Revisiting the synthetic control estimator

The synthetic control (SC) method has been recently proposed as an alternative to estimate treatment effects in comparative case studies. The SC relies on the assumption that there is a weighted average of the control units that reconstruct the potential outcome of the treated unit in the absence of treatment. If these weights were known, then one could estimate the counterfactual for the treated unit using this weighted average. With these weights, the SC would provide an unbiased estimator for the treatment effect even if selection into treatment is correlated with the unobserved heterogeneity. In this paper, we revisit the SC method in a linear factor model where the SC weights are considered nuisance parameters that are estimated to construct the SC estimator. We show that, when the number of control units is fixed, the estimated SC weights will generally not converge to the weights that reconstruct the factor loadings of the treated unit, even when the number of pre-intervention periods goes to infinity. As a consequence, the SC estimator will be asymptotically biased if treatment assignment is correlated with the unobserved heterogeneity. The asymptotic bias only vanishes when the variance of the idiosyncratic error goes to zero. We suggest a slight modification in the SC method that guarantees that the SC estimator is asymptotically unbiased and has a lower asymptotic variance than the difference-in-differences (DID) estimator when the DID identification assumption is satisfied. If the DID assumption is not satisfied, then both estimators would be asymptotically biased, and it would not be possible to rank them in terms of their asymptotic bias.

Sur les tests lisses d'ajustement dans le context des series chronologiques

La plupart des modèles en statistique classique repose sur une hypothèse sur la distribution des données ou sur une distribution sous-jacente aux données. La validité de cette hypothèse permet de faire de l’inférence, de construire des intervalles de confiance ou encore de tester la fiabilité du modèle. La problématique des tests d’ajustement vise à s’assurer de la conformité ou de la cohérence de l’hypothèse avec les données disponibles. Dans la présente thèse, nous proposons des tests d’ajustement à la loi normale dans le cadre des séries chronologiques univariées et vectorielles. Nous nous sommes limités à une classe de séries chronologiques linéaires, à savoir les modèles autorégressifs à moyenne mobile (ARMA ou VARMA dans le cas vectoriel). Dans un premier temps, au cas univarié, nous proposons une généralisation du travail de Ducharme et Lafaye de Micheaux (2004) dans le cas où la moyenne est inconnue et estimée. Nous avons estimé les paramètres par une méthode rarement utilisée dans la littérature et pourtant asymptotiquement efficace. En effet, nous avons rigoureusement montré que l’estimateur proposé par Brockwell et Davis (1991, section 10.8) converge presque sûrement vers la vraie valeur inconnue du paramètre. De plus, nous fournissons une preuve rigoureuse de l’inversibilité de la matrice des variances et des covariances de la statistique de test à partir de certaines propriétés d’algèbre linéaire. Le résultat s’applique aussi au cas où la moyenne est supposée connue et égale à zéro. Enfin, nous proposons une méthode de sélection de la dimension de la famille d’alternatives de type AIC, et nous étudions les propriétés asymptotiques de cette méthode. L’outil proposé ici est basé sur une famille spécifique de polynômes orthogonaux, à savoir les polynômes de Legendre. Dans un second temps, dans le cas vectoriel, nous proposons un test d’ajustement pour les modèles autorégressifs à moyenne mobile avec une paramétrisation structurée. La paramétrisation structurée permet de réduire le nombre élevé de paramètres dans ces modèles ou encore de tenir compte de certaines contraintes particulières. Ce projet inclut le cas standard d’absence de paramétrisation. Le test que nous proposons s’applique à une famille quelconque de fonctions orthogonales. Nous illustrons cela dans le cas particulier des polynômes de Legendre et d’Hermite. Dans le cas particulier des polynômes d’Hermite, nous montrons que le test obtenu est invariant aux transformations affines et qu’il est en fait une généralisation de nombreux tests existants dans la littérature. Ce projet peut être vu comme une généralisation du premier dans trois directions, notamment le passage de l’univarié au multivarié ; le choix d’une famille quelconque de fonctions orthogonales ; et enfin la possibilité de spécifier des relations ou des contraintes dans la formulation VARMA. Nous avons procédé dans chacun des projets à une étude de simulation afin d’évaluer le niveau et la puissance des tests proposés ainsi que de les comparer aux tests existants. De plus des applications aux données réelles sont fournies. Nous avons appliqué les tests à la prévision de la température moyenne annuelle du globe terrestre (univarié), ainsi qu’aux données relatives au marché du travail canadien (bivarié). Ces travaux ont été exposés à plusieurs congrès (voir par exemple Tagne, Duchesne et Lafaye de Micheaux (2013a, 2013b, 2014) pour plus de détails). Un article basé sur le premier projet est également soumis dans une revue avec comité de lecture (Voir Duchesne, Lafaye de Micheaux et Tagne (2016)).

Higher mathematics. A text-book for classical and engineering colleges.

"Bibliography ... general works on the history of mathematics in the nineteenth century": p. 568-570.

Calculus, with analytic geometry.

Includes index.

Libellus post saeculum quam Ioannes Bolyai de Bolya anno MDCCCII A.D. XVIII kalendas ianuarias Claudiopoli natus est ad celebrandam memoriam eius immortalem.

Available on demand as hard copy or computer file from Cornell University Library.

Modeling collisional processes in plasmas using discontinuous numerical methods

Thesis (Ph.D.)--University of Washington, 2016-06

A Kinetic Vlasov Model for Plasma Simulation Using Discontinuous Galerkin Method on Many-Core Architectures

Thesis (Ph.D.)--University of Washington, 2016-03

Conservation of freshwater thermal habitats for Pacific salmon in a changing climate

Thesis (Ph.D.)--University of Washington, 2016-06

Aspects of Markov Chains and Particle Systems

Thesis (Ph.D.)--University of Washington, 2016-06

Quantitative description of the interaction between folate and the folate-binding protein from cow's milk

A detailed study has been carried out on the dependence of folate binding on the concentration of FBP (folate-binding protein) at pH 5.0, conditions selected to prevent complications arising from the pre-existing self-association of the acceptor. In contrast with the mandatory requirement that reversible interaction of ligand with a single acceptor site should exhibit a unique, rectangular hyperbolic binding curve, results obtained by ultrafiltration for the FBP-folate system required description in terms of (i) a sigmoidal relationship between concentrations of bound and free folate and (ii) an inverse dependence of affinity on FBP concentration. These findings have been attributed to the difficulties in determining the free ligand concentration in the FBP-folate mixtures for which reaction is essentially stoichiometric. This explanation also accounts for the similar published behaviour of the FBP-folate system at neutral pH, which had been attributed erroneously to acceptor self-association, a phenomenon incompatible with the experimental findings because of its prediction of a greater affinity for folate with increasing FBP concentration.

Green-Ampt approximations

The solution to the Green and Ampt infiltration equation is expressible in terms of the Lambert W-1 function. Approximations for Green and Ampt infiltration are thus derivable from approximations for the W-1 function and vice versa. An infinite family of asymptotic expansions to W-1 is presented. Although these expansions do not converge near the branch point of the W function (corresponds to Green-Ampt infiltration with immediate ponding), a method is presented for approximating W-1 that is exact at the branch point and asymptotically, with interpolation between these limits. Some existing and several new simple and compact yet robust approximations applicable to Green-Ampt infiltration and flux are presented, the most accurate of which has a maximum relative error of 5 x 10(-5)%. This error is orders of magnitude lower than any existing analytical approximations. (c) 2005 Elsevier Ltd. All rights reserved.

A time-domain test for some types of nonlinearity

The bispectrum and third-order moment can be viewed as equivalent tools for testing for the presence of nonlinearity in stationary time series. This is because the bispectrum is the Fourier transform of the third-order moment. An advantage of the bispectrum is that its estimator comprises terms that are asymptotically independent at distinct bifrequencies under the null hypothesis of linearity. An advantage of the third-order moment is that its values in any subset of joint lags can be used in the test, whereas when using the bispectrum the entire (or truncated) third-order moment is required to construct the Fourier transform. In this paper, we propose a test for nonlinearity based upon the estimated third-order moment. We use the phase scrambling bootstrap method to give a nonparametric estimate of the variance of our test statistic under the null hypothesis. Using a simulation study, we demonstrate that the test obtains its target significance level, with large power, when compared to an existing standard parametric test that uses the bispectrum. Further we show how the proposed test can be used to identify the source of nonlinearity due to interactions at specific frequencies. We also investigate implications for heuristic diagnosis of nonstationarity.

Effect of nitrogen supply on leaf appearance, leaf growth, leaf nitrogen economy and photosynthetic capacity in maize (Zea mays L.)

Leaf area growth and nitrogen concentration per unit leaf area, N-a (g m(-2) N) are two options plants can use to adapt to nitrogen limitation. Previous work indicated that potato (Solanum tuberosum L.) adapts the size of leaves to maintain Na and photosynthetic capacity per unit leaf area. This paper reports on the effect of N limitation on leaf area production and photosynthetic capacity in maize, a C4 cereal. Maize was grown in two experiments in pots in glasshouses with three (0.84-6.0 g N pot(-1)) and five rates (0.5-6.0 g pot(-1)) of N. Leaf tip and ligule appearance were monitored and final individual leaf area was determined. Changes with leaf age in leaf area, leaf N content and light-saturated photosynthetic capacity, P a,, were measured on two leaves per plant in each experiment. The final area of the largest leaf and total plant leaf area differed by 16 and 29% from the lowest to highest N supply, but leaf appearance rate and the duration of leaf expansion were unaffected. The N concentration of expanding leaves (N-a or %N in dry matter) differed by at least a factor 2 from the lowest to highest N supply. A hyperbolic function described the relation between P-max and N-a. The results confirm the 'maize strategy': leaf N content, photosynthetic capacity, and ultimately radiation use efficiency is more sensitive to nitrogen limitation than are leaf area expansion and light interception. The generality of the findings is discussed and it is suggested that at canopy level species showing the 'potato strategy' can be recognized from little effect of nitrogen supply on radiation use efficiency, while the reverse is true for species showing the 'maize strategy' for adaptation to N limitation. (c) 2004 Elsevier B.V. All rights reserved.

A Bethe ansatz solvable model for superpositions of Cooper pairs and condensed molecular bosons

We introduce a general Hamiltonian describing coherent superpositions of Cooper pairs and condensed molecular bosons. For particular choices of the coupling parameters, the model is integrable. One integrable manifold, as well as the Bethe ansatz solution, was found by Dukelsky et al. [J. Dukelsky, G.G. Dussel, C. Esebbag, S. Pittel, Phys. Rev. Lett. 93 (2004) 050403]. Here we show that there is a second integrable manifold, established using the boundary quantum inverse scattering method. In this manner we obtain the exact solution by means of the algebraic Bethe ansatz. In the case where the Cooper pair energies are degenerate we examine the relationship between the spectrum of these integrable Hamiltonians and the quasi-exactly solvable spectrum of particular Schrodinger operators. For the solution we derive here the potential of the Schrodinger operator is given in terms of hyperbolic functions. For the solution derived by Dukelsky et al., loc. cit. the potential is sextic and the wavefunctions obey PT-symmetric boundary conditions. This latter case provides a novel example of an integrable Hermitian Hamiltonian acting on a Fock space whose states map into a Hilbert space of PE-symmetric wavefunctions defined on a contour in the complex plane. (c) 2006 Elsevier B.V. All rights reserved.

Using ancillary statistics in on-line learning algorithms

Neural networks are usually curved statistical models. They do not have finite dimensional sufficient statistics, so on-line learning on the model itself inevitably loses information. In this paper we propose a new scheme for training curved models, inspired by the ideas of ancillary statistics and adaptive critics. At each point estimate an auxiliary flat model (exponential family) is built to locally accommodate both the usual statistic (tangent to the model) and an ancillary statistic (normal to the model). The auxiliary model plays a role in determining credit assignment analogous to that played by an adaptive critic in solving temporal problems. The method is illustrated with the Cauchy model and the algorithm is proved to be asymptotically efficient.