian credible intervals based on the matching prior and reference prior give shorter intervals than the existing confidence intervals by examples.     

On Bartlett correction of empirical likelihood for regularly spaced spatial data

Bartlett correction constitutes one of the attractive features of empirical likelihood because it enables the construction of confidence regions for parameters with improved coverage probabilities. We study the Bartlett correction of spatial frequency domain empirical likelihood (SFDEL) based on general spectral estimating functions for regularly spaced spatial data. This general formulation can be applied to testing and estimation problems in spatial analysis, for example testing covariance isotropy, testing covariance separability as well as estimating the parameters of spatial covariance models. We show that the SFDEL is Bartlett correctable. In particular, the improvement in coverage accuracies of the Bartlett‐corrected confidence regions depends on the underlying spatial structures. The Canadian Journal of Statistics 47: 455–472; 2019 © 2019 Statistical Society of Canada     

The effect of small sample on optimal designs for logistic regression models

Asymptotic methods are commonly used in statistical inference for unknown parameters in binary data models. These methods are based on large sample theory, a condition which may be in conflict with small sample size and hence leads to poor results in the optimal designs theory. In this paper, we apply the second order expansions of the maximum likelihood estimator and derive a matrix formula for the mean square error (MSE) to obtain more precise optimal designs based on the MSE. Numerical results indicate the new optimal designs are more efficient than the optimal designs based on the information matrix.     

Non-parametric estimation of reciprocal coordinate subtangent for right censored dependent scheme

The concept of reciprocal coordinate subtangent (RCST) has been used as a useful tool to study the monotone behavior of a continuous density function and for characterizing probability distributions. In this paper, we propose a non-parametric estimator for RCST based on the censored dependent data. Asymptotic properties of the estimator are established under suitable regularity conditions. A simulation study is carried out to examine the performance of the estimator. The usefulness of the estimator is also examined through a real data.     

变动均值和方差资产配置模型的应用研究

本文在均值-方差模型的基础上，以改善估计误差为主线，选取了10种变动均值-方差的资产配置模型，以等权重策略为基准，运用了确定性等价收益和Alpha值为判断准则，同时考虑了允许卖空限制和非允许卖空的情况，实证研究结果表明：虽然在资本市场中配置模型并不能显著战胜等权重策略，但随着投资范围的扩大，模型开始显现配置效果，尤其在Alpha准则下，变动均值-方差资产配置显著。同时本文还将实证结果和目前我国投资者的实际资产配置情况进行了比较，发现了现实配置结构中的不合理之处，并提出了相应的改善建议。最后对4类常用资产进行了模拟研究，其结果也进一步证实了本文的结论。     

Human Error in Autonomous Underwater Vehicle Deployment: A System Dynamics Approach

The use of autonomous underwater vehicles (AUVs) for various applications have grown with maturing technology and improved accessibility. The deployment of AUVs for under-ice marine science research in the Antarctic is one such example. However, a higher risk of AUV loss is present during such endeavors due to the extremities in the Antarctic. A thorough analysis of risks is therefore crucial for formulating effective risk control policies and achieving a lower risk of loss. Existing risk analysis approaches focused predominantly on the technical aspects, as well as identifying static cause and effect relationships in the chain of events leading to AUV loss. Comparatively, the complex interrelationships between risk variables and other aspects of risk such as human errors have received much lesser attention. In this article, a systems-based risk analysis framework facilitated by system dynamics methodology is proposed to overcome existing shortfalls. To demonstrate usefulness of the framework, it is applied on an actual AUV program to examine the occurrence of human error during Antarctic deployment. Simulation of the resultant risk model showed an overall decline in human error incident rate with the increase in experience of the AUV team. Scenario analysis based on the example provided policy recommendations in areas of training, practice runs, recruitment policy, and setting of risk tolerance level. The proposed risk analysis framework is pragmatically useful for risk analysis of future AUV programs to ensure the sustainability of operations, facilitating both better control and monitoring of risk.     

Visualization of generalized mean estimators using auxiliary information in survey sampling

Abstract

The mean estimators with ratio depend on multiple auxiliary variables and unknown parameters in a finite population setting. We propose a new generalized approach with matrices for modeling the mutivariate mean estimators with two auxiliary variables. Our approach brings naturally a graphical analysis for comparing mean estimators.     

On the Principal Component Liu-type Estimator in Linear Regression

In this article, we present a principal component Liu-type estimator (LTE) by combining the principal component regression (PCR) and LTE to deal with the multicollinearity problem. The superiority of the new estimator over the PCR estimator, the ordinary least squares estimator (OLSE) and the LTE are studied under the mean squared error matrix. The selection of the tuning parameter in the proposed estimator is also discussed. Finally, a numerical example is given to explain our theoretical results.     

大数据整合运用中的逻辑问题研究

为推进大数据技术在司法实践中的运用与发展,概述大数据在司法领域的运用现状,分析大数据在司法实践中整合运用的必要性和可行性。以职务犯罪大数据为例,探讨职务犯罪的特点,其对大数据整合运用的需求更为强烈。大数据具有数量庞大、种类繁多、生成快速、价值密度低等特点,因此必须采取科学有效的方法对其进行整合运用,而逻辑方法在归纳、分析、整合、运用大数据等方面具有不可替代的作用。在大数据整合运用过程中,必须遵循基本的思维规律,避免出现逻辑错误,影响数据的运用效果,甚至发生冤假错案。