A Smoothed-Distribution Form of Nadaraya-Watson Estimation

Given observation-pairs (xi ,yi ), i = 1,...,n , taken to be independent observations of the random pair (X ,Y), we sometimes want to form a nonparametric estimate of m(x) = E(Y/ X = x). Let YE have the empirical distribution of the yi , and let (XS ,YS ) have the kernel-smoothed distribution of the (xi ,yi ). Then the standard estimator, the Nadaraya-Watson form mNW(x) can be interpreted as E(YE?XS = x). The smoothed-distribution estimator ms (x)=E(YS/XS = x) is a more general form than  mNW (x) and often has better properties. Similar considerations apply to estimating Var(Y/X = x), and to local polynomial estimation. The discussion generalizes to vector (xi ,yi ).nonparametric regression, Nadaraya-Watson, kernel density, conditional expectation estimator, conditional variance estimator, local polynomial estimator

Wage Dispersion in a Partially Unionized Labor Force

Wage Dispersion in a Partially Unionized Labor Force This paper critiques Card’s (2001) method for analyzing wage dispersion in a partially unionized labor market based on a disaggregation of the population into skill categories. We argue that disaggregation is a good idea, the use of skill categories less so. We offer a modified model in which each worker is assigned a union-membership probability, a predicted union wage, and a predicted nonunion wage. Our model provides a natural three-way decomposition of variance, and is also suited to counterfactual analysis. By way of an application, we examine the effect of de-unionization on wage dispersion in the United Kingdom between 1983 and 1995, reporting that the decline in membership accounts for only about one-fifth of the observed increase in wage dispersion.wage dispersion, three-way variance decomposition, bivariate kernel density smoothing, union membership, deunionization.

Wage Dispersion in a Partially Unionized Labor Force

Taking as our point of departure a model proposed by David Card (2001), we suggest new methods for analyzing wage dispersion in a partially unionized labor market. Card's method disaggregates the labor population into skill categories, which procedure entails some loss of information. Accordingly, we develop a model in which each worker individually is assigned a union-membership probability and predicted union and nonunion wages. The model yields a natural three-way decomposition of variance. The decomposition permits counterfactual analysis, using concepts and techniques from the theory of factorial experimental design. We examine causes of the increase in U.K. wage dispersion between 1983 and 1995. Of the factors initially considered, the most influential was a change in the structure of remuneration inside both the union and nonunion sectors. Next in importance was the decrease in union membership. Finally, exogenous changes in labor force characteristics had, for most groups considered, only a small negative effect. We supplement this preliminary three-factorial analysis with a five-factorial analysis that allows us to examine effects from the wage-equation parameters in greater detail.wage dispersion, three-way variance decomposition, bivariate kernel density smoothing, union membership, deunionization, factorial experimental design

Development of optical diaphragm deflection sensors

The objective of this project was to develop high-temperature pressure sensors using non-metallic components and optical sensing methods. The sensors are to operate over a temperature range from room temperature approx. 20C to 540C, to respond to internal pressure up to 690 kPa, to respond to external pressure up to 690 kPa, and to withstand external overpressure of 2070 kPa. Project tasks include evaluating sensing techniques and sensor systems. These efforts include materials and sensing method selection, sensor design, sensor fabrication, and sensor testing. Sensors are tested as a function of temperature, pressure, overpressure, and vibration. The project results show that high-temperature pressure sensors based on glass components and optical sensing methods are feasible. The microbend optical diaphragm deflection sensor exhibits the required sensitivity and stability for use as a pressure sensor with temperature compensation. for the microbend sensor, the 95% confidence level deviation of input pressure from the pressure calculated from the overall temperature-compensated calibration equation is 3.7% of full scale. The limitations of the sensors evaluated are primarily due to the restricted temperature range of suitable commercially available optical fibers and the problems associated with glass-to-metal pressure sealing over the entire testing temperature range

A generalization of Clausen's identity

The paper aims to generalize Clausen's identity to the square of any Gauss hypergeometric function. Accordingly, solutions of the related 3rd order linear differential equation are found in terms of certain bivariate series that can reduce to 3F2 series similar to those in Clausen's identity. The general contiguous variation of Clausen's identity is found. The related Chaundy's identity is generalized without any restriction on the parameters of Gauss hypergeometric function. The special case of dihedral Gauss hypergeometric functions is underscored

Dynamics and Steady States in excitable mobile agent systems

We study the spreading of excitations in 2D systems of mobile agents where the excitation is transmitted when a quiescent agent keeps contact with an excited one during a non-vanishing time. We show that the steady states strongly depend on the spatial agent dynamics. Moreover, the coupling between exposition time ($\omega$) and agent-agent contact rate (CR) becomes crucial to understand the excitation dynamics, which exhibits three regimes with CR: no excitation for low CR, an excited regime in which the number of quiescent agents (S) is inversely proportional to CR, and for high CR, a novel third regime, model dependent, here S scales with an exponent $\xi -1$, with $\xi$ being the scaling exponent of $\omega$ with CR

Fine Structure of the 1s3p ^3P_J Level in Atomic ^4He: Theory and Experiment

We report on a theoretical calculation and a new experimental determination of the 1s3p ^3P_J fine structure intervals in atomic ^4He. The values from the theoretical calculation of 8113.730(6) MHz and 658.801(6) MHz for the nu_{01} and nu_{12} intervals, respectively, disagree significantly with previous experimental results. However, the new laser spectroscopic measurement reported here yields values of 8113.714(28) MHz and 658.810(18) MHz for these intervals. These results show an excellent agreement with the theoretical values and resolve the apparent discrepancy between theory and experiment.Comment: 9 pages, 3 figure

Higher-order spin effects in the dynamics of compact binaries I. Equations of motion

We derive the equations of motion of spinning compact binaries including the spin-orbit (SO) coupling terms one post-Newtonian (PN) order beyond the leading-order effect. For black holes maximally spinning this corresponds to 2.5PN order. Our result for the equations of motion essentially confirms the previous result by Tagoshi, Ohashi and Owen. We also compute the spin-orbit effects up to 2.5PN order in the conserved (Noetherian) integrals of motion, namely the energy, the total angular momentum, the linear momentum and the center-of-mass integral. We obtain the spin precession equations at 1PN order beyond the leading term, as well. Those results will be used in a future paper to derive the time evolution of the binary orbital phase, providing more accurate templates for LIGO-Virgo-LISA type interferometric detectors.Comment: transcription error in Eqs. (2.17) correcte

Multiple differences in calling songs and other traits between solitary and gregarious Mormon crickets from allopatric mtDNA clades

BACKGROUND: In acoustic species, traits such as male calling song are likely to diverge quickly between allopatric populations due to sexual selection, and divergence in parameters such as carrier frequency, chirp structure, and other important song characters can influence sexual isolation. Here we make use of two forms of Mormon crickets to examine differences in a broad suite of traits that have the potential to influence speciation via sexual isolation. Mormon crickets in "gregarious" populations aggregate into dense migratory bands, and females are the sexually competitive sex (sex-role reversal). There is also a non-outbreak "solitary" form. These two forms are largely but not perfectly correlated with a significant mtDNA subdivision within the species that is thought to have arisen in allopatry. Combined information about multiple, independently evolving traits, such as morphology and structural and behavioural differences in calling song, provides greater resolution of the overall differences between these allopatric populations, and allows us to assess their stage of divergence. We test two predictions, first that the forms differ in song and second that gregarious males are more reluctant to sing than solitary males due to sex role reversal. We also tested for a difference in the relationship between the size of the forewing resonator, the mirror, and carrier frequency, as most models of sound production in crickets indicate that mirror size should predict carrier frequency. RESULTS: Multivariate analyses showed that solitary and gregarious individuals from different populations representing the two mtDNA clades had almost non-overlapping distributions based on multiple song and morphological measurements. Carrier frequency differed between the two, and gregarious males were more reluctant to sing overall. Mirror size predicted carrier frequency; however, the relationship between mirror size and surface area varied between solitary and gregarious forms, suggesting that factors above and beyond mirror size contribute to carrier frequency. CONCLUSION: The two clades of Mormon crickets differ in a broad suite of independent traits that probably justify subspecies status (the two can successfully mate so may not be reproductively isolated). However, our results emphasize the importance of carefully distinguishing the ultimate causation of differences between traits used to delineate species or subspecies boundaries