This document contains proofs and additional experiments for the paper " The Falling Factorial Basis and Its Statistical Applications ". In Section A, we provide proofs to the key technical results in the main paper. In Section B, we give some motivating arguments and additional experiments for the higher order KS test.

We study a novel spline-like basis, which we name the falling factorial basis, bearing many similarities to the classic truncated power basis. The advantage of the falling factorial basis is that it enables rapid, linear-time computations in basis matrix multiplication and basis matrix inversion. The falling factorial functions are not actually splines, but are close enough to splines that they...

Nanotechnology is forging era-defining breakthroughs across science and engineering. In particular, one-dimensional nanostructures such as nanowires, nanotubes and nanobelts are widely regarded as critical building blocks for creating the next generation of devices in electronics, optics, energy and biomedicine. Motivated by a practical problem of sequential synthesis of nanowires, we propose a...

An algorithmic approach to constructing mixed-level orthogonal and near-orthogonal arrays Quasi Monte Carlo simulations of Brownian sheet with an application to interest rate stochastic string model A method for generating uniformly scattered points on the Lp-norm unit sphere and its application in statistical simulation A new class of model-robust designs A method for screening active effects ...

OBJECTIVE To examine the factor structure of the 144-item Chinese version of the Temperament and Character Inventory (TCI) and its association with age and gender in a large non-clinical population. METHOD We recruited 1966 non-clinical participants in China who completed the TCI Chinese version. They were randomly divided into two independent samples. One sample (n=983) was used for explorat...