Approximate Null Distribution of the Largest Root in Multivariate Analysis.
نویسنده
چکیده
The greatest root distribution occurs everywhere in classical multivariate analysis, but even under the null hypothesis the exact distribution has required extensive tables or special purpose software. We describe a simple approximation, based on the Tracy-Widom distribution, that in many cases can be used instead of tables or software, at least for initial screening. The quality of approximation is studied, and its use illustrated in a variety of setttings.
منابع مشابه
Some New Tables of the Largest Root of a Matrix in Multivariate Analysis: a Computer Approach from 2 to 6
The distribution of the non-null characteristic roots of a matrix derived from sample observations taken from multivariate normal populations is of fundamental of importance in multivariate analysis. The Fisher-Girshick-Shu-Roy distribution (1939), which has interested statisticians for more than 6 decades, is revisited. Instead of using K.C.S. Pillai’s method by neglecting higher order terms o...
متن کاملEnergy Detection of Unknown Signals over Composite multipath/shadowing Fading Channels
In this paper, the performance analysis of an energy detector is exploited over composite multipath/shadowing fading channels, which is modeled by Rayleigh-lognormal (RL) distribution. Based on an approximate channel model which was recently proposed by the author, the RL envelope probability density function (pdf) is approximated by a finite sum of weighted Rayleigh pdfs. Relying on this inter...
متن کاملRoy’s largest root test under rank-one alternatives
Roy's largest root is a common test statistic in multivariate analysis, statistical signal processing and allied fields. Despite its ubiquity, provision of accurate and tractable approximations to its distribution under the alternative has been a longstanding open problem. Assuming Gaussian observations and a rank-one alternative, or concentrated noncentrality, we derive simple yet accurate app...
متن کاملAccurate Inference for the Mean of the Poisson-Exponential Distribution
Although the random sum distribution has been well-studied in probability theory, inference for the mean of such distribution is very limited in the literature. In this paper, two approaches are proposed to obtain inference for the mean of the Poisson-Exponential distribution. Both proposed approaches require the log-likelihood function of the Poisson-Exponential distribution, but the exact for...
متن کاملA novel trace test for the mean parameters in a multivariate growth curve model
A trace test for the mean parameters of the Growth Curve Model is proposed. It is constructed using the restricted maximum likelihood followed by an estimated likelihood ratio approach. The statistic reduces to the Lawley-Hotelling’s trace test for the classical multivariate analysis of variance model. Our test statistic is, therefore, a natural extension of the classical trace test. We show th...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- The annals of applied statistics
دوره 3 4 شماره
صفحات -
تاریخ انتشار 2009