Linearized Restricted Ridge Regression Estimator in Linear Regression

This article primarily aims to put forward the linearized restricted ridge regression (LRRR) estimator in linear regression models. Two types of LRRR estimators are investigated under the PRESS criterion and the optimal LRRR estimators and the optimal restricted generalized ridge regression estimator are obtained. We apply the results to the Hald data and finally make a simulation study by using the method of McDonald and Galarneau.     

Comment on a generalized stochastic restricted ridge regression estimator

In this note, we make some comments about the paper of Alheety and Kibria (2014 Alheety, M.I., Kibria, B.M.G. (2014). A generalized stochastic restricted ridge regression estimator. Commun. Stat. Theor. Meth. 43:4415–4427.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) and correct the wrongly proved Theorems in that paper.     

Computational Method for Jackknifed Generalized Ridge Tuning Parameter based on Generalized Maximum Entropy

In this article, a new method to estimate the Jackknifed generalized ridge tuning parameter, based on the Jackknifed Ridge-trace and an analytical method borrowed from generalized maximum entropy, is presented. The ideas in the article are illustrated and evaluated using to the well-known Portland cement data set and simulations.     

Quick counts from non-selected polling stations

Countless examples of misleading forecasts on behalf of both campaign and exit polls affecting, among others, British, French, and Spanish elections could be found. This has seriously damaged their image. Therefore, procedures should be used that minimize errors, especially on election night when errors are more noticeable, in order to maintain people's trust in surveys. This paper proposes a method to obtain quick and early outcome forecasts on the election night. The idea is to partly sample some (whatever) polling stations and use the consistency that polling stations show between elections to predict the final results. Model accuracy is analysed through simulation using seven different types of samples in four elections. The efficacy of the technique is also tested predicting the 2005 Eusko Legebiltzarra elections from real data. Results confirm that the procedure generates highly reliable and accurate forecasts. Furthermore, compared with the classical quick count strategy, the method is revealed as much more robust and precise.     

Ridge estimation in generalized linear models and proportional hazards regressions

Conventionally, a ridge parameter is estimated as a function of regression parameters based on ordinary least squares. In this article, we proposed an iterative procedure instead of the one-step or conventional ridge method. Additionally, we construct an indicator that measures the potential degree of improvement in mean squared error when ridge estimates are employed. Simulations show that our methods are appropriate for a wide class of non linear models including generalized linear models and proportional hazards (PHs) regressions. The method is applied to a PH regression with highly collinear covariates in a cancer recurrence study.     

Variable selection in linear regression based on ridge estimator

In this article, we consider the problem of variable selection in linear regression when multicollinearity is present in the data. It is well known that in the presence of multicollinearity, performance of least square (LS) estimator of regression parameters is not satisfactory. Consequently, subset selection methods, such as Mallow's Cp, which are based on LS estimates lead to selection of inadequate subsets. To overcome the problem of multicollinearity in subset selection, a new subset selection algorithm based on the ridge estimator is proposed. It is shown that the new algorithm is a better alternative to Mallow's Cp when the data exhibit multicollinearity.     

1997-2002年中国经济社会结构的研究——基于社会核算矩阵更新的分析

摘　　要:本文首先编制了1997年和2002年中国细分社会核算矩阵（social accounting matrix,SAM）,然后利用广义交叉熵法更新SAM系数。基于SAM及SAM更新研究了中国产业结构、收入分配结构和消费结构的水平及其变化。研究发现：第一,总体而言,各产业的中间投入比例降低,增加值占总投入比例上升,但生产性服务业作为其他产业中间投入的比例上升;第二,2002年中国农村居民的收入主要来自不熟练劳动力,资本收入在农村居民收入来源中的比例有所增加;第三,城镇中等偏上收入分组及以上居民所有六大类商品和服务的消费比例均得到提高,而其他低收入分组城镇居民和农村居民则不能兼顾所有商品和服务的消费 。     

Good ridge estimators based on prior information

Ridge regression is re-examined and ridge estimators based on prior information are introduced. A necessary and sufficient condition is given for such ridge estimators to yield estimators of every nonnull linear combination of the regression coefficients with smaller mean square error than that of the Gauss-Markov best linear unbiased estimator.     

Restricted ridge estimator in generalized linear models: Monte Carlo simulation studies on Poisson and binomial distributed responses

It is known that collinearity among the explanatory variables in generalized linear models (GLMs) inflates the variance of maximum likelihood estimators. To overcome multicollinearity in GLMs, ordinary ridge estimator and restricted estimator were proposed. In this study, a restricted ridge estimator is introduced by unifying the ordinary ridge estimator and the restricted estimator in GLMs and its mean squared error (MSE) properties are discussed. The MSE comparisons are done in the context of first-order approximated estimators. The results are illustrated by a numerical example and two simulation studies are conducted with Poisson and binomial responses.     

Forecasting Value at Risk and Expected Shortfall Using a Semiparametric Approach Based on the Asymmetric Laplace Distribution

Value at Risk (VaR) forecasts can be produced from conditional autoregressive VaR models, estimated using quantile regression. Quantile modeling avoids a distributional assumption, and allows the dynamics of the quantiles to differ for each probability level. However, by focusing on a quantile, these models provide no information regarding expected shortfall (ES), which is the expectation of the exceedances beyond the quantile. We introduce a method for predicting ES corresponding to VaR forecasts produced by quantile regression models. It is well known that quantile regression is equivalent to maximum likelihood based on an asymmetric Laplace (AL) density. We allow the density's scale to be time-varying, and show that it can be used to estimate conditional ES. This enables a joint model of conditional VaR and ES to be estimated by maximizing an AL log-likelihood. Although this estimation framework uses an AL density, it does not rely on an assumption for the returns distribution. We also use the AL log-likelihood for forecast evaluation, and show that it is strictly consistent for the joint evaluation of VaR and ES. Empirical illustration is provided using stock index data. Supplementary materials for this article are available online.     

A Generalized View on Continuum Regression

ABSTRACT. We generalize the relationship between continuum regression (Stone & Brooks, 1990) and ridge regression, by showing that any optimization principle will yield a regressor proportional to a ridge regressor, provided only that the principle implies maximizing a function of the regressor's sample correlation coefficient and its sample variance. This relationship shows that continuum regression as defined via ridge regression (least squares ridge regression) is a more generally valid methodology than previously realized, and also opens up for alternative choices of its second and subsequent factors.     

A note on the moments of stochastic shrinkage parameters in ridge regression

The purpose of this note is to gain insight on the performance of two well known operational Ridge Regression estimators by deriving the moments of their stochastic shrinkage parameters. We also show that, under certain conditions, one of them has bounded moments.     

Robust ridge and robust Liu estimator for regression based on the LTS estimator

In the multiple linear regression analysis, the ridge regression estimator and the Liu estimator are often used to address multicollinearity. Besides multicollinearity, outliers are also a problem in the multiple linear regression analysis. We propose new biased estimators based on the least trimmed squares (LTS) ridge estimator and the LTS Liu estimator in the case of the presence of both outliers and multicollinearity. For this purpose, a simulation study is conducted in order to see the difference between the robust ridge estimator and the robust Liu estimator in terms of their effectiveness; the mean square error. In our simulations, the behavior of the new biased estimators is examined for types of outliers: X-space outlier, Y-space outlier, and X-and Y-space outlier. The results for a number of different illustrative cases are presented. This paper also provides the results for the robust ridge regression and robust Liu estimators based on a real-life data set combining the problem of multicollinearity and outliers.     

陕西省区域技术创新能力影响因素分析

根据陕西省1991—2008年统计数据,利用岭回归估计建立模型,运用知识生产函数对陕西省区域技术创新能力影响因素进行实证分析。研究结果表明：科研机构、企业和高校科技投入对陕西区域技术创新产出具有显著的作用,而人力资本投入对陕西区域技术创新产出作用不显著。     

Longitudinal data analysis based on generalized linear partially varying-coefficient models

In this article, we consider a generalized linear partially varying-coefficient model for longitudinal data analysis. A local quasi-likelihood method is proposed to estimate the constant-coefficient and varying-coefficient functions simultaneously based on the local polynomial kernel regression. The corresponding standard error estimates are derived. Large sample properties are investigated. The proposed methodologies are demonstrated by extensive simulation studies and a real example.     

Nonparametric and non-linear models and data mining in time series: a case-study on the Canadian lynx data

Nonparametric regression methods are used as exploratory tools for formulating, identifying and estimating non-linear models for the Canadian lynx data, which have attained bench-mark status in the time series literature since the work of Moran in 1953. To avoid the curse of dimensionality in the nonparametric analysis of this short series with 114 observations, we confine attention to the restricted class of additive and projection pursuit regression (PPR) models and rely on the estimated prediction error variance to compare the predictive performance of various (non-)linear models. A PPR model is found to have the smallest (in-sample) estimated prediction error variance of all the models fitted to these data in the literature. We use a data perturbation procedure to assess and adjust for the effect of data mining on the estimated prediction error variances; this renders most models fitted to the lynx data comparable and nearly equivalent. However, on the basis of the mean-squared error of out-of-sample prediction error, the semiparametric model X_t =1.08+1.37 X_{t −1}+ f ( X_{t −2})+ e_t and Tong's self-exciting threshold autoregression model perform much better than the PPR and other models known for the lynx data.