Bootstrap Statistical Tests of Rank Determination for System Identification

Identification in the context of multivariate state space modelling involves the specification of the dimension of the state vector. One identification approach requires an estimate of the rank of a Hankel matrix. The most frequently used approaches of rank determination rely on information criteria methods. This paper evaluates the performance of some asymptotic tests of rank determination together with their bootstrapped versions against standard information criteria methods. This study is conducted through simulation experiments. Results show that the bootstrapped procedures significantly improve upon the performance of the corresponding asymptotic tests, and are proved better than standard Information Criterion methods.Rank, Bootstrap, Monte Carlo, System identification, Hankel operator

Statistical tests and estimators of the rank of a matrix and their applications in econometric modelling

Testing and estimating the rank of a matrix of estimated parameters is key in a large variety of econometric modelling scenarios. This paper describes general methods to test for and estimate the rank of a matrix, and provides details on a variety of modelling scenarios in the econometrics literature where such methods are required. Four different methods to test the true rank of a general matrix are described, as well as one method that can handle the case of a matrix subject to parameter constraints associated with defineteness structures. The technical requirements for the implementation of the tests of rank of a general matrix differ and hence there are merits to all of them that justify their use in applied work. Nonetheless, we review available evidence of their small sample properties in the context of different modelling scenarios where all, or some, are applicable. JEL Classification: C12, C15, C32model specification, Multiple time series, tests of rank

Statistical Tests of the Rank of a Matrix and Their Applications in Econometric Modelling

Testing the rank of a matrix of estimated parameters is key in a large variety of econometric modelling scenarios. This paper describes general methods to test for the rank of a matrix, and provides details on a variety of modelling scenarios in the econometrics literature where these tests are required.Multiple time series, Model specification, Tests of rank

Ultrastructure of adhesion and movement of the tetraspores of Gelidium Lamour (Geldiaceae; Rhodophyta)

The outer part of the tetraspora cell wall in Gelidium crinale (Turner) J.V. Lamour. and G. spathulatum (Kutz.) Bornet is morphologically described in relation to the movements and displacement of these spores when they settle on a substratum. We also describe the mechanism of adhesión and the transformations undergone by this mechanism over time. The cell wall shows a network of fibrillar threads embedded in abundant mucilage. The deformations that tetraspores undergo show that the cell wall is relatively elastic

Algorithmic Perception of Vertices in Sketched Drawings of Polyhedral Shapes

In this article, visual perception principles were used to build an artificial perception model aimed at developing an algorithm for detecting junctions in line drawings of polyhedral objects that are vectorized from hand-drawn sketches. The detection is performed in two dimensions (2D), before any 3D model is available and minimal information about the shape depicted by the sketch is used. The goal of this approach is to not only detect junctions in careful sketches created by skilled engineers and designers but also detect junctions when skilled people draw casually to quickly convey rough ideas. Current approaches for extracting junctions from digital images are mostly incomplete, as they simply merge endpoints that are near each other, thus ignoring the fact that different vertices may be represented by different (but close) junctions and that the endpoints of lines that depict edges that share a common vertex may not necessarily be close to each other, particularly in quickly sketched drawings. We describe and validate a new algorithm that uses these perceptual findings to merge tips of line segments into 2D junctions that are assumed to depict 3D vertices

Estimating the rank of the spectral density matrix

The rank of the spectral density matrix conveys relevant information in a variety of statistical modelling scenarios. This note shows how to estimate the rank of the spectral density matrix at any given frequency. The method presented is valid for any hermitian positive de?nite matrix estimate that has a normal asymptotic distribution with a covariance matrix whose rank is known. JEL Classification: C12, C32, C52Spectral Density Matrix, Tests of Rank

Aerodynamic data banks for Clark-Y, NACA 4-digit and NACA 16-series airfoil families

With the renewed interest in propellers as means of obtaining thrust and fuel efficiency in addition to the increased utilization of the computer, a significant amount of progress was made in the development of theoretical models to predict the performance of propeller systems. Inherent in the majority of the theoretical performance models to date is the need for airfoil data banks which provide lift, drag, and moment coefficient values as a function of Mach number, angle-of-attack, maximum thickness to chord ratio, and Reynolds number. Realizing the need for such data, a study was initiated to provide airfoil data banks for three commonly used airfoil families in propeller design and analysis. The families chosen consisted of the Clark-Y, NACA 16 series, and NACA 4 digit series airfoils. The various component of each computer code, the source of the data used to create the airfoil data bank, the limitations of each data bank, program listing, and a sample case with its associated input-output are described. Each airfoil data bank computer code was written to be used on the Amdahl Computer system, which is IBM compatible and uses Fortran

Relevant economic issues concerning the optimal rate of inflation

JEL Classification: D60, E31, E41, E61, H21deflation, downward nominal rigidities, inflation costs and benefits, inflation differentials, price stability