Sequential Quantiles via Hermite Series Density Estimation

Sequential quantile estimation refers to incorporating observations into quantile estimates in an incremental fashion thus furnishing an online estimate of one or more quantiles at any given point in time. Sequential quantile estimation is also known as online quantile estimation. This area is relevant to the analysis of data streams and to the one-pass analysis of massive data sets. Applications include network traffic and latency analysis, real time fraud detection and high frequency trading. We introduce new techniques for online quantile estimation based on Hermite series estimators in the settings of static quantile estimation and dynamic quantile estimation. In the static quantile estimation setting we apply the existing Gauss-Hermite expansion in a novel manner. In particular, we exploit the fact that Gauss-Hermite coefficients can be updated in a sequential manner. To treat dynamic quantile estimation we introduce a novel expansion with an exponentially weighted estimator for the Gauss-Hermite coefficients which we term the Exponentially Weighted Gauss-Hermite (EWGH) expansion. These algorithms go beyond existing sequential quantile estimation algorithms in that they allow arbitrary quantiles (as opposed to pre-specified quantiles) to be estimated at any point in time. In doing so we provide a solution to online distribution function and online quantile function estimation on data streams. In particular we derive an analytical expression for the CDF and prove consistency results for the CDF under certain conditions. In addition we analyse the associated quantile estimator. Simulation studies and tests on real data reveal the Gauss-Hermite based algorithms to be competitive with a leading existing algorithm.Comment: 43 pages, 9 figures. Improved version incorporating referee comments, as appears in Electronic Journal of Statistic

On Multiple Zeta Values of Even Arguments

For k <= n, let E(2n,k) be the sum of all multiple zeta values with even arguments whose weight is 2n and whose depth is k. Of course E(2n,1) is the value of the Riemann zeta function at 2n, and it is well known that E(2n,2) = (3/4)E(2n,1). Recently Z. Shen and T. Cai gave formulas for E(2n,3) and E(2n,4). We give two formulas form E(2n,k), both valid for arbitrary k <=n, one of which generalizes the Shen-Cai results; by comparing the two we obtain a Bernoulli-number identity. We also give explicit generating functions for the numbers E(2n,k) and for the analogous numbers E*(2n,k) defined using multiple zeta-star values of even arguments.Comment: DESY number added; misprints fixed; reference added. Second revision (2016): New result on multiple zeta-star values adde

THE ENDOWMENT EFFECT AND WTA: A QUASI-EXPERIMENTAL TEST

This paper reports a test of the endowment effect in an economic analysis of localized air pollution. Regression techniques are used to test the significance of perceived property rights on household WTP for improved air quality versus WTA compensation to forgo an improvement in air quality. Our experiment contributes to the research into the WTP/WTA divergence by providing a new basis for supporting the existence of an endowment effect. Our results are in contrast to recent work by Shogren et al. which supports the substitution proposition of Hanemann while rejecting the endowment effect.Contingent valuation, Endowment effect, Property rights, Substitution effect, Environmental Economics and Policy,

STRUCTURAL CHANGE IN U.S. CHICKEN AND TURKEY SLAUGHTER

Cost function analyses using data from the U.S. Bureau of the Census reveal substantial scale economies in chicken and turkey slaughter. These economies show no evidence of diminishing as plant size increases, are much greater than those realized in cattle and hog slaughter, and have resulted in a huge increase in plant size over the 1972-92 period. The findings also suggest that consolidation in the chicken and turkey slaughter industry is likely to continue, particularly if the growth in the demand for poultry diminishes.chicken slaughter, turkey slaughter, production costs, structural change, Livestock Production/Industries,

Time-Resolved Measurements of Shock-Compressed Matter using X-rays.

Thermonuclear fusion occurs at extremely high pressures and densities. Producing thermonuclear fusion in the laboratory requires a detailed understanding of material properties beyond the scope of condensed matter or classical plasma physics, requiring experimental data to improve models describing matter in these extreme states. This thesis reports the development of two improved methods to probe highly compressed matter using x-ray diagnostics. The first method uses time-resolved x-ray diffraction to infer the stresses in compressed polycrystalline materials. X-ray diffraction is capable of measuring strain states and densities in shock-compressed materials with significantly higher accurately than existing shock timing and velocimetry diagnostics. The analysis discussed in this thesis calculates Debye-Scherrer diffraction patterns from highly stressed polycrystalline samples in the Reuss (iso-stress) limit. In this limit, elastic anisotropy and sample texture effects are directly modeled using elastic constants to calculate lattice strains for all initial crystallite orientations. Example diffraction patterns showing the effects of probing geometry, deviatoric stresses, and sample texture are presented to highlight the versatility of the technique. Finally, I present the design of a recent experiment conducted at the Linac Coherent Light Source to measure the strength of polycrystalline diamond whose data can be analyzed using this technique. The second method uses x-ray fluorescence (XRF) to measure density, ionization state populations, and electron temperature in shocked materials. Spatially resolved K-alpha intensity measurements enable measurements of ion density profiles. Ionization state distributions and electron temperatures are constrained by comparing K-alpha spectra to spectra from atomic-physics simulations using the computer code CRETIN. Analysis of experimental data from the Trident laser facility measuring Ti K-alpha emission spectra from shock-compressed foams demonstrates the use of the technique. This work shows that XRF spectroscopy is a useful technique to complement prior diagnostics to make equation of state measurements of shocked materials containing a suitable tracer element.PHDApplied PhysicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/135774/1/macdonm_1.pd