Accurately sized test statistics with misspecified conditional homoskedasticity

We study the finite-sample performance of test statistics in linear regression models where the error dependence is of unknown form. With an unknown dependence structure, there is traditionally a trade-off between the maximum lag over which the correlation is estimated (the bandwidth) and the amount of heterogeneity in the process. When allowing for heterogeneity, through conditional heteroskedasticity, the correlation at far lags is generally omitted and the resultant inflation of the empirical size of test statistics has long been recognized. To allow for correlation at far lags, we study the test statistics constructed under the possibly misspecified assumption of conditional homoskedasticity. To improve the accuracy of the test statistics, we employ the second-order asymptotic refinement in Rothenberg [Approximate power functions for some robust tests of regression coefficients, Econometrica 56 (1988), pp. 997–1019] to determine the critical values. The simulation results of this paper suggest that when sample sizes are small, modelling the heterogeneity of a process is secondary to accounting for dependence. We find that a conditionally homoskedastic covariance matrix estimator (when used in conjunction with Rothenberg's second-order critical value adjustment) improves test size with only a minimal loss in test power, even when the data manifest significant amounts of heteroskedasticity. In some specifications, the size inflation was cut by nearly 40% over the traditional heteroskedasticity and autocorrelation consistent (HAC) test. Finally, we note that the proposed test statistics do not require that the researcher specify the bandwidth or the kernel.     

Testing exponentiality based on characterizations of the exponential distribution

In this paper, we first present two characterizations of the exponential distribution and next introduce three exact goodness-of-fit test for exponentiality. By simulation, the powers of the proposed tests under various alternatives are compared with the existing tests.     

Model fusion and multiple testing in the likelihood paradigm: shrinkage and evidence supporting a point null hypothesis

ABSTRACT

According to the general law of likelihood, the strength of statistical evidence for a hypothesis as opposed to its alternative is the ratio of their likelihoods, each maximized over the parameter of interest. Consider the problem of assessing the weight of evidence for each of several hypotheses. Under a realistic model with a free parameter for each alternative hypothesis, this leads to weighing evidence without any shrinkage toward a presumption of the truth of each null hypothesis. That lack of shrinkage can lead to many false positives in settings with large numbers of hypotheses. A related problem is that point hypotheses cannot have more support than their alternatives. Both problems may be solved by fusing the realistic model with a model of a more restricted parameter space for use with the general law of likelihood. Applying the proposed framework of model fusion to data sets from genomics and education yields intuitively reasonable weights of evidence.     

Consistent variable selection via the optimal discovery procedure in multiple testing

In this paper, we translate variable selection for linear regression into multiple testing, and select significant variables according to testing result. New variable selection procedures are proposed based on the optimal discovery procedure (ODP) in multiple testing. Due to ODP’s optimality, if we guarantee the number of significant variables included, it will include less non significant variables than marginal p-value based methods. Consistency of our procedures is obtained in theory and simulation. Simulation results suggest that procedures based on multiple testing have improvement over procedures based on selection criteria, and our new procedures have better performance than marginal p-value based procedures.     

Asymptotics of Likelihood Ratio Tests for General One-sided Hypotheses in the Two-sample Normal Model

We consider the general one-sided hypotheses testing problem expressed as H₀: θ₁ ? h(θ₂) versus H₁: θ₁ < h(θ₂), where h( · ) is not necessary differentiable. The values of the right and the left differential coefficients, h′_?( · ) and h′₊( · ), at nondifferentiable points play an essential role in constructing the appropriate testing procedures with asymptotic size α on the basis of the likelihood ratio principle. The likelihood ratio testing procedure is related to an intersection–union testing procedure when h′_?(θ₂) ? h′₊(θ₂) for all θ₂, and to a union–intersection testing procedure when there exists a θ₂ such that h′_?(θ₂) < h′₊(θ₂).     

Nonparametric goodness-of-fit

This paper develops an approach to testing the adequacy of both classical and Bayesian models given sample data. An important feature of the approach is that we are able to test the practical scientific hypothesis of whether the true underlying model is close to some hypothesized model. The notion of closeness is based on measurement precision and requires the introduction of a metric for which we consider the Kolmogorov distance. The approach is nonparametric in the sense that the model under the alternative hypothesis is a Dirichlet process.     

Simultaneous pseudo confidence regions for ratios of the discriminant coefficients

We consider simultaneous confidence regions for some hypotheses on ratios of the discriminant coefficients of the linear discriminant function when the population means and common covariance matrix are unknown. This problem, involving hypotheses on ratios, yields the so-called ‘pseudo’ confidence regions valid conditionally in subsets of the parameter space. We obtain the explicit formulae of the regions and give further discussion on the validity of these regions. Illustrations of the pseudo confidence regions are given.     

英语专业学生批判性思维能力培养的实证研究——以英语作文反馈式评价为媒介

依托Moodle平台,采用对英语专业学生英语作文进行反馈的方式训练学生的批评性思维技能。实验过程中利用"批判性思维质性评价量表"对实验班进行一对一的反馈式评价,实验结论显示,经过系统的训练和有针对性的反馈,实验班的批判性思维技能得到提高,证实了网络平台在思辨能力培养中的作用。     

Means Testing and the Heterogeneity of Housing Assets: Funding Long-Term Care in Spain

The access to publicly funded long‐term care (LTC) in Spain has been traditionally rationed through the use of means tests based on individuals’ current income and needs. However, individuals’ wealth, primarily housing assets, is progressively taken into account. Parallel to this feature, the responsibilities for the organization of LTC services have been devolved to region‐states – autonomous communities (ACs), giving rise to some regional heterogeneity, though limited evidence has been reported on the underlying determinants. This paper examines the current role of housing assets in determining public and private funding for long‐term care in Spain. Secondly, we present a qualitative and quantitative examination of the regional heterogeneity in the provision and public funding criteria determining eligibility for public support for LTC. Finally, we report survey evidence on the individual's willingness to sell (WTS) their housing assets in order to either totally or partially finance the access to LTC. Our findings suggest that housing assets are the main source of wealth accumulation at old age. Yet there is significant regional heterogeneity in the access to LTC resulting from regional differences in the means testing criteria. Progressively, all ACs are considering housing assets in their means testing criteria. Interestingly, individuals’ willingness to sell their housing assets declines with age and is more common among less skilled and widowed individuals.     

汽车零部件可重构力学试验台测控系统设计

汽车零部件可重构力学试验台支持用户改变系统结构实现功能重组,适应于产品快速转型的生产环境。试验台以作动和测量的运动方式划分模块,文章据此建立了具有软硬件同粒度横向并列式结构的试验台测控系统构架,设计了相应硬件和软件结构,最后开发了基于Labview的软件系统。