Bias Correction of ML and QML Estimators in the EGARCH(1,1) Model

n this paper we derive the bias approximations of the Maximum Likelihood (ML) and Quasi-Maximum Likelihood (QML) Estimators of the EGARCH(1,1) parameters and we check our theoretical results through simulations. With the approximate bias expressions up to O(1/T), we are then able to correct the bias of all estimators. To this end, a Monte Carlo exercise is conducted and the results are presented and discussed. We conclude that, for given sets of parameters values, the bias correction works satisfactory for all parameters. The results for the bias expressions can be used in order to formulate the approximate Edgeworth distribution of the estimators.

Foul or Fair?

This paper gives a short overview of Monte Carlo studies on the usefulness of Heckman?s (1976, 1979) two?step estimator for estimating a selection model. It shows that exploratory work to check for collinearity problems is strongly recommended before deciding on which estimator to apply. In the absence of collinearity problems, the full?information maximum likelihood estimator is preferable to the limited?information two?step method of Heckman, although the latter also gives reasonable results. If, however, collinearity problems prevail, subsample OLS (or the Two?Part Model) is the most robust amongst the simple?to? calculate estimators. --

The Imperial IRAS-FSC Redshift Catalogue: luminosity functions, evolution and galaxy bias

We present the luminosity function and selection function of 60 micron galaxies selected from the Imperial IRAS-FSC Redshift Catalogue (IIFSCz). Three methods, including the 1/Vmax} and the parametric and non-parametric maximum likelihood estimator, are used and results agree well with each other. A density evolution proportional to (1+z)^3.4 or a luminosity evolution exp(1.7 t_L / \tau)$ where t_L is the look-back time is detected in the full sample in the redshift range [0.02, 0.1], consistent with previous analyses. Of the four infrared subpopulations, cirrus-type galaxies and M82-type starbursts show similar evolutionary trends, galaxies with significant AGN contributions show stronger positive evolution and Arp 220-type starbursts exhibit strong negative evolution. The dominant subpopulation changes from cirrus-type galaxies to M82-type starbursts at log (L_60 / L_Sun) ~ 10.3. In the second half of the paper, we derive the projected two-point spatial correlation function for galaxies of different infrared template type. The mean relative bias between cirrus-type galaxies and M82-type starbursts, which correspond to quiescent galaxies with optically thin interstellar dust and actively star-forming galaxies respectively, is calculated to be around 1.25. The relation between current star formation rate (SFR) in star-forming galaxies and environment is investigated by looking at the the dependence of clustering on infrared luminosity. We found that M82-type actively star-forming galaxies show stronger clustering as infrared luminosity / SFR increases. The correlation between clustering strength and SFR in the local Universe seems to echo the basic trend seen in star-forming galaxies in the Great Observatories Origins Deep Survey (GOODS) fields at z ~ 1.Comment: 15 pages, 11 figures, accepted for publication in MNRA

On Estimation of the Post-Newtonian Parameters in the Gravitational-Wave Emission of a Coalescing Binary

The effect of the recently obtained 2nd post-Newtonian corrections on the accuracy of estimation of parameters of the gravitational-wave signal from a coalescing binary is investigated. It is shown that addition of this correction degrades considerably the accuracy of determination of individual masses of the members of the binary. However the chirp mass and the time parameter in the signal is still determined to a very good accuracy. The possibility of estimation of effects of other theories of gravity is investigated. The performance of the Newtonian filter is investigated and it is compared with performance of post-Newtonian search templates introduced recently. It is shown that both search templates can extract accurately useful information about the binary.Comment: 34 pages, 118Kb, LATEX format, submitted to Phys. Rev.

Reducing the bias of the maximum likelihood estimator for the Poisson regression model

We derive expressions for the first-order bias of the MLE for a Poisson regression model and show how these can be used to adjust the estimator and reduce bias without increasing MSE. The analytic results are supported by Monte Carlo simulations and three illustrative empirical applications.Poisson regression, maximum likelihood estimation, bias reduction

Nonlinear Factor Models for Network and Panel Data

Factor structures or interactive effects are convenient devices to incorporate latent variables in panel data models. We consider fixed effect estimation of nonlinear panel single-index models with factor structures in the unobservables, which include logit, probit, ordered probit and Poisson specifications. We establish that fixed effect estimators of model parameters and average partial effects have normal distributions when the two dimensions of the panel grow large, but might suffer of incidental parameter bias. We show how models with factor structures can also be applied to capture important features of network data such as reciprocity, degree heterogeneity, homophily in latent variables and clustering. We illustrate this applicability with an empirical example to the estimation of a gravity equation of international trade between countries using a Poisson model with multiple factors.Comment: 49 pages, 6 tables, the changes in v4 include numerical results with more simulations and minor edits in the main text and appendi

Primordial non-Gaussianity and Bispectrum Measurements in the Cosmic Microwave Background and Large-Scale Structure

The most direct probe of non-Gaussian initial conditions has come from bispectrum measurements of temperature fluctuations in the Cosmic Microwave Background and of the matter and galaxy distribution at large scales. Such bispectrum estimators are expected to continue to provide the best constraints on the non-Gaussian parameters in future observations. We review and compare the theoretical and observational problems, current results and future prospects for the detection of a non-vanishing primordial component in the bispectrum of the Cosmic Microwave Background and large-scale structure, and the relation to specific predictions from different inflationary models.Comment: 82 pages, 23 figures; Invited Review for the special issue "Testing the Gaussianity and Statistical Isotropy of the Universe" for Advances in Astronom