In this chapter we study GMM estimation of linear panel data models. Several different types of models are considered, including the linear regression model with strictly or weakly exogenous regressors, the simultaneous regression model, and a dynamic linear model containing a lagged dependent variable as a regressor. In each case, different assumptions about the exogeneity of the explanatory v...

In this article we discuss the geometric quantization on a certain type of infinite dimensional super-disc. Such systems are quite natural when we analyze coupled bosons and fermions. The large-N limit of a system like that corresponds to a certain super-homogeneous space. First, we define an example of a superhomogeneous manifold: a super-disc. We show that it has a natural symplectic form, it...

Let G be a connected, compact, semisimple Lie group. It is known that for a compact closed orientable surface Σ of genus l > 1, the order of the group H(Σ, π1(G)) is equal to the number of connected components of the space Hom(π1(Σ), G)/G which can also be identified with the moduli space of gauge equivalence classes of flat G-bundles over Σ. We show that the same statement for a closed compact...

We consider a general GMM framework where weaker patterns of identi cation may arise: typically, the data generating process is allowed to depend on the sample size. We are interested in providing inference about the identi cation of the structural parameter. First, we propose a consistent Hausman-type test to test whether additional moment conditions enhance its identi cation. Failing to rejec...

The deformed Hermitian Yang-Mills (dHYM) equation is a special Lagrangian type condition in complex geometry. It requires the analogue of phase, defined for Chern connections on holomorphic line bundles using background K\"ahler metric, to be constant. In this paper we introduce and study dHYM equations with variable metric. These are coupled involving both phase radius function, at same time. ...

Let G be an infinite connected graph with vertex set V. {Sn:n∈N0} the simple random walk on and let {ξ(v):v∈V} a collection of i.i.d. variables which are independent walk. Define in scenery as Tn= ∑k=0nξ(Sk), normalization Vn=(∑k=0nξ2(Sk))1∕2 Ln,2=(∑v∈Vln2(v))1∕2. For G=Zd G=Td, d-ary tree, we provide large deviations results for self-normalized process Tnn∕(L n,2Vn) under only finite moment as...

When n is odd, a cohomology of type Hochschild for n-ary partially associative algebras has been defined in Gnedbaye’s thesis. Unfortunately, the cohomology definition is not valid when n is even. This fact is found again in the computations of the n-ary partially associative free algebra. In this work, we define in a first time two approachs of an Hochschild cohomology for n-ary partially asso...

Let G be a compact connected Lie group, and (M,ω) a compact Hamiltonian Gspace with moment map μ. We give a surjectivity result which expresses the K-theory of the symplectic quotient M//G in terms of the equivariant K-theory of the original manifold M , under certain technical conditions on μ. This result is a natural K-theoretic analogue of the Kirwan surjectivity theorem in symplectic geomet...

Let M be a connected smooth G-manifold, where G is a connected compact Lie group. In this paper, we first study the relation between π1 (M) and π1 (M/G). Then we particularly focus on the case when M is a connected Hamiltonian G-manifold with an equivariant moment map φ. In [13], for compact M , we proved that π1 (M) = π1 (M/G) = π1 (Ma) for all a ∈ image(φ), where Ma is the symplectic quotient...