Semiparametric estimation for a class of time-inhomogenous diffusion processes

Copyright @ 2009 Institute of Statistical Science, Academia SinicaWe develop two likelihood-based approaches to semiparametrically estimate a class of time-inhomogeneous diffusion processes: log penalized splines (P-splines) and the local log-linear method. Positive volatility is naturally embedded and this positivity is not guaranteed in most existing diffusion models. We investigate different smoothing parameter selections. Separate bandwidths are used for drift and volatility estimation. In the log P-splines approach, different smoothness for different time varying coefficients is feasible by assigning different penalty parameters. We also provide theorems for both approaches and report statistical inference results. Finally, we present a case study using the weekly three-month Treasury bill data from 1954 to 2004. We find that the log P-splines approach seems to capture the volatility dip in mid-1960s the best. We also present an application to calculate a financial market risk measure called Value at Risk (VaR) using statistical estimates from log P-splines

Measuring the cosmic proper distance from fast radio bursts

The cosmic proper distance $d_P$ is a fundamental distance in the Universe. Unlike the luminosity and angular diameter distances, which correspond to the angular size, the proper distance is the length of light path from the source to observer. However, the proper distance has not been measured before. The recent redshift measurement of a repeat fast radio burst (FRB) can shed light on the proper distance. We show that the proper distance-redshift relation can indeed be derived from dispersion measures (DMs) of FRBs with measured redshifts. From Monte Carlo simulations, we find that about 500 FRBs with DM and redshift measurements can tightly constrain the proper distance-redshift relation. We also show that the curvature of our Universe can be constrained with a model-independent method using this derived proper distance-redshift relation and the observed angular diameter distances. Owing to the high event rate of FRBs, hundreds of FRBs can be discovered in the future by upcoming instruments. The proper distance will play an important role in investigating the accelerating expansion and the geometry of the Universe.Comment: 9 pages, 4 figures, proof versio

Transonic rotor noise: Theoretical and experimental comparisons

Two complementary methods of describing the high speed rotor noise problem are discussed. The first method uses the second order transonic potential equation to define and characterize the nature of the aerodynamic and acoustic fields and to explain the appearance of radiating shock waves. The second employs the Ffowcs Williams and Hawkings equation to successfully calculate the acoustic far field. Good agreement between theoretical and experimental waveforms is shown for transonic hover tip Mach numbers from 0.8 to 0.9

Helicopter impulsive noise: Theoretical and experimental status

The theoretical and experimental status of helicopter impulsive noise is reviewed. The two major source mechanisms of helicopter impulsive noise are addressed: high-speed impulsive noise and blade-vortex interaction impulsive noise. A thorough physical explanation of both generating mechanism is presented together with model and full-scale measurements of the phenomena. Current theoretical prediction methods are compared with experimental findings of isolated rotor tests. The noise generating mechanism of high speed impulsive noise are fairly well understood - theory and experiment compare nicely over Mach number ranges typical of today's helicopters. For the case of blade-vortex interaction noise, understanding of noise generating mechanisms and theoretical comparison with experiment are less satisfactory. Several methods for improving theory-experiment are suggested

Zero-bias anomalies in electrochemically fabricated nanojunctions

A streamlined technique for the electrochemical fabrication of metal nanojunctions (MNJs) between lithographically defined electrodes is presented. The first low-temperature transport measurements in such structures reveal suppression of the conductance near zero-bias. The size of the zero-bias anomaly (ZBA) depends strongly on the fabrication electrochemistry and the dimensions of the resulting MNJ. We present evidence that the nonperturbative ZBA in atomic-scale junctions is due to a density of states suppression in the leads.Comment: 4 pages, 4 figure