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Estimation in a partially linear single-index model with missing response variables and error-prone covariates

JOURNAL OF INEQUALITIES AND APPLICATIONS 2016年第1期2016卷 11-11页

作者： Qi, Xin Wang, De-Hui Jilin Univ Coll Math Changchun 130012 Peoples R China Jilin Univ Zhuhai Coll Zhuhai 519000 Peoples R China

In this paper, the authors study the partially linear single-index model when the covariate X is measured with additive error and the response variable Y is sometimes missing. Based on the least-squared technique, an imputation method is proposed to estimate the regression coefficients, single-index coefficients, and the nonparametric function, respectively. Thereafter, asymptotical normalities of the corresponding estimators are proved. A simulation experiment and an application to a diabetes study are used to illustrate our proposed method.

关键词： partially linear single-index model least-squared local linear regression imputation estimator

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Testing for Change Points in Partially linear Models

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Acta Mathematicae Applicatae Sinica 2015年第4期31卷 879-892页

作者： Li-wen ZHANG Zhong-yi ZHU School of Economics Shanghai University Department of Statistics School of ManagementFudan University

In this paper we provide a method to test the existence of the change points in the nonparametric regression function of partially linear models with conditional heteroscedastic variance. We propose the test statistic and establish its asymptotic properties under some regular conditions. Some simulation studies are given to investigate the performance of the proposed method in finite samples. Finally, the proposed method is applied to a real data for illustration.

关键词： change point partially linear model heteroscedastic variance local linear regression bandwidthselection

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local linear Estimation for Spatiotemporal Models Based on Least Absolute Deviation

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2015年第7期44卷 1508-1522页

作者： Wang, Hongxia Lin, Jinguan Wang, Jinde Southeast Univ Dept Math Nanjing 211189 Jiangsu Peoples R China Nanjing Univ Dept Math Nanjing 210008 Jiangsu Peoples R China

When the data contain outliers or come from population with heavy-tailed distributions, which appear very often in spatiotemporal data, the estimation methods based on least-squares (L-2) method will not perform well. More robust estimation methods are required. In this article, we propose the local linear estimation for spatiotemporal models based on least absolute deviation (L-1) and drive the asymptotic distributions of the L-1-estimators under some mild conditions imposed on the spatiotemporal process. The simulation results for two examples, with outliers and heavy-tailed distribution, respectively, show that the L-1-estimators perform better than the L-2-estimators.

关键词： Least absolute deviation estimation Least-squares method local linear regression Mixing condition

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Nonparametric estimation of fixed effects panel data varying coefficient models

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JOURNAL OF MULTIVARIATE ANALYSIS 2015年 133卷 95-122页

作者： Rodriguez-Poo, Juan M. Soberon, Alexandra Univ Cantabria E-39005 Santander Spain

In this paper, we consider the nonparametric estimation of a varying coefficient fixed effect panel data model. The estimator is based in a within (un-smoothed) transformation of the regression model and then a local linear regression is applied to estimate the unknown varying coefficient functions. It turns out that the standard use of this technique produces a non-negligible asymptotic bias. In order to avoid it, a high dimensional kernel weight is introduced in the estimation procedure. As a consequence, the asymptotic bias is removed but the variance is enlarged, and therefore the estimator shows a very slow rate of convergence. In order to achieve the optimal rate, we propose a one-step backfitting algorithm. The resulting two-step estimator is shown to be asymptotically normal and its rate of convergence is optimal within its class of smoothness functions. It is also oracle efficient. Further, this estimator is compared both theoretically and by Monte-Carlo simulation against other estimators that are based in a within (smoothed) transformation of the regression model. More precisely the profile least-squares estimator proposed in this context in Sun et al. (2009). It turns out that the smoothness in the transformation enlarges the bias and it makes the estimator more difficult to analyze from the statistical point of view. However, the first step estimator, as expected, shows a bad performance when compared against both the two step backfitting algorithm and the profile least-squares estimator. (C) 2014 Elsevier Inc. All rights reserved.

关键词： Varying coefficient models Fixed effects Panel data local linear regression Oracle efficient estimator Within estimator Profile least squares estimator

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Guided Censored regression

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SCANDINAVIAN JOURNAL OF STATISTICS 2015年第1期42卷 214-233页

作者： Talamakrouni, Majda El Ghouch, Anouar van Keilegom, Ingrid Catholic Univ Louvain Inst Stat Biostat & Sci Actuarielles ISBA B-1348 Louvain Belgium

Parametrically guided non-parametric regression is an appealing method that can reduce the bias of a non-parametric regression function estimator without increasing the variance. In this paper, we adapt this method to the censored data case using an unbiased transformation of the data and a local linear fit. The asymptotic properties of the proposed estimator are established, and its performance is evaluated via finite sample simulations.

关键词： least squares estimation local linear regression non-parametric regression parametric regression right censoring synthetic data U-statistics

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Differencing techniques in semi-parametric panel data varying coefficient models with fixed effects: a Monte Carlo study

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COMPUTATIONAL STATISTICS 2015年第3期30卷 885-906页

作者： Rodriguez-Poo, Juan M. Soberon, Alexandra Univ Cantabria E-39005 Santander Spain

Recently, some new techniques have been proposed for the estimation of semi-parametric fixed effects varying coefficient panel data models. These new techniques fall within the class of the so-called differencing estimators. In particular, we consider first-differences and within local linear regression estimators. Analyzing their asymptotic properties it turns out that, keeping the same order of magnitude for the bias term, these estimators exhibit different asymptotic bounds for the variance. In both cases, the consequences are suboptimal non-parametric rates of convergence. In order to solve this problem, by exploiting the additive structure of this model, a one-step backfitting algorithm is proposed. Under fairly general conditions, it turns out that the resulting estimators show optimal rates of convergence and exhibit the oracle efficiency property. Since both estimators are asymptotically equivalent, it is of interest to analyze their behavior in small sample sizes. In a fully parametric context, it is well-known that, under strict exogeneity assumptions the performance of both first-differences and within estimators is going to depend on the stochastic structure of the idiosyncratic random errors. However, in the non-parametric setting, apart from the previous issues other factors such as dimensionality or sample size are of great interest. In particular, we would be interested in learning about their relative average mean square error under different scenarios. The simulation results basically confirm the theoretical findings for both local linear regression and one-step backfitting estimators. However, we have found out that within estimators are rather sensitive to the size of number of time observations.

关键词： Semi-parametric varying coefficients model Panel data local linear regression One-step backfitting algorithm First-differences estimator Within estimator Monte Carlo simulations

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A partially linear single-index transformation model and its nonparametric estimation

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CANADIAN JOURNAL OF STATISTICS-REVUE CANADIENNE DE STATISTIQUE 2015年第1期43卷 97-117页

作者： Ding, Xiaobo Zhou, Xiao-Hua Wang, Qihua Chinese Acad Sci Acad Math & Syst Sci Beijing Peoples R China Vet Affairs Puget Sound Hlth Care Syst HSR& Ctr Excellence Seattle WA 98108 USA Univ Washington Dept Biostat Seattle WA 98195 USA Shenzhen Univ Inst Stat Sci Shenzhen Guangdong Peoples R China

In this paper, we consider the nonparametric estimation of the partially linear single-index transformation model, where the transformation function, single-index function and error distribution are all completely unknown. We first use the minimum average variance estimation method to estimate the regression coefficients, and then propose a new incorporated local linear regression estimator for the derivative function of the single-index function. Accordingly by integration we can obtain the estimator of the single-index function. Finally we propose a constrained least square estimator for the transformation function, where basis function approximation is employed and cross validation method is proposed to select suitable sets of basis functions. Asymptotical properties of the estimators are established. Simulation studies show that our proposed estimators work well. A real-world data analysis of total health care charges was used to illustrate the proposed procedure. The Canadian Journal of Statistics 43: 97-117;2015 (c) 2015 Statistical Society of Canada Resume Les auteurs traitent de l'estimation non parametrique du modele de transformation partiellement lineaire a un indice dans le cas oU la transformation, la fonction d'indice et la distribution de l'erreur sont toutes completement inconnues. Ils estiment d'abord les coefficients de regression par la methode de la variance moyenne minimale, puis ils proposent un nouvel estimateur local de regression lineaire pour la derivee de la fonction d'indice, menant a l'estimation de cette fonction par integration. Finalement, ils proposent un estimateur aux moindres carres avec contraintes pour la fonction de transformation dont une approximation est effectuee a l'aide de fonctions de base, elles-memes selectionnees par une procedure de validation croisee. Les auteurs etablissent les proprietes asymptotiques de leurs estimateurs et montrent a l'aide de simulations que ceux-ci donnent de bons resultats. Ils illustrent ega

关键词： Basis function Cross validation linear inequality restriction local linear regression minimum average variance estimation

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Nonlinearities in the Slovenian apple price transmission

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BRITISH FOOD JOURNAL 2015年第1期117卷 461-478页

作者： Hassouneh, Islam Serra, Teresa Bojnec, Stefan Palestine Polytech Univ Coll Adm Sci & Informat Hebron Israel UPC IRTA CREDA Barcelona Spain Univ Primorska Fac Management Koper Slovenia

Purpose - The purpose of this paper is to assess price linkages and patterns of transmission among producer and consumer markets for apple in Slovenia. Design/methodology/approach - Non-linear error correction models are applied. Non-linearities are allowed by means of threshold and multivariate local linear regression estimation techniques. Monthly prices over the period 2000-2011 are used in the empirical application. Findings - Both techniques provide evidence of non-linearities in price adjustments. Findings suggest that producer and consumer prices tend to increase rather than decrease. Results also indicate that parametric threshold approaches may have difficulties in adequately representing price behavior dynamics. Originality/value - The main contribution of this work to the literature relies on the fact that this is the first attempt to assess vertical price transmission in the apple sector in Central and Eastern European Country markets. Further, it is the first attempt to use multivariate local linear regression techniques in this context.

关键词： Slovenia local linear regression Price transmission Threshold model

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Regularized local linear Model with Core Neighbors for Reflectance Estimation

Regularized Local Linear Model with Core Neighbors for Refle...

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IEEE International Conference on Systems, Man, and Cybernetics (SMC)

作者： Zhang, Wei-Feng Lu, De-Jun South China Agr Univ Coll Math & Informat 483 Wushan Rd Guangzhou 510642 Guangdong Peoples R China

ISBN: (纸本)9781479986965

Regularized local linear model has been shown to be an effective approach for reflectance estimation. This approach estimates the reflectance of each test point by the linear combination of only its neighbors. The choice of neighbors is of crucial importance to achieve high estimation accuracy. We propose a principal components analysis based neighborhood selection method to reduce model bias. The idea is to find a subset of the test point's nearest neighbors, which we term core neighbors, that have the least reconstruction errors by retaining only the main principal components. Experimental results are provided to validate the effectiveness of the proposed approach.

关键词： Reflectance estimation local linear regression Nearest neighbors Principal component analysis

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Oil prices, US stock return, and the dependence between their quantiles

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JOURNAL OF BANKING & FINANCE 2015年 55卷 1-8页

作者： Sim, Nicholas Zhou, Hongtao Univ Adelaide Sch Econ Adelaide SA 5005 Australia Shandong Univ Ctr Econ Res Jinan 250100 Shandong Peoples R China

In this article, we examine the relationship between oil prices and US equities by proposing a novel quantile-on-quantile (QQ) approach to construct estimates of the effect that the quantiles of oil price shocks have on the quantiles of the US stock return. This approach captures the dependence between the distributions of oil price shocks and the US stock return and uncovers two nuance features in the oil stock relationship. First, large, negative oil price shocks (i.e. low oil price shock quantiles) can affect US equities positively when the US market is performing well (i.e. at high US return quantiles). Second, while negative oil price shocks could affect the US stock market, the influence of positive oil price shocks is weak, which suggests that the relationship between oil prices on the US equities is asymmetric. (C) 2015 Elsevier B.V. All rights reserved.

关键词： Oil prices Stock return local linear regression Quantile regression

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