"Set Inference in Latent Variables Models"

We propose a methodology for constructing valid confidence regions in incomplete models with latent variables satisfying moment equality restrictions. These include moment equality and inequality models with latent variables. The confidence regions are obtained by inverting tests based on the characterization of the identified set derived in Ekeland, Galichon, and Henry (2010). A valid boot- strap approximation of the distribution of the test statistic is derived under mild conditions and the confidence regions are shown to have correct asymptotic size.

Lattice Diagram polynomials in one set of variables

The space $M_{\mu/i,j}$ spanned by all partial derivatives of the lattice polynomial $\Delta_{\mu/i,j}(X;Y)$ is investigated in math.CO/9809126 and many conjectures are given. Here, we prove all these conjectures for the $Y$-free component $M_{\mu/i,j}^0$ of $M_{\mu/i,j}$. In particular, we give an explicit bases for $M_{\mu/i,j}^0$ which allow us to prove directly the central {\sl four term recurrence} for these spaces.Comment: 15 page

A Set of Statistical Variables for Hydrodynamic Flow

Through a discussion of some typical unsteady hydrodynamic flows, we argue that the time averaged hydrodynamic functions at each point give a rather sparse filling of the local jet space. This situation then suggests a set of time dependent probability functions that are shown to give evolution uniquely defined by the Navier-Stokes equations through a set of "differential distribution equations." The closure relations are therefore unique and have no ad hoc characteristics. Annealing methods are proposed as a way to arrive at the stable stationary solutions corresponding to time averaged fluid flow with constant driving forces and fixed boundary conditions. Some applications of this method to quantum statistical mechanics and kinetic theory to higher orders are suggested

A Convenient Set of Comoving Cosmological Variables and Their Application

We present a set of cosmological variables, called "supercomoving variables," which are particularly useful for describing the gas dynamics of cosmic structure formation. For ideal gas with gamma=5/3, the supercomoving position, velocity, density, temperature, and pressure are constant in time in a uniform, isotropic, adiabatically expanding universe. Expressed in terms of these supercomoving variables, the cosmological fluid conservation equations and the Poisson equation closely resemble their noncosmological counterparts. This makes it possible to generalize noncosmological results and techniques to cosmological problems, for a wide range of cosmological models. These variables were initially introduced by Shandarin for matter-dominated models only. We generalize supercomoving variables to models with a uniform component corresponding to a nonzero cosmological constant, domain walls, cosmic strings, a nonclumping form of nonrelativistic matter (e.g. massive nettrinos), or radiation. Each model is characterized by the value of the density parameter Omega0 of the nonrelativistic matter component in which density fluctuation is possible, and the density parameter OmegaX of the additional, nonclumping component. For each type of nonclumping background, we identify FAMILIES within which different values of Omega0 and OmegaX lead to fluid equations and solutions in supercomoving variables which are independent of Omega0 and OmegaX. We also include the effects of heating, radiative cooling, thermal conduction, viscosity, and magnetic fields. As an illustration, we describe 3 familiar cosmological problems in supercomoving variables: the growth of linear density fluctuations, the nonlinear collapse of a 1D plane-wave density fluctuation leading to pancake formation, and the Zel'dovich approximation.Comment: 38 pages (AAS latex) + 2 figures (postscript) combined in one gzip-ed tar file. Identical to original posted version, except for addition of 2 references. Monthly Notices of the R.A.S., in pres

Facets of a mixed-integer bilinear covering set with bounds on variables

We derive a closed form description of the convex hull of mixed-integer bilinear covering set with bounds on the integer variables. This convex hull description is determined by considering some orthogonal disjunctive sets defined in a certain way. This description does not introduce any new variables, but consists of exponentially many inequalities. An extended formulation with a few extra variables and much smaller number of constraints is presented. We also derive a linear time separation algorithm for finding the facet defining inequalities of this convex hull. We study the effectiveness of the new inequalities and the extended formulation using some examples

Do local authorities set local fiscal variables to influence population flows?

The paper presents an empirical test of local fiscal competition in Norway based on the observation that interregional migration during the business cycle creates very different incentives for rural and urban municipalities to influence population movements. Panel-data evidence is presented suggesting that municipalities indeed attempt to control population flows. The sensitivity of municipal spending and revenue decisions to population movements varies between municipalities in a way that is consistent with the municipalities' incentives to influence location decisions of households.Fiscal competition; Local government

Inference in Additively Separable Models With a High-Dimensional Set of Conditioning Variables

This paper studies nonparametric series estimation and inference for the effect of a single variable of interest x on an outcome y in the presence of potentially high-dimensional conditioning variables z. The context is an additively separable model E[y|x, z] = g0(x) + h0(z). The model is high-dimensional in the sense that the series of approximating functions for h0(z) can have more terms than the sample size, thereby allowing z to have potentially very many measured characteristics. The model is required to be approximately sparse: h0(z) can be approximated using only a small subset of series terms whose identities are unknown. This paper proposes an estimation and inference method for g0(x) called Post-Nonparametric Double Selection which is a generalization of Post-Double Selection. Standard rates of convergence and asymptotic normality for the estimator are shown to hold uniformly over a large class of sparse data generating processes. A simulation study illustrates finite sample estimation properties of the proposed estimator and coverage properties of the corresponding confidence intervals. Finally, an empirical application to college admissions policy demonstrates the practical implementation of the proposed method