Essays on bootstrap in econometrics

Ma thèse est composée de trois essais sur l'inférence par le bootstrap à la fois dans les modèles de données de panel et les modèles à grands nombres de variables instrumentales #VI# dont un grand nombre peut être faible. La théorie asymptotique n'étant pas toujours une bonne approximation de la distribution d'échantillonnage des estimateurs et statistiques de tests, je considère le bootstrap comme une alternative. Ces essais tentent d'étudier la validité asymptotique des procédures bootstrap existantes et quand invalides, proposent de nouvelles méthodes bootstrap valides. Le premier chapitre #co-écrit avec Sílvia Gonçalves# étudie la validité du bootstrap pour l'inférence dans un modèle de panel de données linéaire, dynamique et stationnaire à effets fixes. Nous considérons trois méthodes bootstrap: le recursive-design bootstrap, le fixed-design bootstrap et le pairs bootstrap. Ces méthodes sont des généralisations naturelles au contexte des panels des méthodes bootstrap considérées par Gonçalves et Kilian #2004# dans les modèles autorégressifs en séries temporelles. Nous montrons que l'estimateur MCO obtenu par le recursive-design bootstrap contient un terme intégré qui imite le biais de l'estimateur original. Ceci est en contraste avec le fixed-design bootstrap et le pairs bootstrap dont les distributions sont incorrectement centrées à zéro. Cependant, le recursive-design bootstrap et le pairs bootstrap sont asymptotiquement valides quand ils sont appliqués à l'estimateur corrigé du biais, contrairement au fixed-design bootstrap. Dans les simulations, le recursive-design bootstrap est la méthode qui produit les meilleurs résultats. Le deuxième chapitre étend les résultats du pairs bootstrap aux modèles de panel non linéaires dynamiques avec des effets fixes. Ces modèles sont souvent estimés par l'estimateur du maximum de vraisemblance #EMV# qui souffre également d'un biais. Récemment, Dhaene et Johmans #2014# ont proposé la méthode d'estimation split-jackknife. Bien que ces estimateurs ont des approximations asymptotiques normales centrées sur le vrai paramètre, de sérieuses distorsions demeurent à échantillons finis. Dhaene et Johmans #2014# ont proposé le pairs bootstrap comme alternative dans ce contexte sans aucune justification théorique. Pour combler cette lacune, je montre que cette méthode est asymptotiquement valide lorsqu'elle est utilisée pour estimer la distribution de l'estimateur split-jackknife bien qu'incapable d'estimer la distribution de l'EMV. Des simulations Monte Carlo montrent que les intervalles de confiance bootstrap basés sur l'estimateur split-jackknife aident grandement à réduire les distorsions liées à l'approximation normale en échantillons finis. En outre, j'applique cette méthode bootstrap à un modèle de participation des femmes au marché du travail pour construire des intervalles de confiance valides. Dans le dernier chapitre #co-écrit avec Wenjie Wang#, nous étudions la validité asymptotique des procédures bootstrap pour les modèles à grands nombres de variables instrumentales #VI# dont un grand nombre peu être faible. Nous montrons analytiquement qu'un bootstrap standard basé sur les résidus et le bootstrap restreint et efficace #RE# de Davidson et MacKinnon #2008, 2010, 2014# ne peuvent pas estimer la distribution limite de l'estimateur du maximum de vraisemblance à information limitée #EMVIL#. La raison principale est qu'ils ne parviennent pas à bien imiter le paramètre qui caractérise l'intensité de l'identification dans l'échantillon. Par conséquent, nous proposons une méthode bootstrap modifiée qui estime de facon convergente cette distribution limite. Nos simulations montrent que la méthode bootstrap modifiée réduit considérablement les distorsions des tests asymptotiques de type Wald #$t$# dans les échantillons finis, en particulier lorsque le degré d'endogénéité est élevé.

A Bootstrap Test for the Probability of Ruin in the Compound Poisson Risk Process

In this article we propose a bootstrap test for the probability of ruin in the compound Poisson risk process. We adopt the P-value approach, which leads to a more complete assessment of the underlying risk than the probability of ruin alone. We provide second-order accurate P-values for this testing problem and consider both parametric and nonparametric estimators of the individual claim amount distribution. Simulation studies show that the suggested bootstrap P-values are very accurate and outperform their analogues based on the asymptotic normal approximation.

A stochastic metapopulation model accounting for habitat dynamics

A stochastic metapopulation model accounting for habitat dynamics is presented. This is the stochastic SIS logistic model with the novel aspect that it incorporates varying carrying capacity. We present results of Kurtz and Barbour, that provide deterministic and diffusion approximations for a wide class of stochastic models, in a form that most easily allows their direct application to population models. These results are used to show that a suitably scaled version of the metapopulation model converges, uniformly in probability over finite time intervals, to a deterministic model previously studied in the ecological literature. Additionally, they allow us to establish a bivariate normal approximation to the quasi-stationary distribution of the process. This allows us to consider the effects of habitat dynamics on metapopulation modelling through a comparison with the stochastic SIS logistic model and provides an effective means for modelling metapopulations inhabiting dynamic landscapes.

On a Second Order Condition for Max-Semistable Laws

2000 Mathematics Subject Classification: 62G32, 62G20.

Normal forms, stability and splitting of invariant manifolds I. Gevrey Hamiltonians

In this paper, we give a new construction of resonant normal forms with a small remainder for near-integrable Hamiltonians at a quasi-periodic frequency. The construction is based on the special case of a periodic frequency, a Diophantine result concerning the approximation of a vector by independent periodic vectors and a technique of composition of periodic averaging. It enables us to deal with non-analytic Hamiltonians, and in this first part we will focus on Gevrey Hamiltonians and derive normal forms with an exponentially small remainder. This extends a result which was known for analytic Hamiltonians, and only in the periodic case for Gevrey Hamiltonians. As applications, we obtain an exponentially large upper bound on the stability time for the evolution of the action variables and an exponentially small upper bound on the splitting of invariant manifolds for hyperbolic tori, generalizing corresponding results for analytic Hamiltonians.

Microscopic description of the twist mode in normal and superfluid trapped Fermi gases

We investigate the "twist" mode (rotation of the upper against the lower hemisphere) of a dilute atomic Fermi gas in a spherical trap. The normal and superfluid phases are considered. The linear response to this external perturbation is calculated within the microscopic Hartree-Fock-Bogoliubov approach. In the normal phase the excitation spectrum is concentrated in a rather narrow peak very close to the trapping frequency. In the superfluid phase the strength starts to be damped and fragmented and the collectivity of the mode is progressively lost when the temperature decreases. In the weak-pairing regime some reminiscence of the collective motion still exists, whereas in the strong-pairing regime the twist mode is completely washed out. The disappearance of the twist mode in the strong-pairing regime with decreasing temperature is interpreted in the framework of the two-fluid model.

Infrared intensities of furan, pyrrole and thiophene: beyond the double harmonic approximation

Infrared intensities of the fundamental, overtone and combination transitions in furan, pyrrole and thiophene have been calculated using the variational normal coordinate code MULTIMODE. We use pure vibrational wavefunctions, and quartic force fields and cubic dipole moment vector surfaces, generated by density functional theory. The results are compared graphically with second-order perturbation calculations and with relative intensities from experiment for furan and pyrrole.

Cubic approximation for the transverse displacement in BEM for elastic plates analysis

This work presents an application for the plate analysis formulation by BEM where 3 boundary equations are used, written for the transverse displacement w and the normal and tangential derivatives partial derivativew/partial derivativen and partial derivativew/partial derivatives. In this extension, the transverse displacement w is approximated by a cubic polynomial and, as a consequence, partial derivativew/partial derivatives has a quadratic approximation. This alternative BEM formulation improves the analysis of thin plates, when compared to the formulation using the linear approximation for the displacements, mainly in the obtaining of the bending moments at the boundary of the plate. The implementation of this proposal to the computational codes is simple. (C) 2004 Published by Elsevier Ltd.

Classical and quantal aspects of resonant normal forms

The Birkhoff-Gustavson normal form is employed to study separately chaos and resonances in a system with two degrees of freedom. In the integrable regime, tunnelling effects are appreciable when the nearest level spacings show oscillations. Tunnelling among states in the libration and rotation tori regions is also observed. The regularity of avoided crossings due to tunnelling indicates a collective effect and is associated with an isolated resonance. The spectral fluctuations also show a strong level correlation. The Husimi distribution, on the other hand, is insensitive to avoided crossings. An integrable approximation to the overlap of resonances is obtained and a theoretical description is given for an isolated cubic resonance plus a complex orbit. In the non-integrable regime chaos is stronger after overlapping and preferentially at low energies.

Estimation of spontaneous blinking main sequence in normal subjects and patients with Graves' upper eyelid retraction

Purpose. We quantified the main sequence of spontaneous blinks in normal subjects and Graves' disease patients with upper eyelid retraction using a nonlinear and two linear models, and examined the variability of the main sequence estimated with standard linear regression for 10-minute periods of time. Methods. A total of 20 normal subjects and 12 patients had their spontaneous blinking measured with the magnetic search coil technique when watching a video during one hour. The main sequence was estimated with a power-law function, and with standard and trough the origin linear regressions. Repeated measurements ANOVA was used to test the mean sequence stability of 10-minute bins measured with standard linear regression. Results. In 95% of the sample the correlation coefficients of the main sequence ranged from 0.60 to 0.94. Homoscedasticity of the peak velocity was not verified in 20% of the subjects and 25% of the patients. The power-law function provided the best main sequence fitting for subjects and patients. The mean sequence of 10-minute bins measured with standard linear regression did not differ from the one-hour period value. For the entire period of observation and the slope obtained by standard linear regression, the main sequence of the patients was reduced significantly compared to the normal subjects. Conclusions. Standard linear regression is a valid and stable approximation for estimating the main sequence of spontaneous blinking. However, the basic assumptions of the linear regression model should be examined on an individual basis. The maximum velocity of large blinks is slower in Graves' disease patients than in normal subjects. © 2013 The Association for Research in Vision and Ophthalmology, Inc.

Filamentary microstructure and linear temperature dependence of normal state transport in optimized high temperature superconductors

A filamentary model of “metallic” conduction in layered high temperature superconductive cuprates explains the concurrence of normal state resistivities (Hall mobilities) linear in T (T−2) with optimized superconductivity. The model predicts the lowest temperature T0 for which linearity holds and it also predicts the maximum superconductive transition temperature Tc. The theory abandons the effective medium approximation that includes Fermi liquid as well as all other nonpercolative models in favor of countable smart basis states.

Theory of strongly correlated electron systems. I. Intersite coulomb interaction and the approximation of renormalized fermions in total energy calculations

The diagrammatic strong-coupling perturbation theory (SCPT) for correlated electron systems is developed for intersite Coulomb interaction and for a nonorthogonal basis set. The construction is based on iterations of exact closed equations for many - electron Green functions (GFs) for Hubbard operators in terms of functional derivatives with respect to external sources. The graphs, which do not contain the contributions from the fluctuations of the local population numbers of the ion states, play a special role: a one-to-one correspondence is found between the subset of such graphs for the many - electron GFs and the complete set of Feynman graphs of weak-coupling perturbation theory (WCPT) for single-electron GFs. This fact is used for formulation of the approximation of renormalized Fermions (ARF) in which the many-electron quasi-particles behave analogously to normal Fermions. Then, by analyzing: (a) Sham's equation, which connects the self-energy and the exchange- correlation potential in density functional theory (DFT); and (b) the Galitskii and Migdal expressions for the total energy, written within WCPT and within ARF SCPT, a way we suggest a method to improve the description of the systems with correlated electrons within the local density approximation (LDA) to DFT. The formulation, in terms of renormalized Fermions LIDA (RF LDA), is obtained by introducing the spectral weights of the many electron GFs into the definitions of the charge density, the overlap matrices, effective mixing and hopping matrix elements, into existing electronic structure codes, whereas the weights themselves have to be found from an additional set of equations. Compared with LDA+U and self-interaction correction (SIC) methods, RF LDA has the advantage of taking into account the transfer of spectral weights, and, when formulated in terms of GFs, also allows for consideration of excitations and nonzero temperature. Going beyond the ARF SCPT, as well as RF LIDA, and taking into account the fluctuations of ion population numbers would require writing completely new codes for ab initio calculations. The application of RF LDA for ab initio band structure calculations for rare earth metals is presented in part 11 of this study (this issue). (c) 2005 Wiley Periodicals, Inc.

Angiogenic Effects Of Cryosurgery With Liquid Nitrogen On The Normal Skin Of Rats, Through Morphometric Study.

Cryosurgery is an efficient therapeutic technique used to treat benign and malignant cutaneous diseases. The primary active mechanism of cryosurgery is related to vascular effects on treated tissue. After a cryosurgical procedure, exuberant granulation tissue is formed at the injection site, probably as a result of angiogenic stimulation of the cryogen and inflammatory response, particularly in endothelial cells. To evaluate the angiogenic effects of freezing, as part of the phenomenon of healing rat skin subjected to previous injury. Two incisions were made in each of the twenty rats, which were divided randomly into two groups of ten. After 3 days, cryosurgery with liquid nitrogen was performed in one of incisions. The rats' samples were then collected, cut and stained to conduct histopathological examination, to assess the local angiogenesis in differing moments and situations. It was possible to demonstrate that cryosurgery, in spite of promoting cell death and accentuated local inflammation soon after its application, induces quicker cell proliferation in the affected tissue and maintenance of this rate in a second phase, than in tissue healing without this procedure. These findings, together with the knowledge that there is a direct relationship between mononuclear cells and neovascularization (the development of a rich system of new vessels in injury caused by cold), suggest that cryosurgery possesses angiogenic stimulus, even though complete healing takes longer to occur. The significance level for statistical tests was 5% (p<0,05).

Kinesiographic Study Of Masticatory Movements In Denture Wearers With Normal And Resorbed Denture-bearing Areas.

An unfavorable denture-bearing area could compromise denture retention and stability, limit mastication, and possibly alter masticatory motion. The purpose of this study was to evaluate the masticatory movements of denture wearers with normal and resorbed denture-bearing areas. Completely edentulous participants who received new complete dentures were selected and divided into 2 groups (n=15) according to the condition of their denture-bearing areas as classified by the Kapur method: a normal group (control) (mean age, 65.9 ± 7.8 years) and a resorbed group (mean age, 70.2 ± 7.6 years). Masticatory motion was recorded and analyzed with a kinesiographic device. The patients masticated peanuts and Optocal. The masticatory movements evaluated were the durations of opening, closing, and occlusion; duration of the masticatory cycle; maximum velocities and angles of opening and closing; total masticatory area; and amplitudes of the masticatory cycle. The data were analyzed by 2-way ANOVA and the Tukey honestly significant difference post hoc test (α=.05). The group with a resorbed denture-bearing area had a smaller total masticatory area in the frontal plane and shorter horizontal masticatory amplitude than the group with normal denture-bearing area (P<.05). Denture wearers with resorbed denture-bearing areas showed reduced jaw motion during mastication.