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1.
In this article, we study the variable selection of partially linear single-index model(PLSIM). Based on the minimized average variance estimation, the variable selection of PLSIM is done by minimizing average variance with adaptive ll penalty. Implementation algorithm is given. Under some regular conditions, we demonstrate the oracle properties of aLASSO procedure for PLSIM. Simulations are used to investigate the effectiveness of the proposed method for variable selection of PLSIM.  相似文献   

2.
A robust and efficient shrinkage-type variable selection procedure for varying coefficient models is proposed,selection consistency and oracle properties are established.Furthermore,a BIC-type criterion is suggested for shrinkage parameter selection and theoretical property is discussed.Numerical studies and real data analysis also are included to illustrate the finite sample performance of our method.  相似文献   

3.
In this paper,the authors investigate three aspects of statistical inference for the partially linear regression models where some covariates are measured with errors.Firstly, a bandwidth selection procedure is proposed,which is a combination of the differencebased technique and GCV method.Secondly,a goodness-of-fit test procedure is proposed, which is an extension of the generalized likelihood technique.Thirdly,a variable selection procedure for the parametric part is provided based on the nonconcave penalization and corrected profile least squares.Same as"Variable selection via nonconcave penalized likelihood and its oracle properties"(J.Amer.Statist.Assoc.,96,2001,1348-1360),it is shown that the resulting estimator has an oracle property with a proper choice of regularization parameters and penalty function.Simulation studies are conducted to illustrate the finite sample performances of the proposed procedures.  相似文献   

4.
In this paper, we investigate the variable selection problem of the generalized regression models. To estimate the regression parameter, a procedure combining the rank correlation method and the adaptive lasso technique is developed, which is proved to have oracle properties. A modified IMO (iterative marginal optimization) algorithm which directly aims to maximize the penalized rank correlation function is proposed. The effects of the estimating procedure are illustrated by simulation studies.  相似文献   

5.
This article considers a semiparametric varying-coefficient partially linear binary regression model. The semiparametric varying-coefficient partially linear regression binary model which is a generalization of binary regression model and varying-coefficient regression model that allows one to explore the possibly nonlinear effect of a certain covariate on the response variable. A Sieve maximum likelihood estimation method is proposed and the asymptotic properties of the proposed estimators are discussed. One of our main objects is to estimate nonparametric component and the unknowen parameters simultaneously. It is easier to compute, and the required computation burden is much less than that of the existing two-stage estimation method. Under some mild conditions, the estimators are shown to be strongly consistent. The convergence rate of the estimator for the unknown smooth function is obtained, and the estimator for the unknown parameter is shown to be asymptotically efficient and normally distributed. Simulation studies are carried out to investigate the performance of the proposed method.  相似文献   

6.
In this paper,we present a variable selection procedure by combining basis function approximations with penalized estimating equations for varying-coefficient models with missing response at random.With appropriate selection of the tuning parameters,we establish the consistency of the variable selection procedure and the optimal convergence rate of the regularized estimators.A simulation study is undertaken to assess the finite sample performance of the proposed variable selection procedure.  相似文献   

7.
Distribution estimation is very important in order to make statistical inference for parameters or its functions based on this distribution.In this work we propose an estimator of the distribution of some variable with non-smooth auxiliary information,for example,a symmetric distribution of this variable.A smoothing technique is employed to handle the non-differentiable function.Hence,a distribution can be estimated based on smoothed auxiliary information.Asymptotic properties of the distribution estimator are derived and analyzed.The distribution estimators based on our method are found to be significantly efficient than the corresponding estimators without these auxiliary information.Some simulation studies are conducted to illustrate the finite sample performance of the proposed estimators.  相似文献   

8.
Based on the data-cutoff method,we study quantile regression in linear models,where the noise process is of Ornstein-Uhlenbeck type with possible jumps.In single-level quantile regression,we allow the noise process to be heteroscedastic,while in composite quantile regression,we require that the noise process be homoscedastic so that the slopes are invariant across quantiles.Similar to the independent noise case,the proposed quantile estimators are root-n consistent and asymptotic normal.Furthermore,the adaptive least absolute shrinkage and selection operator(LASSO)is applied for the purpose of variable selection.As a result,the quantile estimators are consistent in variable selection,and the nonzero coefficient estimators enjoy the same asymptotic distribution as their counterparts under the true model.Extensive numerical simulations are conducted to evaluate the performance of the proposed approaches and foreign exchange rate data are analyzed for the illustration purpose.  相似文献   

9.
This article considers a semiparametric varying-coefficient partially linear regression model with current status data. The semiparametric varying-coefficient partially linear regression model which is a generalization of the partially linear regression model and varying-coefficient regression model that allows one to explore the possibly nonlinear effect of a certain covariate on the response variable. A Sieve maximum likelihood estimation method is proposed and the asymptotic properties of the proposed estimators are discussed. Under some mild conditions, the estimators are shown to be strongly consistent. The convergence rate of the estimator for the unknown smooth function is obtained and the estimator for the unknown parameter is shown to be asymptotically efficient and normally distributed. Simulation studies are conducted to examine the small-sample properties of the proposed estimates and a real dataset is used to illustrate our approach.  相似文献   

10.
Time- and state-domain methods are two common approaches for nonparametrically estimating the volatility of financial assets. Economic conditions vary over time in real financial market. It is reasonable to expect that volatility depends on both time and price level for a given state variable. Recently, Fan, et al (2007) proposed the idea of dynamically integrated method in both time-and state domain. This idea has become an interesting topic in the estimation of volatility. In this paper, our purpose is to discuss the integrated method in the estimation of volatility. Simulations are conducted to demonstrate that the newly integrated method outperforms some old ones, and the results of simulations demonstrate this fact. Furthermore, we establish its asymptotic properties.  相似文献   

11.
When the data has heavy tail feature or contains outliers, conventional variable selection methods based on penalized least squares or likelihood functions perform poorly. Based on Bayesian inference method, we study the Bayesian variable selection problem for median linear models. The Bayesian estimation method is proposed by using Bayesian model selection theory and Bayesian estimation method through selecting the Spike and Slab prior for regression coefficients, and the effective posterior Gibbs sampling procedure is also given. Extensive numerical simulations and Boston house price data analysis are used to illustrate the effectiveness of the proposed method.  相似文献   

12.
??When the data has heavy tail feature or contains outliers, conventional variable selection methods based on penalized least squares or likelihood functions perform poorly. Based on Bayesian inference method, we study the Bayesian variable selection problem for median linear models. The Bayesian estimation method is proposed by using Bayesian model selection theory and Bayesian estimation method through selecting the Spike and Slab prior for regression coefficients, and the effective posterior Gibbs sampling procedure is also given. Extensive numerical simulations and Boston house price data analysis are used to illustrate the effectiveness of the proposed method.  相似文献   

13.
部分线性单指标模型的复合分位数回归及变量选择   总被引:1,自引:0,他引:1  
本文提出复合最小化平均分位数损失估计方法 (composite minimizing average check loss estimation,CMACLE)用于实现部分线性单指标模型(partial linear single-index models,PLSIM)的复合分位数回归(composite quantile regression,CQR).首先基于高维核函数构造参数部分的复合分位数回归意义下的相合估计,在此相合估计的基础上,通过采用指标核函数进一步得到参数和非参数函数的可达最优收敛速度的估计,并建立所得估计的渐近正态性,比较PLSIM的CQR估计和最小平均方差估计(MAVE)的相对渐近效率.进一步地,本文提出CQR框架下PLSIM的变量选择方法,证明所提变量选择方法的oracle性质.随机模拟和实例分析验证了所提方法在有限样本时的表现,证实了所提方法的优良性.  相似文献   

14.

Variable selection for multivariate nonparametric regression models usually involves parameterized approximation for nonparametric functions in the objective function. However, this parameterized approximation often increases the number of parameters significantly, leading to the “curse of dimensionality” and inaccurate estimation. In this paper, we propose a novel and easily implemented approach to do variable selection in nonparametric models without parameterized approximation, enabling selection consistency to be achieved. The proposed method is applied to do variable selection for additive models. A two-stage procedure with selection and adaptive estimation is proposed, and the properties of this method are investigated. This two-stage algorithm is adaptive to the smoothness of the underlying components, and the estimation consistency can reach a parametric rate if the underlying model is really parametric. Simulation studies are conducted to examine the performance of the proposed method. Furthermore, a real data example is analyzed for illustration.

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15.
主要研究因变量存在缺失且协变量部分包含测量误差情形下,如何对变系数部分线性模型同时进行参数估计和变量选择.我们利用插补方法来处理缺失数据,并结合修正的profile最小二乘估计和SCAD惩罚对参数进行估计和变量选择.并且证明所得的估计具有渐近正态性和Oracle性质.通过数值模拟进一步研究所得估计的有限样本性质.  相似文献   

16.
Regularization methods, including Lasso, group Lasso, and SCAD, typically focus on selecting variables with strong effects while ignoring weak signals. This may result in biased prediction, especially when weak signals outnumber strong signals. This paper aims to incorporate weak signals in variable selection, estimation, and prediction. We propose a two‐stage procedure, consisting of variable selection and postselection estimation. The variable selection stage involves a covariance‐insured screening for detecting weak signals, whereas the postselection estimation stage involves a shrinkage estimator for jointly estimating strong and weak signals selected from the first stage. We term the proposed method as the covariance‐insured screening‐based postselection shrinkage estimator. We establish asymptotic properties for the proposed method and show, via simulations, that incorporating weak signals can improve estimation and prediction performance. We apply the proposed method to predict the annual gross domestic product rates based on various socioeconomic indicators for 82 countries.  相似文献   

17.
Partially linear model is a class of commonly used semiparametric models, this paper focus on variable selection and parameter estimation for partially linear models via adaptive LASSO method. Firstly, based on profile least squares and adaptive LASSO method, the adaptive LASSO estimator for partially linear models are constructed, and the selections of penalty parameter and bandwidth are discussed. Under some regular conditions, the consistency and asymptotic normality for the estimator are investigated, and it is proved that the adaptive LASSO estimator has the oracle properties. The proposed method can be easily implemented. Finally a Monte Carlo simulation study is conducted to assess the finite sample performance of the proposed variable selection procedure, results show the adaptive LASSO estimator behaves well.  相似文献   

18.
本文研究测量误差模型的自适应LASSO(least absolute shrinkage and selection operator)变量选择和系数估计问题.首先分别给出协变量有测量误差时的线性模型和部分线性模型自适应LASSO参数估计量,在一些正则条件下研究估计量的渐近性质,并且证明选择合适的调整参数,自适应LASSO参数估计量具有oracle性质.其次讨论估计的实现算法及惩罚参数和光滑参数的选择问题.最后通过模拟和一个实际数据分析研究了自适应LASSO变量选择方法的表现,结果表明,变量选择和参数估计效果良好.  相似文献   

19.
In high dimensional data modeling, Multivariate Adaptive Regression Splines (MARS) is a popular nonparametric regression technique used to define the nonlinear relationship between a response variable and the predictors with the help of splines. MARS uses piecewise linear functions for local fit and apply an adaptive procedure to select the number and location of breaking points (called knots). The function estimation is basically generated via a two-stepwise procedure: forward selection and backward elimination. In the first step, a large number of local fits is obtained by selecting large number of knots via a lack-of-fit criteria; and in the latter one, the least contributing local fits or knots are removed. In conventional adaptive spline procedure, knots are selected from a set of all distinct data points that makes the forward selection procedure computationally expensive and leads to high local variance. To avoid this drawback, it is possible to restrict the knot points to a subset of data points. In this context, a new method is proposed for knot selection which bases on a mapping approach like self organizing maps. By this method, less but more representative data points are become eligible to be used as knots for function estimation in forward step of MARS. The proposed method is applied to many simulated and real datasets, and the results show that it proposes a time efficient forward step for the knot selection and model estimation without degrading the model accuracy and prediction performance.  相似文献   

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