AN ADAPTIVE COMPOSITE QUANTILE APPROACH TO DIMENSION REDUCTION

Sufficient dimension reduction [Li 1991] has long been a prominent issue in multivariate nonparametric regression analysis. To uncover the central dimension reduction space, we propose in this paper an adaptive composite quantile approach. Compared to existing methods, (1) it requires minimal assumptions and is capable of revealing all dimension reduction directions; (2) it is robust against outliers and (3) it is structure-adaptive, thus more efficient. Asymptotic results are proved and numerical examples are provided, including a real data analysis

Uniform Bahadur Representation for Local Polynomial Estimates of M-Regression and Its Application to The Additive Model

We use local polynomial fitting to estimate the nonparametric M-regression function for strongly mixing stationary processes $\{(Y_{i},\underline{X}_{i})\}$. We establish a strong uniform consistency rate for the Bahadur representation of estimators of the regression function and its derivatives. These results are fundamental for statistical inference and for applications that involve plugging in such estimators into other functionals where some control over higher order terms are required. We apply our results to the estimation of an additive M-regression model.Comment: 40 page

Global Bahadur representation for nonparametric censored regression quantiles and its applications

This paper is concerned with the nonparametric estimation of regression quantiles where the response variable is randomly censored. Using results on the strong uniform convergence of U-processes, we derive a global Bahadur representation for the weighted local polynomial estimators, which is sufficiently accurate for many further theoretical analyses including inference. We consider two applications in detail: estimation of the average derivative, and estimation of the component functions in additive quantile regression models.

Uniform Bahadur Representation for LocalPolynomial Estimates of M-Regressionand Its Application to The Additive Model

We use local polynomial fitting to estimate the nonparametric M-regression function for strongly mixing stationary processes {(Y_i,?X_i ) } . We establish a strong uniform consistency rate for the Bahadur representation of estimators of the regression function and its derivatives. These results are fundamental for statistical inference and for applications that involve plugging such estimators into other functional where some control over higher order terms are required. We apply our results to the estimation of an additive M-regression model.

IRCI Free Range Reconstruction for SAR Imaging with Arbitrary Length OFDM Pulse

Our previously proposed OFDM with sufficient cyclic prefix (CP) synthetic aperture radar (SAR) imaging algorithm is inter-range-cell interference (IRCI) free and achieves ideally zero range sidelobes for range reconstruction. In this OFDM SAR imaging algorithm, the minimum required CP length is almost equal to the number of range cells in a swath, while the number of subcarriers of an OFDM signal needs to be more than the CP length. This makes the length of a transmitted OFDM sequence at least almost twice of the number of range cells in a swath and for a wide swath imaging, the transmitted OFDM pulse length becomes long, which may cause problems in some radar applications. In this paper, we propose a CP based OFDM SAR imaging with arbitrary pulse length, which has IRCI free range reconstruction and its pulse length is independent of a swath width. We then present a novel design method for our proposed arbitrary length OFDM pulses. Simulation results are presented to illustrate the performances of the OFDM pulse design and the arbitrary pulse length CP based OFDM SAR imaging.Comment: 29 pages, 10 figures, regular pape

Quantile Estimation of A general Single-Index Model

The single-index model is one of the most popular semiparametric models in Econometrics. In this paper, we define a quantile regression single-index model, which includes the single-index structure for conditional mean and for conditional variance.Comment: 32page