Fixed Size Confidence Regions for Parameters of Stationary Processes Based on a Minimum Contrast Estimator

For parameters of stationary processes with zero mean and spectral density, sequential procedures are proposed for constructing fixed size confidence ellipsoidal regions for unknown parameters using a minimum contrast estimator. The confidence ellipsoids are shown to be asymptotically consistent and the associated stopping rules are shown to be asymptotically efficient as the size of the region becomes small when the assumed parametric model is correct. Monte Carlo simulations are given to investigate the performance of our proposed sequential procedures.

Asymptotically efficient estimation of the change point for semiparametric GARCH models

GARCH process, change point, maximum likelihood estimator, Bayesian estimator, asymptotic efficiency

Sufficient conditions for open manifolds to be diffeomorphic to Euclidean spaces

Let M be a complete non-compact connected Riemannian n-dimensional manifold. We first prove that, for any fixed point p in M, the radial Ricci curvature of M at p is bounded from below by the radial curvature function of some non-compact n-dimensional model. Moreover, we then prove, without the pointed Gromov-Hausdorff convergence theory, that, if model volume growth is sufficiently close to 1, then M is diffeomorphic to Euclidean n-dimensional space. Hence, our main theorem has various advantages of the Cheeger-Colding diffeomorphism theorem via the Euclidean volume growth. Our main theorem also contains a result of do Carmo and Changyu as a special case.Comment: This version 3 (13 pages, no figures) is a version to appear in Differential Geometry and its Application

Asymptotic Efficient Estimation of the Change Point in Time Series Regression Models

This paper discusses the problem of estimating unknown change point in the trend function of a time series regression model. The error process considered here is a Gaussian stationary process with spectral density. The asymptotic properties of quasi maximum likelihood (QMLE) and quasi Bayes (QBE) estimators are studied. Consistency, limiting distributions and convergence of higher order moments of the estimators are obtained. It is also shown that the QBE is asymptotically efficient, and that the QMLE is not so general.Time series regression, change point, quasi maximum likelihood estimator, quasi Byes estimator, asymptotic efficiency, Whittle likelihood

The connected components of the space of Alexandrov surfaces

Denote by $\mathcal{A}(\kappa)$ the set of all compact Alexandrov surfaces with curvature bounded below by $\kappa$ without boundary, endowed with the topology induced by the Gromov-Hausdorff metric. We determine the connected components of $\mathcal{A}(\kappa)$ and of its closure

A mixture transition distribution modeling for higher-order circular Markov processes

The stationary higher-order Markov process for circular data is considered. We employ the mixture transition distribution (MTD) model to express the transition density of the process on the circle. The underlying circular transition distribution is based on Wehrly and Johnson's bivariate joint circular models. The structures of the circular autocorrelation function together with the circular partial autocorrelation function are found to be similar to those of the autocorrelation and partial autocorrelation functions of the real-valued autoregressive process when the underlying binding density has zero sine moments. The validity of the model is assessed by applying it to some Monte Carlo simulations and real directional data

Complete noncompact Alexandrov spaces of nonnegative curvature

1. Introduction. An Alexandrov space X with curvature bounded below is a length space with the property that the Alexandrov-Toponogov comparison theorem holds for all small geodesic triangles. It is interesting to investigate the properties of finite (Hausdorff) dimensional Alexandrov spaces of nonnegative curvature in connection with Riemannian geometry and Hausdorff convergence as well. In The Toponogov splitting theorem holds for complete noncompact Alexandrov spaces of nonnegative curvature. It was discussed in [10] for length spaces of nonnegative Toponogov curvature and in The purpose of this article is to show that some of the Riemannian results can be extended to Alexandrov spaces. We first establish the end structure of complete noncompact Alexandrov spaces of nonnegative curvature. We next provide a natural extension of the Myers-Toponogov compactness theorem for complete Alexandrov spaces of nonnegative curvature

Labor Due Diligence: An essential tool in mergers and acquisitions

Presently, labor audit, also known as labor due diligence, is a very important tool used in theprocess of merges and acquisitions. According to the results obtained, negotiations on the final price of the merge or acquisition will depend on it.In the present article, the author explains the procedure, emphasizing the importance that its correct application might have in any merger or acquisition process, being adetermining factor for the process’ success.En la actualidad, la auditoria laboral, tambiénconocida como due diligence laboral, es una herramienta  imprescindible cuando  se  presentan casos de fusiones y adquisiciones. Desus resultados dependerá, en gran medida, el futuro de las negociaciones que preceden auna posible reorganización societaria.En el presente artículo, la autora explica el procedimiento del due diligence laboral, resaltando las implicancias que su correcto desarrollo puede tener en todo proceso de fusión o adquisición, siendo un factor deter-minante para su éxito