Estimation bias and bias correction in reduced rank autoregressions

This paper characterizes the finite-sample bias of the maximum likelihood estimator (MLE) in a reduced rank vector autoregression and suggests two simulation-based bias corrections. One is a simple bootstrap implementation that approximates the bias at the MLE. The other is an iterative root-finding algorithm implemented using stochastic approximation methods. Both algorithms are shown to be improvements over the MLE, measured in terms of mean square error and mean absolute deviation. An illustration to US macroeconomic time series is given.     

Misogynistic cultural argument in parental alienation versus child sexual abuse cases

This article argues that major advances in parental alienation (PA) theory, since its inception as the Parental Alienation Syndrome (PAS), have not consistently been applied in custody litigation practice, because they do not serve advocacy needs; whereas, the misogynistic cultural argument in PAS, when relied on implicitly but not stated explicitly, can win cases. It first discusses advances in modern PA theory that eliminate misogyny. It then reviews feminist advances (1960s to 1980s) to show the threat to patriarchal power, and the fathers’ rights backlash, to explain their demand for legal redress. The hypothesis that a misogynistic cultural framework undermines evidence-based reasoning in child custody cases is supported with studies associating misogynistic beliefs with irrational thinking in multiple scientific areas, including child custody; and documents that show misogyny is a serious concern in the U.S. legal system. The article concludes by stating the need for evidence of misogynistic bias in custody decisions.     

Bias-corrected estimators of scalar skew normal

One problem of skew normal model is the difficulty in estimating the shape parameter, for which the maximum likelihood estimate may be infinite when sample size is moderate. The existing estimators suffer from large bias even for moderate size samples. In this article, we proposed five estimators of the shape parameter for a scalar skew normal model, either by bias correction method or by solving a modified score equation. Simulation studies show that except bootstrap estimator, the proposed estimators have smaller bias compared to those estimators in literature for small and moderate samples.     

Data sharpening on unknown manifold

This article is concerned with data sharpening (DS) technique in nonparametric regression under the setting where the multivariate predictor is embedded in an unknown low-dimensional manifold. Theoretical asymptotic bias is derived, which reveals that the proposed DS estimator has a reduced bias compared to the usual local linear estimator. The asymptotic normality of the DS estimator is also developed. It can be confirmed from simulation and applications to real data that the bias reduction for the DS estimator supported on unknown manifold is evident.     

Local power of panel unit root tests allowing for structural breaks

The asymptotic local power of least squares–based fixed-T panel unit root tests allowing for a structural break in their individual effects and/or incidental trends of the AR(1) panel data model is studied. Limiting distributions of these tests are derived under a sequence of local alternatives, and analytic expressions show how their means and variances are functions of the break date and the time dimension of the panel. The considered tests have nontrivial local power in a N^?1/2 neighborhood of unity when the panel data model includes individual intercepts. For panel data models with incidental trends, the power of the tests becomes trivial in this neighborhood. However, this problem does not always appear if the tests allow for serial correlation in the error term and completely vanishes in the presence of cross-section correlation. These results show that fixed-T tests have very different theoretical properties than their large-T counterparts. Monte Carlo experiments demonstrate the usefulness of the asymptotic theory in small samples.     

Intentionally biased bootstrap methods

A class of weighted bootstrap techniques, called biased bootstrap or b-bootstrap methods, is introduced. It is motivated by the need to adjust empirical methods, such as the 'uniform' bootstrap, in a surgical way to alter some of their features while leaving others unchanged. Depending on the nature of the adjustment, the b-bootstrap can be used to reduce bias, or to reduce variance or to render some characteristic equal to a predetermined quantity. Examples of the last application include a b-bootstrap approach to hypothesis testing in nonparametric contexts, where the b-bootstrap enables simulation 'under the null hypothesis', even when the hypothesis is false, and a b-bootstrap competitor to Tibshirani's variance stabilization method. An example of the bias reduction application is adjustment of Nadaraya–Watson kernel estimators to make them competitive with local linear smoothing. Other applications include density estimation under constraints, outlier trimming, sensitivity analysis, skewness or kurtosis reduction and shrinkage.     

资本技能互补与技术进步的技能偏向决定

本文基于三要素双层嵌套式CES生产函数和质量阶梯型技术创新模型,通过对企业行为的理论分析,揭示了决定技术进步方向的各种因素,发现技术进步的方向取决于技术进步的直接效应、资本技能互补的间接效应和劳动力市场内部的规模效应。其中,资本技能互补效应引致技术进步偏向于技能的机制有二：一是通过体现于资本的技术水平提高偏向于技能劳动,二是通过资本规模的扩大偏向于技能劳动。运用贝叶斯参数估计方法对中国1991-2016年期间技术进步技能偏向指数的实证测算结果表明,资本技能互补效应对于决定技术进步的技能偏向作用巨大,尽管在此期间直接效应偏向于非技能劳动,但是由于资本技能互补的间接效应和要素配置的规模效应偏向于技能劳动,且二者的作用强度均大于直接效应,从而使得中国的技术整体呈现出技能劳动偏向。     

Bias-Corrected maximum likelihood estimation of the parameters of the weighted Lindley distribution

The two-parameter weighted Lindley distribution is useful for modeling survival data, whereas its maximum likelihood estimators (MLEs) are biased in finite samples. This motivates us to construct nearly unbiased estimators for the unknown parameters. We adopt a “corrective” approach to derive modified MLEs that are bias-free to second order. We also consider an alternative bias-correction mechanism based on Efron’s bootstrap resampling. Monte Carlo simulations are conducted to compare the performance between the proposed and two previous methods in the literature. The numerical evidence shows that the bias-corrected estimators are extremely accurate even for very small sample sizes and are superior than the previous estimators in terms of biases and root mean squared errors. Finally, applications to two real datasets are presented for illustrative purposes.     

A Three‐step Method for Choosing the Number of Bootstrap Repetitions

This paper considers the problem of choosing the number of bootstrap repetitions B for bootstrap standard errors, confidence intervals, confidence regions, hypothesis tests, p‐values, and bias correction. For each of these problems, the paper provides a three‐step method for choosing B to achieve a desired level of accuracy. Accuracy is measured by the percentage deviation of the bootstrap standard error estimate, confidence interval length, test's critical value, test's p‐value, or bias‐corrected estimate based on B bootstrap simulations from the corresponding ideal bootstrap quantities for which B=∞. The results apply quite generally to parametric, semiparametric, and nonparametric models with independent and dependent data. The results apply to the standard nonparametric iid bootstrap, moving block bootstraps for time series data, parametric and semiparametric bootstraps, and bootstraps for regression models based on bootstrapping residuals. Monte Carlo simulations show that the proposed methods work very well.