We elucidate a theoretical reason that deep neural networks (DNNs) perform better than
other models in some cases from the viewpoint of their statistical properties for non-smooth …

This book introduces important results and techniques in property testing, where the goal is
to design algorithms that decide whether their input satisfies a predetermined property in …

The usual second order nonparametric kernel estimators are of wide uses in data analysis
and visualization but constrained with slow convergence rate. Higher order kernels provide …

Risk measures, such as value‐at‐risk and expected shortfall, are widely used in finance.
With the necessary sample size being computed using asymptotic expansions for relative …

The efficiency of the beta polynomial kernels in the multivariate setting is the focus of this
paper. The univariate kernel density estimation is of wide applications in nonparametric …

The usual second order nonparametric kernel estimators are of wide uses in data analysis
and visualization but constrained with slow convergence rate. Higher order kernels provide …