Asymptotics of Hankel determinants with a one-cut regular potential and Fisher-Hartwig singularities

We obtain asymptotics of large Hankel determinants whose weight depends on a one-cut regular potential and any number of Fisher-Hartwig singularities. This generalises two results: 1) a result of Berestycki, Webb and Wong [5] for root-type singularities, and 2) a result of Its and Krasovsky [37] for a Gaussian weight with a single jump-type singularity. We show that when we apply a piecewise constant thinning on the eigenvalues of a random Hermitian matrix drawn from a one-cut regular ensemble, the gap probability in the thinned spectrum, as well as correlations of the characteristic polynomial of the associated conditional point process, can be expressed in terms of these determinants.Comment: 41 pages, 4 figure

A smoothed maximum score estimator for the binary choice panel data model with individual fixed effects and applications to labour force participation

In a binary choice panel data model with individual effects and two time periods, Manski proposed the maximum score estimator, based on a discontinuous objective function, and proved its consistency under weak distributional assumptions. However, the rate of convergence of this estimator is low (N) and its limit distribution cannot be used for making inference. This paper overcomes this problem by applying the idea of Horowitz to smooth Manski's objective function. The paper extends the resulting smoothed maximum score estimator to the case of more than two time periods and to unbalanced panels (assuming away selectivity effects). Under weak assumptions the estimator is consistent and asymptotically normal with a rate of convergence that is at least N 2/5 and can be made arbitrarily close to N1/2, depending on the strength of the smoothness assumptions imposed. Statistical inferences can be made. The estimator is applied to an equation for labour force participation of married Dutch.Estimation;Labour Supply;Panel Data;Labour Participation;smoothing;statistics

Equivalence Scales for the Former West Germany

Equivalence scales provide answers to questions like how much a household with four children needs to spend compared to a household with two children or how much a childless couple needs to spend compared to a single person household to attain the same welfare level. These are important questions for child allowances, social benefits and to assess the cost of children over the life-cycle for example. The latter is also interesting from a theoretical point of view, especially if future events are allowed to be uncertain. We discuss equivalence scales in an intertemporal setting with uncertainty. To estimate equivalence scales we use subjective data on satisfaction with life and satisfaction with income to represent the welfare level. Because satisfaction is measured on a discrete scale we use limited dependent variable models in estimation. The results are based on a panel from German households (GSOEP). Using satisfaction with life data we find that larger households do not need any additional income to be as satisfied with their life as a couple. Using satisfaction with income, however, indicates that an increase in the household size leads to a significant drop in the satisfaction with their income. This result is used to compute equivalence scales.(lifetime) equivalence scales;panel data;parametric models

On the consistency of Fr\'echet means in deformable models for curve and image analysis

A new class of statistical deformable models is introduced to study high-dimensional curves or images. In addition to the standard measurement error term, these deformable models include an extra error term modeling the individual variations in intensity around a mean pattern. It is shown that an appropriate tool for statistical inference in such models is the notion of sample Fr\'echet means, which leads to estimators of the deformation parameters and the mean pattern. The main contribution of this paper is to study how the behavior of these estimators depends on the number n of design points and the number J of observed curves (or images). Numerical experiments are given to illustrate the finite sample performances of the procedure

Asymptotics for Toeplitz determinants: perturbation of symbols with a gap

We study the determinants of Toeplitz matrices as the size of the matrices tends to infinity, in the particular case where the symbol has two jump discontinuities and tends to zero on an arc of the unit circle at a sufficiently fast rate. We generalize an asymptotic expansion by Widom [22], which was known for symbols supported on an arc. We highlight applications of our results in the Circular Unitary Ensemble and in the study of Fredholm determinants associated to the sine kernel.Comment: 28 pages, 5 figure