arXiv subjects

Zhibiao Zhao

Publications and source records attributed to Zhibiao Zhao.

5 recordsLinked to original sources

arXiv2014

Asymptotics of nonparametric L-1 regression models with dependent data

We investigate asymptotic properties of least-absolute-deviation or median quantile estimates of the location and scale functions in nonparametric regression models with dependent data from multiple subjects. Under a general dependence structure that allows for longitudinal data and some spatially correlated data, we establish uniform Bahadur representations for the proposed median quantile estimates. The obtained Bahadur representations provide deep insights into the asymptotic behavior of the estimates. Our main theoretical development is based on studying the modulus of continuity of kernel weighted empirical process through a coupling argument. Progesterone data is used for an illustration.

math.ST↗

arXiv2013

Inference for modulated stationary processes

We study statistical inferences for a class of modulated stationary processes with time-dependent variances. Due to non-stationarity and the large number of unknown parameters, existing methods for stationary, or locally stationary, time series are not applicable. Based on a self-normalization technique, we address several inference problems, including a self-normalized central limit theorem, a self-normalized cumulative sum test for the change-point problem, a long-run variance estimation through blockwise self-normalization, and a self-normalization-based wild bootstrap. Monte Carlo simulation studies show that the proposed self-normalization-based methods outperform stationarity-based alternatives. We demonstrate the proposed methodology using two real data sets: annual mean precipitation rates in Seoul from 1771-2000, and quarterly U.S. Gross National Product growth rates from 1947-2002.

math.ST↗

arXiv2012

Profile control charts based on nonparametric $L$-1 regression methods

Classical statistical process control often relies on univariate characteristics. In many contemporary applications, however, the quality of products must be characterized by some functional relation between a response variable and its explanatory variables. Monitoring such functional profiles has been a rapidly growing field due to increasing demands. This paper develops a novel nonparametric $L$-1 location-scale model to screen the shapes of profiles. The model is built on three basic elements: location shifts, local shape distortions, and overall shape deviations, which are quantified by three individual metrics. The proposed approach is applied to the previously analyzed vertical density profile data, leading to some interesting insights.

stat.AP↗

arXiv2008

Confidence bands in nonparametric time series regression

We consider nonparametric estimation of mean regression and conditional variance (or volatility) functions in nonlinear stochastic regression models. Simultaneous confidence bands are constructed and the coverage probabilities are shown to be asymptotically correct. The imposed dependence structure allows applications in many linear and nonlinear auto-regressive processes. The results are applied to the S&P 500 Index data.

math.ST↗

arXiv2008

Parametric and nonparametric models and methods in financial econometrics

Financial econometrics has become an increasingly popular research field. In this paper we review a few parametric and nonparametric models and methods used in this area. After introducing several widely used continuous-time and discrete-time models, we study in detail dependence structures of discrete samples, including Markovian property, hidden Markovian structure, contaminated observations, and random samples. We then discuss several popular parametric and nonparametric estimation methods. To avoid model mis-specification, model validation plays a key role in financial modeling. We discuss several model validation techniques, including pseudo-likelihood ratio test, nonparametric curve regression based test, residuals based test, generalized likelihood ratio test, simultaneous confidence band construction, and density based test. Finally, we briefly touch on tools for studying large sample properties.

q-fin.ST↗