MATHEMATICAL ENGINEERING TECHNICAL REPORTS The Tube Method for the Moment Index in Projection Pursuit
نویسندگان
چکیده
The projection pursuit index defined by a sum of squares of the third and the fourth sample cumulants is known as the moment index proposed by Jones and Sibson [14]. Limiting distribution of the maximum of the moment index under the null hypothesis that the population is multivariate normal is shown to be the maximum of a Gaussian random field with a finite Karhunen-Loève expansion. An approximate formula for tail probability of the maximum, which corresponds to the p-value, is given by virtue of the tube method through determining Weyl’s invariants of all degrees and the critical radius of the index manifold of the Gaussian random field.
منابع مشابه
The tube method for the moment index in projection pursuit
The projection pursuit index defined by a sum of squares of the third and the fourth sample cumulants is known as the moment index proposed by Jones and Sibson (1987). The limiting distribution of the maximum of the moment index under the null hypothesis that the population is multivariate normal is shown to be the maximum of a Gaussian random field with a finite Karhunen-Loève expansion. An ap...
متن کاملانجام یک مرحله پیش پردازش قبل از مرحله استخراج ویژگی در طبقه بندی داده های تصاویر ابر طیفی
Hyperspectral data potentially contain more information than multispectral data because of their higher spectral resolution. However, the stochastic data analysis approaches that have been successfully applied to multispectral data are not as effective for hyperspectral data as well. Various investigations indicate that the key problem that causes poor performance in the stochastic approaches t...
متن کاملApplicability of damage indices for detection of cracking in steel moment connections
Analytical detection of cracking in connections of steel moment resisting frames using simple damage indices is important since these cracks are not visible unless the connections are uncovered. In this paper, applicability of three cumulative damage indices for detection of cracking in a cover plate welded moment connection is investigated. The damage indices considered in this study are based...
متن کاملExperimental Study of Heat Transfer Rate in a Shell and Tube Heat Exchanger with Air Bubble Injection (TECHNICAL NOTE)
Shell and tube heat exchangers are widely being used in many of industrial and power engineering applications. Different techniques have been employed in order to enhance the performance of the heat exchanger. Air bubble injection is one method to increase the turbulence of the flowing fluids which in turn enhance the heat transfer performance. Injecting air bubbles is one of the promising tech...
متن کاملFlexural Performance of High-strength Prestressed Concrete-encased Concrete-filled Steel Tube Sections
The sections composed of concrete and steel, which include concrete-encased concrete-filled tubes, generally have defects due to the low tensile strength of concrete. Therefore, an appropriate method was used for the combination of concrete-filled tubes (CFT) and prestressing strands which is encased in concrete. The conventional design guidelines are commonly developed for materials with norma...
متن کامل