Statistical inference in a panel data semiparametric regression model with serially correlated errors

We consider a panel data semiparametric partially linear regression model with an unknown vector β of regression coefficients, an unknown nonparametric function g(·) for nonlinear component, and unobservable serially correlated errors. The correlated errors are modeled by a vector autoregressive process which involves a constant intraclass correlation. Applying the pilot estimators of β and g(·), we construct estimators of the autoregressive coefficients, the intraclass correlation and the error variance, and investigate their asymptotic properties. Fitting the error structure results in a new semiparametric two-step estimator of β, which is shown to be asymptotically more efficient than the usual semiparametric least squares estimator in terms of asymptotic covariance matrix. Asymptotic normality of this new estimator is established, and a consistent estimator of its asymptotic covariance matrix is presented. Furthermore, a corresponding estimator of g(·) is also provided. These results can be used to make asymptotically efficient statistical inference. Some simulation studies are conducted to illustrate the finite sample performances of these proposed estimators.     

L-Factor of Irreducible x1×x2(×)σ

The L-factor of irreducible x1×x2(×)σ defined by Piatetski-Shapiro is computed by using non-split Bessel functional.     

Surfaces of M_k^2\times \mathbb R invariant under a one-parameter group of isometries

We assume that an immersed constant mean curvature surface ${\varSigma } \looparrowright {M_k} \times \mathbb R $ satisfies a relation involving the mean curvature, the Gaussian curvature and the angle that the unit vector of the factor $\mathbb R $ makes with the normal to the surface. This relation, although given initially in its pointwise form, can be shown to be equivalent to an integral relation. From the assumed relation, it follows that $\varSigma $ is invariant under a one-parameter group of isometries of $M_k^2\times \mathbb{R }$ which are induced by the isometries of $M_k^2$  . An application is made to describe qualitatively those surfaces for which the Abresch-Rosenberg complex quadratic form vanishes.     

Rank-one convex hulls in \mathbb{R}^{2\times2}

We study the rank-one convex hull of compact sets . We show that if K contains no two matrices whose difference has rank one, and if K contains no four matrices forming a T ₄ configuration, then the rank-one convex hull K ^rc is equal to K. Furthermore, we give a simple numerical criterion for testing for T ₄ configurations. Received: 20 August 2003, Accepted: 3 March 2004, Published online: 12 May 2004 Mathematics Subject Classification (2000): 49J45, 52A30 An erratum to this article can be found at     

A Construction of Partial Difference Sets in {\mathbb{Z}}_{p^{2 \times } } {\mathbb{Z}}_{p^{2 \times \cdot \cdot \cdot \times } } {\mathbb{Z}}_{p^2 }

In this paper, we give a construction of partial difference sets in _p ² x _p ² x ... x _p ²using some finite local rings.Dedicated to Hanfried Lenz on the occasion of his 80th birthdayThe work of this paper was done when the authors visited the University of Hong Kong.     

Surfaces in $${\mathbb{S}^2\times\mathbb{R}}$$ with a canonical principal direction

We show a way to choose nice coordinates on a surface in and use this to study minimal surfaces. We show that only open parts of cylinders over a geodesic in are both minimal and flat. We also show that the condition that the projection of the direction tangent to onto the tangent space of the surface is a principal direction, is equivalent to the condition that the surface is normally flat in . We present classification theorems under the extra assumption of minimality or flatness. J. Fastenakels is a research assistant of the Research Foundation—Flanders (FWO). J. Van der Veken is a postdoctoral researcher supported by the Research Foundation—Flanders (FWO). This work was partially supported by project G.0432.07 of the Research Foundation—Flanders (FWO).     

Statistical inference in constrained latent class models for multinomial data based on $$\phi $$-divergence measures

In this paper we explore the possibilities of applying \(\phi \)-divergence measures in inferential problems in the field of latent class models (LCMs) for multinomial data. We first treat the problem of estimating the model parameters. As explained below, minimum \(\phi \)-divergence estimators (M\(\phi \)Es) considered in this paper are a natural extension of the maximum likelihood estimator (MLE), the usual estimator for this problem; we study the asymptotic properties of M\(\phi \)Es, showing that they share the same asymptotic distribution as the MLE. To compare the efficiency of the M\(\phi \)Es when the sample size is not big enough to apply the asymptotic results, we have carried out an extensive simulation study; from this study, we conclude that there are estimators in this family that are competitive with the MLE. Next, we deal with the problem of testing whether a LCM for multinomial data fits a data set; again, \(\phi \)-divergence measures can be used to generate a family of test statistics generalizing both the classical likelihood ratio test and the chi-squared test statistics. Finally, we treat the problem of choosing the best model out of a sequence of nested LCMs; as before, \(\phi \)-divergence measures can handle the problem and we derive a family of \(\phi \)-divergence test statistics based on them; we study the asymptotic behavior of these test statistics, showing that it is the same as the classical test statistics. A simulation study for small and moderate sample sizes shows that there are some test statistics in the family that can compete with the classical likelihood ratio and the chi-squared test statistics.     

Metrics with nonnegative curvature on {S^2 \times \mathbb{R}^4}

We study nonnegatively curved metrics on S²×\mathbbR⁴{S^2\times\mathbb{R}^4}. First, we prove rigidity theorems for connection metrics; for example, the holonomy group of the normal bundle of the soul must lie in a maximal torus of SO(4). Next, we prove that Wilking’s almost-positively curved metric on S ² × S ³ extends to a nonnegatively curved metric on S²×\mathbbR⁴{S^2\times\mathbb{R}^4} (so that Wilking’s space becomes the distance sphere of radius 1 about the soul). We describe in detail the geometry of this extended metric.     

L-functions on $GSp_2 \times Gl_2$ of mixed weights

In this paper we investigate the properties of the automorphic (standard) L-function on for the case, where the automorphic form comes from a holomorphic Siegel modular form and a holomorphic elliptic modular form. To cover arbitrary weights, we use two different types of differential operators. Received March 23, 1999 / Published online July 20, 2000     

缺项算子矩阵的本性谱

Let =(A C X B)be a 2×2 operator matrix acting on the Hilbert space н( )κ.For given A ∈B (H),B ∈B(K)and C ∈B(K,H)the set Ux∈B(H,к)σe(Mx)is determined,where σe(T)denotes the essential spectrum.     

Statistical inference with partial prior information based on a Gauss-type inequality

Potter and Anderson [1] have developed a Bayesian decision procedure requiring the specification of a class of prior distributions restricted to have a minimal probability content for a given subset of the parameter space. They do not, however, provide a method for the selection of that subset. We show how a generalization of Gauss' inequality can be used to determine the relevant parameter subset.     

Blocks with Defect Group \boldsymbol{Q_{2^n}\times C_{2^m}} and \boldsymbol{SD_{2^n}\times C_{2^m}}

We determine the numerical invariants of blocks with defect group $Q_{2^n}\times C_{2^m}$ and $SD_{2^n}\times C_{2^m}$ , where $Q_{2^n}$ denotes a quaternion group of order 2 ⁿ , $C_{2^m}$ denotes a cyclic group of order 2 ^m , and $SD_{2^n}$ denotes a semidihedral group of order 2 ⁿ . This generalizes Olsson’s results for m?=?0. As a consequence, we prove Brauer’s k(B)-Conjecture, Olsson’s Conjecture, Brauer’s Height-Zero Conjecture, the Alperin–McKay Conjecture, Alperin’s Weight Conjecture and Robinson’s Ordinary Weight Conjecture for these blocks. Moreover, we show that the gluing problem has a unique solution in this case. This paper follows (and uses) (Sambale, J Pure Appl Algebra 216:119–125, 2012; Proc Amer Math Soc, 2012).     

Classification of rotational special Weingarten surfaces of minimal type in {\mathbb{S}^2 \times \mathbb{R}} and {\mathbb{H}^2 \times \mathbb{R}}

In this paper we classify the complete rotational special Weingarten surfaces in ${\mathbb{S}^2 \times \mathbb{R}}$ and ${\mathbb{H}^2 \times \mathbb{R}}$ ; i.e. rotational surfaces in ${\mathbb{S}^2 \times \mathbb{R}}$ and ${\mathbb{H}^2 \times \mathbb{R}}$ whose mean curvature H and extrinsic curvature K _e satisfy H = f(H ² ? K _e ), for some function ${f \in \mathcal{C}^1([0,+\infty))}$ such that f(0) = 0 and 4x(f′(x))² < 1 for any x ≥ 0. Furthermore we show the existence of non-complete examples of such surfaces.     

Bases of admissible inference rules for table modal logics of depth 2

In the present article, we prove the theorem which states that every table modal logic λ of depth 2 over S4 has a finite basis of admissible inference rules. In addition, it is established that a finite algebra ℒ belongs to F_ω(λ)^Q iff there exist numbers n₁…, n_k such that (Lemma 5). Let F be a λ-frame of depth 2 and b a cluster of the second layer in F. We show that for any n₁,…,n_k, there exist no p-morphisms from (F_n1⊔…⊔F_nk)⁺ a local component K (b) such that, for any n, there is no p-morphism from any local component of F_n onto K (b) (Lemma 6). Translated fromAlgebra i Logika, Vol. 35, pp. 612–622, September–October, 1996.     

$K_v$的最大$K_2K_3$填充设计

Abstract Let Kv be the complete graph on v vertices, and G a finite simple undirected graph without isolated vertices. A G-packing of Kv, denoted by （v, G, 1）-packing, is a pair （X,A） where X is the vertex set of K＋ and ＋4 is a family of edge-disjoint subgraphs isomorphic to G in Kv. In this paper, the maximum number of subgraphs in a （v, G, 1）-packing is determined when G is K2 x K3, the Cartesian product of K2 and K3, leaving two orders undetermined. This design originated from the use of DNA library screening.     

Global convergence of an isentropic Euler-Poisson system in $\R^+ \times \R^d$

We prove the global-in-time convergence of an Euler-Poisson system near a constant equilibrium state in the whole space $\R^d$, as physical parameters tend to zero. The result follows from the uniform global existence of smooth solutions by means of energy estimates together with compactness arguments. For this purpose, we establish uniform estimates for $\dive \,u$ and $\curle \,u$ instead of $\nabla u$.     

Using bimodal kernel for inference in nonparametric regression with correlated errors

For nonparametric regression model with fixed design, it is well known that obtaining a correct bandwidth is difficult when errors are correlated. Various methods of bandwidth selection have been proposed, but their successful implementation critically depends on a tuning procedure which requires accurate information about error correlation. Unfortunately, such information is usually hard to obtain since errors are not observable. In this article a new bandwidth selector based on the use of a bimodal kernel is proposed and investigated. It is shown that the new bandwidth selector is quite useful for the tuning procedures of various other methods. Furthermore, the proposed bandwidth selector itself proves to be quite effective when the errors are severely correlated.