Randomized Response and the Binary Probit Model

The paper analyzes eects of randomized response with respect to some binary dependent variable on the estimation of the probit model. This approach is used in interviews when asking sensitive questions. Alternatively randomization can be considered as a means of statistical disclosure control which has been termed post randomization method (PRAM). The paper shows that all properties concerning parameter estimation are maintained although there is a loss in (asymptotic) eciency.Asymptotic Eciency Maximum Likelihood; Post Randomisation; Statistical Disclosure.

Panel Regression with Random Noise

The paper explores the effect of measurement errors on the estimation of a linear panel data model. The conventional fixed effects estimator, which ignores measurement errors, is biased. By correcting for the bias one can construct consistent and asymptotically normal estimators. In addition, we find estimates for the asymptotic variances of these estimators. The paper focuses on multiplicative errors, which are often deliberately added to the data in order to minimize their disclosure risk. They can be analyzed in a similar way as additive errors, but with some important and consequential differences.panel regression, multiplicative measurement errors, bias correction, asymptotic variance, disclosure control

Estimation of the Probit Model from Anonymized Micro Data

The demand of scientists for confidential micro data from official sources has created discussion of how to anonymize these data in such a way that they can be given to the scientific community. We report results from a German project which exploits various options of anonymization for producing such ”scientific-use- files”. The main concern in the project however is whether estimation of stochastic models from these perturbed data is possible and – more importantly – leads to reliable results. In this paper we concentrate on estimation of the probit model under the assumption that only anonymized data are available. In particular we assume that the binary dependent variable has undergone post-randomization (PRAM) and that the set of explanatory variables has been perturbed by addition of noise. We employ a maximum likelihood estimator which is consistent if only the dependent variable has been anonymized by PRAM. The errors-in-variables structure of the regressors then is handled by the simulation extrapolation (SIMEX) estimation procedure where we compare performance of quadratic and nonlinear (rational) extrapolation.anonymization, misclassification, noise addition, post-randomization, SIMEX procedure, statistical disclosure.

A Microeconometric Characterisation of Household Consumption Using Quantile Regression

The paper uses micro cross-section data from the GfK consumer panel for econometric demand analysis of private households in Germany. Contrary to most research which considered \average" behavior we extend this approach to consumer behavior for di®erent \intensities" of consumption. Our analytical tool is quantile regression which allows us to describe the conditional distribu- tion for any quantile including the (conditional) median representing \average" behavior. As an illustrative example we use the demand for beer and wine. The paper shows quite distinct patterns regarding price and income e®ects for di®erent goods which leads us to an extended characterization of household demand.econometric demand analysis, Engel curve, demand system, micro data

Synchrotron Radiation as the Source of GRB Spectra, Part I: Theory

We investigate synchrotron emission models as the source of gamma ray burst spectra. We show that allowing for synchrotron self absorption and a ``smooth cutoff'' to the electron energy distribution produces a wide range of low energy spectral behavior. We show that there exists a correlation between the value of the peak of the $\nu F_{\nu}$ spectrum, $E_{p}$, and the low energy spectral index $\alpha$ as determined by spectral fits over a finite bandwidth. Finally, we discuss the implications of synchrotron emission from internal shocks for GRB spectral evolution.Comment: To appear in the proceedings of the 5th Huntsville Symposium on Gamma Ray Burst

On the Kinetic Energy and Radiative Efficiency of Gamma-Ray Bursts

Using measured X-ray luminosities to 17 Gamma-Ray Bursts (GRBs) during the afterglow phase and accounting for radiative losses, we calculate the kinetic energy of these bursts and investigate its relation to other GRB properties. We then use the observed radiated energy during the prompt phase to determine the radiative efficiency of these bursts, and explore how the efficiency relates to other GRB observables. We find that the kinetic energy in the afterglow phase is directly correlated with the radiated energy, total energy as well as possibly the jet opening angle and spectral peak energy. More importantly, we find the intriguing fact that the efficiency is correlated with the radiated energy, and mildly with the total energy, jet opening angle and spectral peak energy. XRF020903 also seems to follow the trends we find for our GRB sample. We discuss the implications of these results for the GRB radiation and jet models.Comment: 9 pages, 7 figures; Revised version, accepted to Ap

On the Structure of Quasi-Universal Jets for Gamma-Ray Bursts

The idea that GRBs originate from uniform jets has been used to explain numerous observations of breaks in the GRB afterglow lightcurves. We explore the possibility that GRBs instead originate from a structured jet that may be quasi-universal, where the variation in the observed properties of GRBs is due to the variation in the observer viewing angle. We test how various models reproduce the jet data of Bloom, Frail, & Kulkarni (2003), which show a negative correlation between the isotropic energy output and the inferred jet opening angle (in a uniform jet configuration). We find, consistent with previous studies, that a power-law structure for the jet energy as a function of angle gives a good description. However, a Gaussian jet structure can also reproduce the data well, particularly if the parameters of the Gaussian are allowed some scatter. We place limits on the scatter of the parameters in both the Gaussian and power-law models needed to reproduce the data, and discuss how future observations will better distinguish between these models for the GRB jet structure. In particular, the Gaussian model predicts a turnover at small opening angles and in some cases a sharp cutoff at large angles, the former of which may already have been observed. We also discuss the predictions each model makes for the observed luminosity function of GRBs and compare these predictions with the existing data.Comment: 13 pages, including 10 figures; To appear in Ap