中国系统性金融风险对宏观经济的影响研究

基于2007年1月至2017年12月月度数据,本文首先选取金融机构极值风险、金融体系间的传染效应、金融市场的波动性和不稳定性、流动性和信用风险4个层面的14个代表性指标测度了系统性金融风险;然后运用分位数回归度量了单个系统性风险指标对宏观经济的影响;最后运用偏最小二乘分位数回归法构建一个系统性金融风险综合指标进一步实证分析系统性金融风险对宏观经济的影响。研究结果表明：①单个系统性金融风险指数中机构极值风险类别下的指标对宏观经济的影响最大,其中金融体系巨灾风险指数影响效果最显著;②运用偏最小二乘分位数回归构造的系统性金融风险综合指标较之单个系统性金融风险指标,能够更稳健地反映系统性金融风险对宏观经济的影响状况;③从测度效果来看,单个系统性风险指标和系统性金融风险综合指标在下尾分布（0.2分位数）的结果明显优于中间分布（0.5分位数）和上尾分布（0.8分位数）。     

Estimating the error variance after a pre-test for an inequality restriction on the coefficients

Estimation of the regression error variance after a preliminary test of an inequality constraint on the coefficient vector is considered. We derive the exact finite sample risk of several inequality restricted and pre-test estimators of σ². These estimators are associated with the maximum likelihood, least squares and minimum mean squared error component estimators. Optimal critical values for the pre-test according to a mini-max regret criterion are numerically calculated. Furthermore, we examine the robustness of the optimal choice of critical values and the risk properties of the estimators of σ² to model mis-specification through the exclusion of relevant regressors.     

A ray method of confidence band construction for multiple linear regression models

This paper addresses the problem of confidence band construction for a standard multiple linear regression model. A “ray” method of construction is developed which generalizes the method of Graybill and Bowden [1967. Linear segment confidence bands for simple linear regression models. J. Amer. Statist. Assoc. 62, 403–408] for a simple linear regression model to a multiple linear regression model. By choosing suitable directions for the rays this method requires only critical points from t-distributions so that the confidence bands are easy to construct. Both one-sided and two-sided confidence bands can be constructed using this method. An illustration of the new method is provided.     

Bayesian regression under combinations of constraints

A Bayesian method for regression under several types of constraints is proposed. The constraints can be range-restricted and include shape restrictions, constraints on the value of the regression function, smoothness conditions and combinations of these types of constraints. The support of the prior distribution is included in the set of piecewise linear functions. It is shown that the proposed prior can be arbitrarily close to the distribution induced by the addition of a polynomial plus an (m−1)-fold integrated Brownian motion. Hence, despite its piecewise linearity, the regression function behaves (approximately) like an m−1 times continuously differentiable random function. Furthermore, thanks to the piecewise linear property, many combinations of constraints can easily be considered. The regression function is estimated by the posterior mode computed by a simulated annealing algorithm. The constraints on the shape and the values of the regression function are taken into account thanks to the proposal distribution, while the smoothness condition is handled by the acceptation step. Simulations from the posterior distribution are obtained by a Gibbs sampling algorithm.     

Evaluation strategies for case series: is Cox regression an alternative to the self controlled case series method for terminal events?

In this paper, we deal with the analysis of case series. The self-controlled case series method (SCCS) was developed to analyse the temporal association between time-varying exposure and an outcome event. We apply the SCCS method to the vaccination data of the German Examination Survey for Children and Adolescents (KiGGS). We illustrate that the standard SCCS method cannot be applied to terminal events such as death. In this situation, an extension of SCCS adjusted for terminal events gives unbiased point estimators. The key question of this paper is whether the general Cox regression model for time-dependent covariates may be an alternative to the adjusted SCCS method for terminal events. In contrast to the SCCS method, Cox regression is included in most software packages (SPSS, SAS, STATA, R, …) and it is easy to use. We can show that Cox regression is applicable to test the null hypothesis. In our KiGGS example without censored data, the Cox regression and the adjusted SCCS method yield point estimates almost identical to the standard SCCS method. We have conducted several simulation studies to complete the comparison of the two methods. The Cox regression shows a tendency to underestimate the true effect with prolonged risk periods and strong effects (Relative Incidence >2). If risk of the event is strongly affected by the age, the adjusted SCCS method slightly overestimates the predefined exposure effect. Cox regression has the same efficiency as the adjusted SCCS method in the simulation.     

The exact risk performance of a pre-test estimator in a heteroskedastic linear regression model under the balanced loss function

We examine the risk of a pre-test estimator for regression coefficients after a pre-test for homoskedasticity under the Balanced Loss Function (BLF). We show analytically that the two stage Aitken estimator is dominated by the pre-test estimator with the critical value of unity, even if the BLF is used. We also show numerically that both the two stage Aitken estimator and the pre-test estimator can be dominated by the ordinary least squares estimator when “goodness of fit” is regarded as more important than precision of estimation.     

Improved kth power expectile regression with nonignorable dropouts

The kth ( 1<k≤2) power expectile regression (ER) can balance robustness and effectiveness between the ordinary quantile regression and ER simultaneously. Motivated by a longitudinal ACTG 193A data with nonignorable dropouts, we propose a two-stage estimation procedure and statistical inference methods based on the kth power ER and empirical likelihood to accommodate both the within-subject correlations and nonignorable dropouts. Firstly, we construct the bias-corrected generalized estimating equations by combining the kth power ER and inverse probability weighting approaches. Subsequently, the generalized method of moments is utilized to estimate the parameters in the nonignorable dropout propensity based on sufficient instrumental estimating equations. Secondly, in order to incorporate the within-subject correlations under an informative working correlation structure, we borrow the idea of quadratic inference function to obtain the improved empirical likelihood procedures. The asymptotic properties of the corresponding estimators and their confidence regions are derived. The finite-sample performance of the proposed estimators is studied through simulation and an application to the ACTG 193A data is also presented.     

A generalized likelihood ratio test for monitoring profile data

Profile data emerges when the quality of a product or process is characterized by a functional relationship among (input and output) variables. In this paper, we focus on the case where each profile has one response variable Y, one explanatory variable x, and the functional relationship between these two variables can be rather arbitrary. The basic concept can be applied to a much wider case, however. We propose a general method based on the Generalized Likelihood Ratio Test (GLRT) for monitoring of profile data. The proposed method uses nonparametric regression to estimate the on-line profiles and thus does not require any functional form for the profiles. Both Shewhart-type and EWMA-type control charts are considered. The average run length (ARL) performance of the proposed method is studied. It is shown that the proposed GLRT-based control chart can efficiently detect both location and dispersion shifts of the on-line profiles from the baseline profile. An upper control limit (UCL) corresponding to a desired in-control ARL value is constructed.     

Shrinkage estimation of varying covariate effects based on quantile regression

Varying covariate effects often manifest meaningful heterogeneity in covariate-response associations. In this paper, we adopt a quantile regression model that assumes linearity at a continuous range of quantile levels as a tool to explore such data dynamics. The consideration of potential non-constancy of covariate effects necessitates a new perspective for variable selection, which, under the assumed quantile regression model, is to retain variables that have effects on all quantiles of interest as well as those that influence only part of quantiles considered. Current work on l ₁-penalized quantile regression either does not concern varying covariate effects or may not produce consistent variable selection in the presence of covariates with partial effects, a practical scenario of interest. In this work, we propose a shrinkage approach by adopting a novel uniform adaptive LASSO penalty. The new approach enjoys easy implementation without requiring smoothing. Moreover, it can consistently identify the true model (uniformly across quantiles) and achieve the oracle estimation efficiency. We further extend the proposed shrinkage method to the case where responses are subject to random right censoring. Numerical studies confirm the theoretical results and support the utility of our proposals.     

Bias-corrected estimators for dispersion models with dispersion covariates

In this paper we discuss bias-corrected estimators for the regression and the dispersion parameters in an extended class of dispersion models (Jørgensen, 1997b). This class extends the regular dispersion models by letting the dispersion parameter vary throughout the observations, and contains the dispersion models as particular case. General formulae for the O(n⁻¹) bias are obtained explicitly in dispersion models with dispersion covariates, which generalize previous results obtained by Botter and Cordeiro (1998), Cordeiro and McCullagh (1991), Cordeiro and Vasconcellos (1999), and Paula (1992). The practical use of the formulae is that we can derive closed-form expressions for the O(n⁻¹) biases of the maximum likelihood estimators of the regression and dispersion parameters when the information matrix has a closed-form. Various expressions for the O(n⁻¹) biases are given for special models. The formulae have advantages for numerical purposes because they require only a supplementary weighted linear regression. We also compare these bias-corrected estimators with two different estimators which are also bias-free to order O(n⁻¹) that are based on bootstrap methods. These estimators are compared by simulation.     

中年女性血红蛋白参考值与地理因素的非线性模型

文章收集了中国268个单位用氰化高铁血红蛋白(HiCN)法测定的25917例中年女性血红蛋白参考值,运用非线性回归分析的方法,研究了其与地理因素的关系,发现中年女性血红蛋白参考值与地理因素之间有很显著的相关关系,得到一个多元非线性回归方程。因此知道了某地的地理因素,就可以用非线性回归方程估算这个地区的血红蛋白参考值。依据血红蛋白参考值与地理因素的依赖关系可以把中国分为青藏区、西南区、西北区、东南区、华北区、东北区六个区,为制定中年女性血红蛋白参考值的统一标准提供科学了依据。     

Censored median regression and profile empirical likelihood

We implement profile empirical likelihood-based inference for censored median regression models. Inference for any specified subvector is carried out by profiling out the nuisance parameters from the “plug-in” empirical likelihood ratio function proposed by Qin and Tsao. To obtain the critical value of the profile empirical likelihood ratio statistic, we first investigate its asymptotic distribution. The limiting distribution is a sum of weighted chi square distributions. Unlike for the full empirical likelihood, however, the derived asymptotic distribution has intractable covariance structure. Therefore, we employ the bootstrap to obtain the critical value, and compare the resulting confidence intervals with the ones obtained through Basawa and Koul’s minimum dispersion statistic. Furthermore, we obtain confidence intervals for the age and treatment effects in a lung cancer data set.     

An exponentially weighted quantile regression via SVM with application to estimating multiperiod VaR

The square root of time rule under RiskMetrics has been used as an important tool to estimate multiperiod value at risk (VaR). However, the conditions for the rule are too restrictive to get empirical support in practice since multiperiod VaR is a complex nonlinear function of the holding period and the one-step ahead volatility forecast. In this paper, we propose a new model by considering an exponentially weighted quantile regression via SVM to provide greater accuracy for multiperiod VaR measure. In both numerical simulations and empirical studies on three stock indices, the proposed model outperforms several traditional methods including the volatility models, filtered historical simulation, and linear quantile regression approaches in terms of the value of the number of significant entries, the mean absolute error, and the p value of prediction test in Harvey et al. (Int J Forecast 13:281–291, 1997).     

Automatic bandwidth selection for modified m-smoother ∗

Traditional parametric and nonparametric regression techniques encounter serious over smoothing problems when jump point discontinuities exist in the underlying mean function. Recently, Chu, Glad, Godtliebsen and Marron (1998) developed a method using a modified M-smoothing technique to preserve jumps and spikes while producing a smooth estimate of the mean function. The performance of Chu etal.'s (1998) method is quite sensitive to the choice of the required bandwidths g and h. Furthermore, it is not obvious how to extend certain commonly used automatic bandwidth selection procedures when jumps and spikes are present. In this paper we propose a rule of thumb method of choosing the smoothing parameters based on asymptotic optimal bandwidth formulas and robust estimates of unknown quantities. We also evaluate the proposed bandwidth selection method via a small simulation study.     

Reducing bias in parameter estimates from stepwise regression in proportional hazards regression with right-censored data

When variable selection with stepwise regression and model fitting are conducted on the same data set, competition for inclusion in the model induces a selection bias in coefficient estimators away from zero. In proportional hazards regression with right-censored data, selection bias inflates the absolute value of parameter estimate of selected parameters, while the omission of other variables may shrink coefficients toward zero. This paper explores the extent of the bias in parameter estimates from stepwise proportional hazards regression and proposes a bootstrap method, similar to those proposed by Miller (Subset Selection in Regression, 2nd edn. Chapman & Hall/CRC, 2002) for linear regression, to correct for selection bias. We also use bootstrap methods to estimate the standard error of the adjusted estimators. Simulation results show that substantial biases could be present in uncorrected stepwise estimators and, for binary covariates, could exceed 250% of the true parameter value. The simulations also show that the conditional mean of the proposed bootstrap bias-corrected parameter estimator, given that a variable is selected, is moved closer to the unconditional mean of the standard partial likelihood estimator in the chosen model, and to the population value of the parameter. We also explore the effect of the adjustment on estimates of log relative risk, given the values of the covariates in a selected model. The proposed method is illustrated with data sets in primary biliary cirrhosis and in multiple myeloma from the Eastern Cooperative Oncology Group.     

Empirical Likelihood Intervals for Conditional Value‐at‐Risk in Heteroscedastic Regression Models

Abstract. Non‐parametric regression models have been studied well including estimating the conditional mean function, the conditional variance function and the distribution function of errors. In addition, empirical likelihood methods have been proposed to construct confidence intervals for the conditional mean and variance. Motivated by applications in risk management, we propose an empirical likelihood method for constructing a confidence interval for the pth conditional value‐at‐risk based on the non‐parametric regression model. A simulation study shows the advantages of the proposed method.     

A ridge-type estimator and good prior means

Swindel (1976) introduced a modified ridge regression estimator based on prior information. A necessary and sufficient condition is derived for Swindel's proposed estimator to have lower risk than the conventional ordinary ridge regression estimator when both estimators are computed using the same value of k.     

Semivarying coefficient least-squares support vector regression for analyzing high-dimensional gene-environmental data

In the context of genetics and genomic medicine, gene-environment (G×E) interactions have a great impact on the risk of human diseases. Some existing methods for identifying G×E interactions are considered to be limited, since they analyze one or a few number of G factors at a time, assume linear effects of E factors, and use inefficient selection methods. In this paper, we propose a new method to identify significant main effects and G×E interactions. This is based on a semivarying coefficient least-squares support vector regression (LS-SVR) technique, which is devised by utilizing flexible semiparametric LS-SVR approach for censored survival data. This semivarying coefficient model is used to deal with the nonlinear effects of E factors. We also derive a generalized cross validation (GCV) function for determining the optimal values of hyperparameters of the proposed method. This GCV function is also used to identify significant main effects and G×E interactions. The proposed method is evaluated through numerical studies.     

Sliced inverse moment regression using weighted chi-squared tests for dimension reduction

We propose a new method for dimension reduction in regression using the first two inverse moments. We develop corresponding weighted chi-squared tests for the dimension of the regression. The proposed method considers linear combinations of sliced inverse regression (SIR) and the method using a new candidate matrix which is designed to recover the entire inverse second moment subspace. The optimal combination may be selected based on the p-values derived from the dimension tests. Theoretically, the proposed method, as well as sliced average variance estimate (SAVE), is more capable of recovering the complete central dimension reduction subspace than SIR and principle Hessian directions (pHd). Therefore it can substitute for SIR, pHd, SAVE, or any linear combination of them at a theoretical level. Simulation study indicates that the proposed method may have consistently greater power than SIR, pHd, and SAVE.     

Adaptation over parametric families of symmetric linear estimators

This paper treats an abstract parametric family of symmetric linear estimators for the mean vector of a standard linear model. The estimator in this family that has smallest estimated quadratic risk is shown to attain, asymptotically, the smallest risk achievable over all candidate estimators in the family. The asymptotic analysis is carried out under a strong Gauss–Markov form of the linear model in which the dimension of the regression space tends to infinity. Leading examples to which the results apply include: (a) penalized least squares fits constrained by multiple, weighted, quadratic penalties; and (b) running, symmetrically weighted, means. In both instances, the weights define a parameter vector whose natural domain is a continuum.