Author: Yichen Gao
Publisher:
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Category :
Languages : en
Pages :

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Author: Jia Chen
Publisher:
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Category : Asymptotic distribution (Probability theory)
Languages : en
Pages :

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Estimation theory in a nonstationary environment has been very popular in recent years. Existing studies focus on nonstationarity in parametric linear, parametric nonlinear and nonparametric nonlinear models. In this paper, we consider a partially linear model of the form Yt = X t +g(Vt)+ t, t = 1, · · ·, n, where {Vt} is a sequence of -null recurrent Markov chains, {Xt} is a sequence of either strictly stationary or nonstationary regressors and { t} is a stationary sequence. We propose to estimate both a and g(·) semiparametrically. We then show that the proposed estimator of is still asymptotically normal with the same rate as for the case of stationary time series. We also establish the asymptotic normality for the nonparametric estimator of the function g(·) and the uniform consistency of the nonparametric estimator. The simulated example is given to show that our theory and method work well in practice.

Author: Jeffrey Racine
Publisher: Oxford University Press
ISBN: 0199857954
Category : Business & Economics
Languages : en
Pages : 562

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This volume, edited by Jeffrey Racine, Liangjun Su, and Aman Ullah, contains the latest research on nonparametric and semiparametric econometrics and statistics. These data-driven models seek to replace the classical parametric models of the past, which were rigid and often linear. Chapters by leading international econometricians and statisticians highlight the interface between econometrics and statistical methods for nonparametric and semiparametric procedures. They provide a balanced view of new developments in the modeling of cross-section, time series, panel, and spatial data. Topics of the volume include: the methodology of semiparametric models and special regressor methods; inverse, ill-posed, and well-posed problems; methodologies related to additive models; sieve regression, nonparametric and semiparametric regression, and the true error of competing approximate models; support vector machines and their modeling of default probability; series estimation of stochastic processes and their application in Econometrics; identification, estimation, and specification problems in semilinear time series models; nonparametric and semiparametric techniques applied to nonstationary or near nonstationary variables; the estimation of a set of regression equations; and a new approach to the analysis of nonparametric models with exogenous treatment assignment.

Author: Bo Kai
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Category :
Languages : en
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In this dissertation, several new statistical procedures in nonparametric and semiparametric models are proposed. The concerns of the research are efficiency, robustness and sparsity. In Chapter 3, we propose complete composite quantile regression (CQR) procedures for estimating both the regression function and its derivatives in fully nonparametric regression models by using local smoothing techniques. The CQR estimator was recently proposed by Zou and Yuan (2008) for estimating the regression coefficients in the classical linear regression model. The asymptotic theory of the proposed estimator was established. We show that, compared with the classical local linear least squares estimator, the new method can significantly improve the estimation efficiency of the local linear least squares estimator for commonly used non-normal error distributions, and at the same time, the loss in efficiency is at most 8.01% in the worst case scenario. In Chapter 4, we further consider semiparametric models. The complexity of semiparametric models poses new challenges to parametric inferences and model selection that frequently arise from real applications. We propose new robust inference procedures for the semiparametric varying-coefficient partially linear model. We first study a quantile regression estimate for the nonparametric varying-coefficient functions and the parametric regression coefficients. To improve efficiency, we further develop a composite quantile regression procedure for both parametric and nonparametric components. To achieve sparsity, we develop a variable selection procedure for this model to select significant variables. We study the sampling properties of the resulting quantile regression estimate and composite quantile regression estimate. With proper choices of penalty functions and regularization parameters, we show the proposed variable selection procedure possesses the oracle property in the terminology of Fan and Li (2001). In Chapter 5, we propose a novel estimation procedure for varying coefficient models based on local ranks. By allowing the regression coefficients to change with certain covariates, the class of varying coefficient models offers a flexible semiparametric approach to modeling nonlinearity and interactions between covariates. Varying coefficient models are useful nonparametric regression models and have been well studied in the literature. However, the performance of existing procedures can be adversely influenced by outliers. The new procedure provides a highly efficient and robust alternative to the local linear least squares method and can be conveniently implemented using existing R software packages. We study the sample properties of the proposed procedure and establish the asymptotic normality of the resulting estimate. We also derive the asymptotic relative efficiency of the proposed local rank estimate to the local linear estimate for the varying coefficient model. The gain of the local rank regression estimate over the local linear regression estimate can be substantial. We further develop nonparametric inferences for the rank-based method. Monte Carlo simulations are conducted to access the finite sample performance of the proposed estimation procedure. The simulation results are promising and consistent with our theoretical findings. All the proposed procedures are supported by intensive finite sample simulation studies and most are illustrated with real data examples.

Author: Haiqiang Chen
Publisher:
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Category :
Languages : en
Pages :

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Author: Jeffrey Racine
Publisher: Oxford University Press
ISBN: 0199857946
Category : Business & Economics
Languages : en
Pages : 562

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Book Description
This volume, edited by Jeffrey Racine, Liangjun Su, and Aman Ullah, contains the latest research on nonparametric and semiparametric econometrics and statistics. Chapters by leading international econometricians and statisticians highlight the interface between econometrics and statistical methods for nonparametric and semiparametric procedures.

Author: Yiguo Sun
Publisher:
ISBN:
Category :
Languages : en
Pages :

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Author: Degao Li
Publisher:
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Category :
Languages : en
Pages : 0

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This paper is concerned with the regression coefficient and autoregressive order shrinkage and selection via the smoothly clipped absolute deviation (SCAD) penalty for a partially linear model with time-series errors. By combining the profile semi-parametric least squares method and SCAD penalty technique, a new penalized estimation for the regression and autoregressive parameters in the model is proposed. We show that the asymptotic property of the resultant estimator is the same as if the order of autoregressive error structure and non-zero regression coefficients are known in advance, thus achieving the oracle property in the sense of Fan and Li (2001). In addition, based on a prewhitening technique, we construct a two-stage local linear estimator (TSLLE) for the non-parametric component. It is shown that the TSLLE is more asymtotically efficient than the one that ignores the autoregressive time-series error structure. Some simulation studies are conducted to illustrate the finite sample performance of the proposed procedure. An example of application on electricity usage data is also illustrated.

Author: Sittisak Leelahanon
Publisher:
ISBN:
Category :
Languages : en
Pages : 134

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Author: Jingxin Zhao
Publisher:
ISBN:
Category : Estimation theory
Languages : en
Pages : 118

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The semi-parametric model enjoys a relatively flexible structure and keeps some of the simplicity in the statistical analysis. Hence, there are abundance discussions on semi-parametric models in the literature. The concept of partial consistency was firstly brought up in Neyman and Scott (1948). It was said the in cases where infinite parameters are involved, consistent estimators are always attainable for those "structural" parameters. The "structural' parameters are finite and govern infinite samples. Since the nonparametric model can be regarded as a parametric model with infinite parameters, then the semi-parametric model can be easily transformed into a infinite-parametric model with some "structural" parameters. Therefore, based on this idea, we develop several new methods for the estimating and model checking problems in semi-parametric models. The implementation of applying partial consistency is through the method "local average". We consider the nonparametric part as piecewise constant so that infinite parameters are created. The "structural" parameters shall be the parametric part, the model residual variance and so on. Due to the partial consistency phenomena, classical statistic tools can then be applied to obtain consistent estimators for those "structural" parameters. Furthermore, we can take advantage of the rest of parameters to estimate the nonparametric part. In this thesis, we take the varying coefficient model as the example. The estimation of the functional coefficient is discussed and relative model checking methods are presented. The proposed new methods, no matter for the estimation or the test, have remarkably lessened the computation complexity. At the same time, the estimators and the tests get satisfactory asymptotic statistical properties. The simulations we conducted for the new methods also support the asymptotic results, giving a relatively efficient and accurate performance. What's more, the local average method is easy to understand and can be flexibly applied to other type of models. Further developments could be done on this potential method. In Chapter 2, we introduce a local average method to estimate the functional coefficients in the varying coefficient model. As a typical semi-parametric model, the varying coefficient model is widely applied in many areas. The varying coefficient model could be seen as a more flexible version of classical linear model, while it explains well when the regression coefficients do not stay constant. In addition, we extend this local average method to the semi-varying coefficient model, which consists of a linear part and a varying coefficient part. The procedures of the estimations are developed, and their statistical properties are investigated. Plenty of simulations and a real data application are conducted to study the performance of the proposed method. Chapter 3 is about the local average method in variance estimation. Variance estimation is a fundamental problem in statistical modeling and plays an important role in the inferences in model selection and estimation. In this chapter, we have discussed the problem in several nonparametric and semi-parametric models. The proposed method has the advantages of avoiding the estimation of the nonparametric function and reducing the computational cost, and can be easily extended to more complex settings. Asymptotic normality is established for the proposed local average estimators. Numerical simulations and a real data analysis are presented to illustrate the finite sample performance of the proposed method. Naturally, we move to the model checking problem in Chapter 4, still taking varying coefficient models as an example. One important and frequently asked question is whether an estimated coefficient is significant or really "varying". In the literature, the relative hypothesis tests usually require fitting the whole model, including the nuisance coefficients. Consequently, the estimation procedure could be very compute-intensive and time-consuming. Thus, we bring up several tests which can avoid unnecessary functions estimation. The proposed tests are very easy to implement and their asymptotic distributions under null hypothesis have been deduced. Simulations are also studied to show the properties of the tests.