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.     

Originary différance: “A quantum vitalism”

Review of Alexander Wendt, Quantum Mind and Social Science: unifying physical and social ontology (2015).     

Generalized Expected Utility, Heteroscedastic Error, and Path Dependence in Risky Choice

We evaluate the fit of several generalized expected utility models under homoscedasticity and three different heteroscedastic error structures for the data set first reported in Hey and Orme (1994). Standard chi-squared tests are used for nested tests, and both the Akaike (1973) information criterion and its consistent version (Hurvich and Tsai, 1989) are used for non-nested ranking of these models. A testing framework is developed that explicitly accounts for the path-dependent nature of the model selection problem. Not only does the selection of preference models depend on the error structure assumed, but the reverse is also true: the selection of the error structure depends on the preference structure assumed. An erratum to this article is available at .     

我国工业重工化对经济增长影响的实证分析

近些年来,我国出现了重新重工业化的趋势,重工业在我国经济中发挥着特殊重要的作用.采用1981-2006年的数据,在单位根检验、协整检验和格兰杰因果关系检验的基础上建立了误差修正模型,以此说明我国重工业与经济增长的长期均衡的正向关系和短期动态关系,指出我国应大力发展重工业,走一条新型工业化的道路.     

中国ETF基金价格“已实现”波动率、跟踪误差之间的Granger关系研究

在高频数据条件下,中国ETF基金价格"已实现"波动率与跟踪误差之间是否存在着因果关系并存在着信息的先导效应？基于"已实现"波动、跟踪误差计算方法及Granger因果检验过程、VAR模型等,本文对此进行了深入研究。研究结果认为:中国ETF基金价格"已实现"波动率与两种跟踪误差分别具有Granger因果关系,后者是前者的Granger原因;中国ETF基金价格"已实现"波动率序列与两种跟踪误差序列的同期及一、二阶滞后相关性较高,而跟踪误差滞后于"已实现"波动率;当ETF基金的跟踪误差受外部市场条件的某一冲击后,将给ETF基金价格"已实现"波动率带来同向的冲击,这一冲击具有一定的持续性和滞后性。     

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.     

Issues for stratified randomization based on a factor derived from a continuous baseline variable

Stratified randomization based on the baseline value of the primary analysis variable is common in clinical trial design. We illustrate from a theoretical viewpoint the advantage of such a stratified randomization to achieve balance of the baseline covariate. We also conclude that the estimator for the treatment effect is consistent when including both the continuous baseline covariate and the stratification factor derived from the baseline covariate. In addition, the analysis of covariance model including both the continuous covariate and the stratification factor is asymptotically no less efficient than including either only the continuous baseline value or only the stratification factor. We recommend that the continuous baseline covariate should generally be included in the analysis model. The corresponding stratification factor may also be included in the analysis model if one is not confident that the relationship between the baseline covariate and the response variable is linear. In spite of the above recommendation, one should always carefully examine relevant historical data to pre-specify the most appropriate analysis model for a perspective study.     

A more powerful unconditional exact test of homogeneity for 2 × c contingency table analysis

The classical unconditional exact p-value test can be used to compare two multinomial distributions with small samples. This general hypothesis requires parameter estimation under the null which makes the test severely conservative. Similar property has been observed for Fisher's exact test with Barnard and Boschloo providing distinct adjustments that produce more powerful testing approaches. In this study, we develop a novel adjustment for the conservativeness of the unconditional multinomial exact p-value test that produces nominal type I error rate and increased power in comparison to all alternative approaches. We used a large simulation study to empirically estimate the 5th percentiles of the distributions of the p-values of the exact test over a range of scenarios and implemented a regression model to predict the values for two-sample multinomial settings. Our results show that the new test is uniformly more powerful than Fisher's, Barnard's, and Boschloo's tests with gains in power as large as several hundred percent in certain scenarios. Lastly, we provide a real-life data example where the unadjusted unconditional exact test wrongly fails to reject the null hypothesis and the corrected unconditional exact test rejects the null appropriately.     

Penalized contrast estimation in functional linear models with circular data

Our aim is to estimate the unknown slope function in the functional linear model when the response Y is real and the random function X is a second-order stationary and periodic process. We obtain our estimator by minimizing a standard (and very simple) mean-square contrast on linear finite dimensional spaces spanned by trigonometric bases. Our approach provides a penalization procedure which allows to automatically select the adequate dimension, in a non-asymptotic point of view. In fact, we can show that our penalized estimator reaches the optimal (minimax) rate of convergence in the sense of the prediction error. We complete the theoretical results by a simulation study and a real example that illustrates how the procedure works in practice.     

Notes on estimation of the intraclass correlation under the AB/BA crossover trial

Under the AB/BA crossover trial, we focus our attention on estimation of the intraclass correlation in normal data. We develop both point and interval estimators in closed form for the intraclass correlation. We employ Monte Carlo simulation to study the performance of these estimators in a variety of situations. We note that the estimators developed here for the intraclass correlation remain valid even when there are possibly unexpected carry-over effects.