Regression quantiles for time series

This is the publisher's version, also available electronically from http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=92739&fulltextType=RA&fileId=S0266466602181096.In this paper we study nonparametric estimation of regression quantiles for time series data by inverting a weighted Nadaraya–Watson (WNW) estimator of conditional distribution function, which was first used by Hall, Wolff, and Yao (1999, Journal of the American Statistical Association 94, 154–163). First, under some regularity conditions, we establish the asymptotic normality and weak consistency of the WNW conditional distribution estimator for [alpha]-mixing time series at both boundary and interior points, and we show that the WNW conditional distribution estimator not only preserves the bias, variance, and, more important, automatic good boundary behavior properties of local linear “double-kernel” estimators introduced by Yu and Jones (1998, Journal of the American Statistical Association 93, 228–237), but also has the additional advantage of always being a distribution itself. Second, it is shown that under some regularity conditions, the WNW conditional quantile estimator is weakly consistent and normally distributed and that it inherits all good properties from the WNW conditional distribution estimator. A small simulation study is carried out to illustrate the performance of the estimates, and a real example is also used to demonstrate the methodology

Nonparametric estimation of varying coefficient dynamic panel models

This is the publisher's version, also available electronically from http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=2059888&fileId=S0266466608080523.We suggest using a class of semiparametric dynamic panel data models to capture individual variations in panel data. The model assumes linearity in some continuous/discrete variables that can be exogenous/endogenous and allows for nonlinearity in other weakly exogenous variables. We propose a nonparametric generalized method of moments (NPGMM) procedure to estimate the functional coefficients, and we establish the consistency and asymptotic normality of the resulting estimators

Nonparametric estimation of additive nonlinear ARX time series: Local Linear Fitting and Projections

This is the publisher's version, also available electronically from http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=55027&fulltextType=RA&fileId=S0266466600164011.We consider the estimation and identification of the components (endogenous and exogenous) of additive nonlinear ARX time series models. We employ a local polynomial fitting scheme coupled with projections. We establish the weak consistency (with rates) and the asymptotic normality of the projection estimates of the additive components. Expressions for the asymptotic bias and variance are given

Kaplan–Meier Estimator under Association

AbstractConsider a long term study, where a series of possibly censored failure times is observed. Suppose the failure times have a common marginal distribution functionF, but they exhibit a mode of dependence characterized by positive or negative association. Under suitable regularity conditions, it is shown that the Kaplan–Meier estimatorFnofFis uniformly strongly consistent; rates for the convergence are also provided. Similar results are established for the empirical cumulative hazard rate function involved. Furthermore, a stochastic process generated byFnis shown to be weakly convergent to an appropriate Gaussian process. Finally, an estimator of the limiting variance of the Kaplan–Meier estimator is proposed and it is shown to be weakly convergent

Functional Coefficient Models for Economic and Financial Data

This paper gives a selective overview on the functional coefficient models with their particular applications in economics and finance. Functional coefficient models are very useful analytic tools to explore complex dynamic structures and evolutions for functional data in various areas, particularly in economics and finance. They are natural generalizations of classical parametric models with good interpretability by allowing coefficients to be governed by some variables or to change over time, and also they have abilities to capture nonlinearity and heteroscedasticity. Furthermore, they can be regarded as one of dimensionality reduction methods for functional data exploration and have nice interpretability. Due to their great properties, functional coefficient models have had many methodological and theoretical developments and they have become very popular in various applications

The examination of residual plots

This is the publisher's version, also available electronically from http://www3.stat.sinica.edu.tw/statistica/j8n2/j8n29/j8n29.htm.Linear and squared residual plots are proposed to assess nonlinearity and heteroscedasticity in regression diagnostics. It is shown that linear residual plots are useful for diagnosing nonlinearity and squared residual plots are powerful for detecting nonconstant variance. A paradigm for the graphical interpretation of residual plots is presented

Denoised least squares estimators: An application to estimating advertising effectiveness

This is the publisher's version, also available electronically from http://www3.stat.sinica.edu.tw/statistica/j10n4/j10n412/j10n412.htm.It is known in marketing science that an advertiser under- or overspends millions of dollars on advertising because the estimation of advertising effectiveness is biased. This bias is induced by measurement noise in advertising variables, such as awareness and television rating points, which are provided by commercial market research firms based on small-sample surveys of consumers. In this paper, we propose a denoised regression approach to deal with the problem of noisy variables. We show that denoised least squares estimators are consistent. Simulation results indicate that the denoised regression approach outperforms the classical regression approach. A marketing example is presented to illustrate the use of denoised least squares estimators

Semiparametric Quantile Regression Estimation in Dynamic Models with Partially Varying Coefficients

We study quantile regression estimation for dynamic models with partially varying coefficients so that the values of some coefficients may be functions of informative covariates. Estimation of both parametric and nonparametric functional coefficients are proposed. In particular, we propose a three stage semiparametric procedure. Both consistency and asymptotic normality of the proposed estimators are derived. We demonstrate that the parametric estimators are root-n consistent and the estimation of the functional coefficients is oracle. In addition, efficiency of parameter estimation is discussed and a simple efficient estimator is proposed. A simple and easily implemented test for the hypothesis of varying-coefficient is proposed. A Monte Carlo experiment is conducted to evaluate the performance of the proposed estimators.  This paper is forthcoming in Journal of Econometrics