The traditional(plug-in) return for the Markowitz mean-variance (MV) optimization has been demonstrated to seriously overestimate the theoretical optimal return, especially when the dimension to sample size ratio $p/n$ is large. The newly developed bootstrap-corrected estimator corrects the...

In this article we propose a quick, efficient, and easy method to detect whether a time series Yt possesses any nonlinear feature. The advantage of our proposed nonlinearity test is that it is not required to know the exact nonlinear features and the detailed nonlinear forms of Yt. Our proposed...

In Jin et al. (2014), the limiting spectral distribution (LSD) of a symmetrized auto-cross covariance matrix is derived using matrix manipulation. The goal of this note is to provide a new method to derive the LSD, which greatly simplifies the derivation in Jin et al. (2014). Moreover, as a...

We derive the limiting process of the stochastic dominance statistics for risk averters as well as for risk seekers when the underlying processes might be dependent or independent. We take account of the dependency of the partitions and propose a bootstrap method to decide the critical point. In...

Many kernel-based learning algorithms have the computational load scaled with the sample size n due to the column size of a full kernel Gram matrix K. This article considers the Nyström low-rank approximation. It uses a reduced kernel K̂, which is n×m, consisting of m columns (say columns...

The traditional linear Granger test has been widely used to examine the linear causality among several time series in bivariate settings as well as multivariate settings. Hiemstra and Jones [19] develop a nonlinear Granger causality test in bivariate settings to investigate the nonlinear...

In order to investigate property of the eigenvector matrix of sample covariance matrix <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\mathbf {S}_n$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msub> <mi mathvariant="bold">S</mi> <mi>n</mi> </msub> </math> </EquationSource> </InlineEquation>, in this paper, we establish the central limit theorem of linear spectral statistics associated with a new form of empirical spectral distribution <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$H^{\mathbf {S}_n}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msup> <mi>H</mi> <msub> <mi mathvariant="bold">S</mi> <mi>n</mi>...</msub></msup></math></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation>

In the spiked population model introduced by Johnstone (2001) [11], the population covariance matrix has all its eigenvalues equal to unit except for a few fixed eigenvalues (spikes). The question is to quantify the effect of the perturbation caused by the spike eigenvalues. Baik and Silverstein...

We propose and develop mean-variance-ratio (MVR) statistics for comparing the performance of prospects (e.g., investment portfolios, assets, etc.) after the effect of the background risk has been mitigated. We investigate the performance of the statistics in large and small samples and show that...