Hailin Sang

ASYMPTOTIC PROPERTIES OF SELF-NORMALIZED LINEAR PROCESSES WITH LONG MEMORY

In this paper we study the convergence to fractional Brownian motion for long memory time series having independent innovations with infinite second moment. For the sake of applications we derive the self-normalized version of this theorem. The study is motivated by models arising in economic applications where often the linear processes have long memory, and the innovations have heavy tails.

Uniform asymptotics for kernel density estimators with variable bandwidths

It is shown that the Hall, Hu and Marron [Hall, P., Hu, T., and Marron J.S. (1995), ‘Improved Variable Window Kernel Estimates of Probability Densities’, Annals of Statistics, 23, 1–10] modification of Abramsons [Abramson, I. (1982), ‘On Bandwidth Variation in Kernel Estimates – A Square-root Law’, Annals of Statistics, 10, 1217–1223] variable bandwidth kernel density estimator satisfies the optimal asymptotic properties for estimating densities with four uniformly continuous derivatives, uniformly on bounded sets where the preliminary estimator of the density is bounded away from zero.

On kernel estimators of density for reversible Markov chains

In this paper we investigate the kernel estimator of the density for a stationary reversible Markov chain. The proofs are based on a new central limit theorem for a triangular array of reversible Markov chains obtained under conditions imposed to covariances, which has interest in itself.

The Self-normalized Asymptotic Results for Linear Processes

The linear process is a tool for studying stationary time series. One can have a better understanding of many important time series by studying the corresponding linear processes. The strength of dependence and the tail properties of time series built upon linear processes can be expressed in terms of the linear process itself through the innovations and their weights. In this paper we survey recent developments on some asymptotics of linear processes. These asymptotics include central limit theorem, functional central limit theorem and their self-normalized forms.

On the estimation of smooth densities by strict probability densities at optimal rates in sup-norm

It is shown that the variable bandwidth density estimator proposed by McKay (1993a and b) following earlier findings by Abramson (1982) approximates density functions in

Exact moderate and large deviations for linear random fields

C^4(\mathbb R^d)

Adjusting for Misclassification: A Three-Phase Sampling Approach

at the minimax rate in the supremum norm over bounded sets where the preliminary density estimates on which they are based are bounded away from zero. A somewhat more complicated estimator proposed by Jones McKay and Hu (1994) to approximate densities in

Exact Moderate and Large Deviations for Linear Processes

C^6(\mathbb R)

Central Limit Theorem for Linear Processes with Infinite Variance

is also shown to attain minimax rates in sup norm over the same kind of sets. These estimators are strict probability densities.

Memory properties of transformations of linear processes

By extending the methods in Peligrad et al. (2014a, b), we establish exact moderate and large deviation asymptotics for linear random fields with independent innovations. These results are useful for studying nonparametric regression with random field errors and strong limit theorems.