Improved two-parameter estimators for the negative binomial and Poisson regression models

Negative binomial regression (NBR) and Poisson regression (PR) applications have become very popular in the analysis of count data in recent years. However, if there is a high degree of relationship between the independent variables, the problem of multicollinearity arises in these models. We introduce new two-parameter estimators (TPEs) for the NBR and the PR models by unifying the two-parameter estimator (TPE) of Özkale and Kaç?ranlar [The restricted and unrestricted two-parameter estimators. Commun Stat Theory Methods. 2007;36:2707–2725]. These new estimators are general estimators which include maximum likelihood (ML) estimator, ridge estimator (RE), Liu estimator (LE) and contraction estimator (CE) as special cases. Furthermore, biasing parameters of these estimators are given and a Monte Carlo simulation is done to evaluate the performance of these estimators using mean square error (MSE) criterion. The benefits of the new TPEs are also illustrated in an empirical application. The results show that the new proposed TPEs for the NBR and the PR models are better than the ML estimator, the RE and the LE.     

Double robust estimator in general treatment regimes based on Covariate-balancing

Double robust estimators have double the chance of being a consistent estimator of a causal effect in binary treatments cases. In this paper, we proposed an estimator of a causal effect for general treatment regimes based on covariate-balancing. Under parametrical situation, our estimator has double robustness.     

Confidence intervals based on the deviance statistic for the hyperparameters in state space models

The main objective of this work is to evaluate the performance of confidence intervals, built using the deviance statistic, for the hyperparameters of state space models. The first procedure is a marginal approximation to confidence regions, based on the likelihood test, and the second one is based on the signed root deviance profile. Those methods are computationally efficient and are not affected by problems such as intervals with limits outside the parameter space, which can be the case when the focus is on the variances of the errors. The procedures are compared to the usual approaches existing in the literature, which includes the method based on the asymptotic distribution of the maximum likelihood estimator, as well as bootstrap confidence intervals. The comparison is performed via a Monte Carlo study, in order to establish empirically the advantages and disadvantages of each method. The results show that the methods based on the deviance statistic possess a better coverage rate than the asymptotic and bootstrap procedures.     

MSE performance of the weighted average estimators consisting of shrinkage estimators when each individual regression coefficient is estimated

In this paper, we analytically derive the exact formula for the mean squared error (MSE) of two weighted average (WA) estimators for each individual regression coefficient. Further, we execute numerical evaluations to investigate small sample properties of the WA estimators, and compare the MSE performance of the WA estimators with the other shrinkage estimators and the usual OLS estimator. Our numerical results show that (1) the WA estimators have smaller MSE than the other shrinkage estimators and the OLS estimator over a wide region of parameter space; (2) the range where the relative MSE of the WA estimator is smaller than that of the OLS estimator gets narrower as the number of explanatory variables k increases.     

正态回归模型中未知参数几种估计的比较分析

给出了正态回归模型中未知参数的无偏估计,最小二乘估计与极大似然估计及其求解过程,并通过数值模拟说明了异同点,验证了相应的结论。     

贫困脆弱性视角下参与式社区综合发展的精准“防贫”效应分析

利用贵州省纳雍县两个贫困行政村跨期十数年的农户追踪调查数据,从贫困脆弱性视角量化分析、评价不同时期参与式社区综合发展的“防贫”效应及其精准性。结果表明,欠发达地区农户的贫困脆弱性在1999-2011年期间降幅巨大（约下降99%）,抗风险冲击能力得到极大提升。总体上,参与式社区综合发展的“防贫”即期效应显著,可使农户贫困脆弱性指数降低5个百分点以上,然其“防贫”时滞效应却并不突出。分不同群体考察,参与式社区综合发展“防贫”虽存在一定“漏出效应”和“溢出效应”,但包容性较强、瞄准精度尚可,能惠及大多数“重度脆弱户”和“中度、轻度脆弱户”;换言之,除“微度脆弱户”、“极度脆弱户”及部分“重度脆弱户”外,其间各贫困脆弱组农户均能从中得到保障,然贫困脆弱性强度越高,所受保障程度愈小。不仅如此,参与式社区综合发展此种“防贫”的精准度可持续性差,无明显时滞效应。     

基于股价预测的泛证券投资组合策略

本文基于期望效用最大化和L₁-中位数估计研究了在线投资组合选择问题。与EG（Exponential Gradient）策略仅利用单期价格信息估计价格趋势不同,本文将利用多期价格信息估计价格趋势,以提高在线策略的性能。首先,基于多期价格数据,利用L₁-中位数估计得到预期价格趋势。然后,通过期望效用最大化,提出一个新的具有线型时间复杂度的在线策略,EGLM（Exponential Gradient via L₁-Median）。并通过相对熵函数定义资产权重向量的距离,进而证明了EGLM策略具有泛证券投资组合性质。最后,利用国内外6个证券市场的历史数据进行实证分析,结果表明相较于UP（Universal Portfolio）策略和EG策略,EGLM策略有更好的竞争性能。     

高频数据瞬时波动率核估计的窗宽选择及算法研究

在瞬时波动率的各种估计量中,非参数估计量因其能准确地度量瞬时波动率,一直是学者们的研究热点。然而,这类估计量在实际应用中都面临着最优窗宽的确定问题。由于最优窗宽中往往携带一些难以估计的未知参数,使得在实际应用过程中确定最优窗宽的具体数值存在困难。本文以瞬时波动率的核估计量为例,借鉴非参数回归分析中窗宽选择的思想,构建了一种能从数据中准确计算出最优窗宽具体值的算法。理论的分析和数值上的验证表明：文中所构建的算法具有良好的稳定性、适应性和收敛速度。算法的提出为瞬时波动率的后续应用研究铺平道路。     

ESTIMATING A PARAMETER WHEN IT IS KNOWN THAT THE PARAMETER EXCEEDS A GIVEN VALUE

In some statistical problems a degree of explicit, prior information is available about the value taken by the parameter of interest, θ say, although the information is much less than would be needed to place a prior density on the parameter's distribution. Often the prior information takes the form of a simple bound, ‘θ > θ₁ ’ or ‘θ < θ₁ ’, where θ₁ is determined by physical considerations or mathematical theory, such as positivity of a variance. A conventional approach to accommodating the requirement that θ > θ₁ is to replace an estimator, , of θ by the maximum of and θ₁. However, this technique is generally inadequate. For one thing, it does not respect the strictness of the inequality θ > θ₁ , which can be critical in interpreting results. For another, it produces an estimator that does not respond in a natural way to perturbations of the data. In this paper we suggest an alternative approach, in which bootstrap aggregation, or bagging, is used to overcome these difficulties. Bagging gives estimators that, when subjected to the constraint θ > θ₁ , strictly exceed θ₁ except in extreme settings in which the empirical evidence strongly contradicts the constraint. Bagging also reduces estimator variability in the important case for which is close to θ₁, and more generally produces estimators that respect the constraint in a smooth, realistic fashion.     

Another look at Huber's estimator: A new minimax estimator in regression with stochastically bounded noise

Huber's estimator has had a long lasting impact, particularly on robust statistics. It is well known that under certain conditions, Huber's estimator is asymptotically minimax. A moderate generalization in rederiving Huber's estimator shows that Huber's estimator is not the only choice. We develop an alternative asymptotic minimax estimator and name it regression with stochastically bounded noise (RSBN). Simulations demonstrate that RSBN is slightly better in performance, although it is unclear how to justify such an improvement theoretically. We propose two numerical solutions: an iterative numerical solution, which is extremely easy to implement and is based on the proximal point method; and a solution by applying state-of-the-art nonlinear optimization software packages, e.g., SNOPT. Contribution: the generalization of the variational approach is interesting and should be useful in deriving other asymptotic minimax estimators in other problems.