Events
Department of Mathematics and Statistics
Texas Tech University
This paper studies the estimation of multi-dimensional heterogeneous parameters in a nonlinear panel data model with endogeneity. These heterogeneous parameters are modeled with group patterns. Through estimating multiple memberships for each unit, the proposed method is robust to limited information from a subset of clusters: either due to sparse interactions of characteristics or weak identification of some combinations of heterogeneous parameters. We estimate the memberships along with the group-specific and common parameters in a nonlinear GMM framework and derive their large sample properties. Finally, we apply this approach to the estimation of heterogeneous firm-level production functions parameters which are converted into markup estimates.
Zoom Meeting link
Meeting ID: 904 545 1744
Differential categories, introduced in last week's talk by Jean-Simon Pacaud Lemay, provide a categorical framework for the algebraic foundations of differential calculus. Within this setting we can capture familiar notions such as derivations, Kähler differentials, differential algebras and de Rham cohomology. Along this line, in this talk, we will show how to define differential graded algebras in a differential category. In the case of polynomial differentiation, this construction recovers the classical commutative differential graded algebras, while for smooth functions it yields differential graded $C^\infty$-rings in the sense of Dmitri Pavlov. To further justify our definition, we will explain how the monad of a differential category can be lifted to its category of chain complexes and how the algebras of the lifted monad correspond precisely to differential graded algebras of the base category, with the free ones given by the de Rham complexes. Finally, we will discuss how the category of chain complexes of a differential category is itself a differential category, pointing towards the prospect of differential dg-categories. This is joint work with Jean-Simon Pacaud Lemay.We study a class of rotational hypersurfaces with five parameters in the six-dimensional Euclidean space $\mathbb{E}^6$. We derive the associated curvature functions and examine the geometric properties of these hypersurfaces. Furthermore, we apply the Laplace--Beltrami operator and determine the conditions under which the relation $\Delta \mathbf{x} = \mathcal{B} \mathbf{x}$ holds, where $\mathcal{B}$ is a $6 \times 6$ matrix.
 | Wednesday
Oct. 1
|
| Algebra and Number Theory
No Seminar
|
Abstract Motivated by nonlinear approximation results for classes of parametric partial differential equations (PDEs), we seek to better understand so-called library approximations to analytic functions of countably infinite number of variables. Rather than approximating a function of interest by a single space, a library approximation uses a collection of spaces and the best space may be chosen for any point in the domain. In the setting of this paper, we use a specific library which consists of local Taylor approximations on sufficiently small rectangular subdomains of the (rescaled) parameter domain Y := [−1, 1]^N. When the function of interest is the solution of a certain type of parametric PDE, recent results prove an upper bound on the number of spaces required to achieve a desired target accuracy. In this talk, we discuss a similar result for a more general class of functions with anisotropic analyticity. In this way we show both where the previous theory depends on being in the setting of parametric PDEs with affine diffusion coefficients, and prove a more general result outside of this setting.
When: 4:00 pm (Lubbock's local time is GMT -5)
Where: room Math 011 (Math Basement)
ZOOM details:
- Choice #1: use this
Direct Link that embeds meeting ID and passcode
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* Meeting ID: 915 2866 2672
* Passcode: applied
abstract noon CDT (UT-5)
Zoom link available from Dr. Brent Lindquist upon request.