Extrapolation‐based Bandwidth Selectors: A Review and Comparative Study with Discussion on Bivariate Applications

Cross‐validation is a widely used tool in selecting the smoothing parameter in a non‐parametric procedure. However, it suffers from large sampling variation and tends to overfit the data set. Many attempts have been made to reduce the variance of cross‐validation. This paper focuses on two recent proposals of extrapolation‐based cross‐validation bandwidth selectors: indirect cross‐validation and subsampling‐extrapolation technique. In univariate case, we notice that using a fixed value parameter surrogate for indirect cross‐validation works poorly when the true density is hard to estimate, while the subsampling‐extrapolation technique is more robust to non‐normality. We investigate whether a hybrid bandwidth selector could benefit from the advantages of both approaches and compare the performance of different extrapolation‐based bandwidth selectors through simulation studies, real data analyses and large sample theory. A discussion on their extension to bivariate case is also presented.     

Integrated Covariance Estimation using High-frequency Data in the Presence of Noise

We analyze the effects of nonsynchronicity and market microstructurenoise on realized covariance type estimators. Hayashi and Yoshida(2005) propose a simple estimator that resolves the problemof nonsynchronicity and is unbiased and consistent for the integratedcovariance in the absence of noise. When noise is present, however,we find that this estimator is biased, and show how the biascan be corrected for. Ultimately, we propose a subsampling versionof the bias-corrected estimator which improves its efficiency.Empirically, we find that the usual assumption of a martingaleprice process plus an independently and identically distributed(i.i.d.) noise does not describe the dynamics of the observedprice process across stocks, which confirms the practical relevanceof our general noise specification and the estimation techniqueswe propose. Finally, a simulation experiment is carried outto complement the theoretical results.     

Subsampling inference for the mean in the heavy-tailed case

In this article, asymptotic inference for the mean of i.i.d. observations in the context of heavy-tailed distributions is discussed. While both the standard asymptotic method based on the normal approximation and Efron's bootstrap are inconsistent when the underlying distribution does not possess a second moment, we propose two approaches based on the subsampling idea of Politis and Romano (1994) which will give correct answers. The first approach uses the fact that the sample mean, properly standardized, will under some regularity conditions have a limiting stable distribution. The second approach consists of subsampling the usual t-statistic and is somewhat more general. A simulation study compares the small sample performance of the two methods. Received: December 1998