Test for Heteroscedasticity in Partially Linear Regression Models

Testing heteroscedasticity determines whether the regression model can predict the dependent variable consistently across all values of the explanatory variables. Since the proposed tests could not detect heteroscedasticity in all cases, more precisely in heavy-tailed distributions, the authors established new comprehensive test statistic based on Levene's test. The authors built the asymptotic normality of the test statistic under the null hypothesis of homoscedasticity based on the recent theory of analysis of variance for the infinite factors level. The proposed test uses the residuals from a regression model fit of the mean function with Levene's test to assess homogeneity of variance. Simulation studies show that our test yields better than other methods in almost all cases even if the variance is a nonlinear function. Finally, the proposed method is implemented through a real data-set.     

Robust Estimation for Partial Functional Linear Regression Model Based on Modal Regression

This paper presents a robust estimation procedure by using modal regression for the partial functional linear regression, which combines the common linear model with the functional linear regression model. The outstanding merit of the new method is that it is robust against outliers or heavy-tail error distributions while performs no worse than the least-square-based estimation method for normal error cases. The slope function is fitted by B-spline. Under suitable conditions, the authors obtain the convergence rates and asymptotic normality of the estimators. Finally, simulation studies and a real data example are conducted to examine the finite sample performance of the proposed method. Both the simulation results and the real data analysis confirm that the newly proposed method works very well.     

Heteroscedasticity Detection and Estimation with Quantile Difference Method

When dealing with regression analysis, heteroscedasticity is a problem that the authors have to face with. Especially if little information can be got in advance, detection of heteroscedasticity as well as estimation of statistical models could be even more difficult. To this end, this paper proposes a quantile difference method (QDM) that can effectively estimate the heteroscedastic function. This method, being completely free from the estimation of mean regression function, is simple, robust and easy to implement. Moreover, the QDM method enables the detection of heteroscedasticity without any restrictions on error terms, consequently being widely applied. What is worth mentioning is that based on the proposed approach estimators of both mean regression function and heteroscedastic function can be obtained. In the end, the authors conduct some simulations to examine the performance of the proposed methods and use a real data to make an illustration.     

模糊线性回归及其应用实例

本文首先探讨了模糊线性回归模型的理论与方法,然后建立了天津市自来水行业职工人数预测模型,根据社会和经济发展目标,预测出天津自来水行业未来职工总人数。本文提出的方法与模型具有普遍意义与实用价值。     

Diagnostics in Linear Regresion Model

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Consistent Estimation of Order for Regression in the Presence of Serial Correlation and Heteroscedasticity

1　 IntroductionIn econometric regression models,serial correlation and heteroscedasticity are twocommonly encoutered features of disturbance behavior and may often occursimultaneously. For example,the effects of omitted variables may give rise to bothproblems simultaneously.Therefore,an econometric regression model where both serialcorrelation and heteroscedasticity are present would be feasible.There are literaturesconcerning efficient estimation of regressions with both serial correlation a…     

基于GM(1,1)模型和线性回归的组合预测新方法

为解决 GM(1 ,1 )预测中存在的历史数据的跳变问题 ,依据灰色灾变预测原理 ,利用线性回归适用短期预测的特点 ,提出了一种新的预测方法 :用 GM(1 ,1 )模型预测将来可能的数据跳变日期点 ,对其他非跳变点使用分段线性回归函数进行预测 .通过对浙江省农村用电量的预测 ,结果表明该方法很好地克服了 GM(1 ,1 )模型和线性回归模型的缺陷 ,在实际中取得了较好的效果 .     

Estimation in Partially Observed Functional Linear Quantile Regression

Currently, working with partially observed functional data has attracted a greatly increasing attention, since there are many applications in which each functional curve may be observed only on a subset of a common domain, and the incompleteness makes most existing methods for functional data analysis ineffective. In this paper, motivated by the appealing characteristics of conditional quantile regression, the authors consider the functional linear quantile regression, assuming the explanatory f...     

区间数据下EV线性回归模型修正的广义最小二乘估计

研究了当响应变量为区间数据时的EV线性回归模型,通过构造区间数据的无偏转换,并对广义最小二乘估计作适当修正,得到了回归参数的估计,在较一般的条件下证明了强相合性和渐近正态性.最后作了若干模拟计算,从模拟的结果发现,利用本文提出的方法所获得的估计具有较高的精度.     

A New Method of State Estimation for Singular Discrete-time Stochastic Linear System

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成分数据的线性回归模型

在许多社会、经济、技术问题中，成分数据通常被用于研究作为整体的各部分的比率情况。本文结合对称的logratio变换与偏最小二乘回归方法，提出一种成分数据回归建模的方法。该方法可以克服经典线性回归方法在成分数据建模中的诸多困难。并反由于所采用的数学变换具有对称性，因此变换以后的变量可以较好地反映原始变量的含义，便于建立一个容易解释的数学模型。本文还采用北京市三次产业就业需求预测作为案例，说明成分数据回归建模的工作过程和应用价值，并通过计算结果验证了本文所提方法的有效性和合理性。     

关于多品种有约束存储模型的一种非线性整数规划方法

对多品种有约束的存贮论问题,传统的存贮模型是通过给每一种货假设一个决策变量（定量时间或定货量）再用Kuhn-Tuchker条件求得“最优解”,实际上这样的结果并非最优解。它存在着订货次数过多,资源利用率低,总费用过高等缺点。本文通过对时间的有效切割入手,建立了一非线性整数规划模型比较好地解决了这一问题,本文在提出新的方法的同时,将之与传统有约束存贮模型和无约束存贮模型作了充分的对比。     

GLM约束估计及病态问题研究

利用Ｌａｇｒａｎｇｅ乘子方法解决了广义线性模型（ＧＬＭ）的约束估计问题，并由此引出了广义线性模型的病态问题。通过从减小参数估计的均方误差及消除自变量间的多重共线性着手，本文探讨了改进病态矩阵有效方法。     

Estimation in Linear Regression with Laplace Measurement Error Using Tweedie-Type Formula

Based on a Tweedie-type formula developed under the Laplace distribution, this paper proposes a new bias-corrected estimator of the regression parameters in a simple linear model when the measurement error follows a Laplace distribution. Large sample properties, including the consistency and the asymptotic normality, are investigated. The finite sample performance of the proposed estimators are evaluated via simulation studies, as well as comparison studies with some existing estimation procedures.     

一元线性模型异方差的局部多项式回归

本文将局部多项式回归的非参数方法用于线性模型中异方差的估计 ,改进了传统的两阶段法 ,得到了估计的一致性和渐近正态性 ,为探讨估计的有限样本性 ,给出了若干模拟的例子。     

Double Penalized Quantile Regression for the Linear Mixed Effects Model

Journal of Systems Science and Complexity - This paper proposes a double penalized quantile regression for linear mixed effects model, which can select fixed and random effects simultaneously....     

估计Verhulst 模型中参数的线性规划方法及应用

估计灰色Verhulst模型中的参数通常采用最小二乘准则,而在模型精度检验时又经常采用平均相对误差.本文主要在平均相对误差达到最小准则或最大相对误差达到最小准则下,阐明了Verhulst模型中参数估计问题可转化为线性规划问题,可以利用线性规划方法估计Verhulst模型中的参数.实际应用表明本文的方法是可行的且有效的,比传统方法预测精度高.     

一种灰色预测模型的新方法

给出了一种灰色预测模型的新方法。该方法运用线性回归对数据进行分组,并对各组数据进行指数插值;运用二次规划进行权重选择;运用灰色灾变预测确定权重的时序集,从而求得预测值。这种方法提高了预测精度,并反映了事物波浪式前进发展的本质,拓广了灰色预测的范围。     

应用混沌相空间模线性回归模型研究短期负荷预报

在一维 Lyapunov指数预报模型的基础上提出了混沌相空间模线性回归模型 ,并将该模型应用于短期负荷预报 .对厦门市实际负荷时间序列进行预报 ,取得了较满意的结果 .     

A New Estimation for Informed Trading Based on SSNF Method

This paper estimates the information-based trading using spatially selective noise filtration (SSNF) method. The SSNF method is a kind of filtration technique based on the different spatial correlation of the wavelet transform at several adjacent scales. Using SSNF method, the information shock caused by the informed traders could be extracted from the prices effectively, then the PINs at different scales could be calculated. The measure of informed trading can capture some asymmetric information properties, which is consistent with some empirical consensuses. Furthermore, compared with the MLE method in EKOP model, the method has computational facilities in avoiding the overflow or underflow problem, the boundary solutions problem and the initial values problem. And the method could be applied to the high-frequency world in both order-driven and quote-driven market.