The convergence of the empirical distribution of canonical correlation coefficients
نویسندگان
چکیده
Suppose that {Xjk, j = 1, · · · , p1; k = 1, · · · , n} are independent and identically distributed (i.i.d) real random variables with EX11 = 0 and EX 2 11 = 1, and that {Yjk, j = 1, · · · , p2; k = 1, · · · , n} are i.i.d real random variables with EY11 = 0 and EY 2 11 = 1, and that {Xjk, j = 1, · · · , p1; k = 1, · · · , n} are independent of {Yjk, j = 1, · · · , p2; k = 1, · · · , n}. This paper investigates the canonical correlation coefficients r1 ≥ r2 ≥ · · · ≥ rp1 , whose squares λ1 = r 1, λ2 = r 2, · · · , λp1 = r p1 are the eigenvalues of the matrix Sxy = A −1 x AxyA −1 y A T xy, where Ax = 1 n n ∑ k=1 xkx T k , Ay = 1 n n ∑ k=1 yky T k , Axy = 1 n n ∑
منابع مشابه
On the Canonical-Based Goodness-of-fit Tests for Multivariate Skew-Normality
It is well-known that the skew-normal distribution can provide an alternative model to the normal distribution for analyzing asymmetric data. The aim of this paper is to propose two goodness-of-fit tests for assessing whether a sample comes from a multivariate skew-normal (MSN) distribution. We address the problem of multivariate skew-normality goodness-of-fit based on the empirical Laplace tra...
متن کاملAlmost Sure Convergence Rates for the Estimation of a Covariance Operator for Negatively Associated Samples
Let {Xn, n >= 1} be a strictly stationary sequence of negatively associated random variables, with common continuous and bounded distribution function F. In this paper, we consider the estimation of the two-dimensional distribution function of (X1,Xk+1) based on histogram type estimators as well as the estimation of the covariance function of the limit empirical process induced by the se...
متن کاملAn Empirical Correlation for Estimation of the Thermal Conductivity of Saturated Liquid Refrigerants
Thermodynamic data on environmental refrigerants have attracted considerable interest in the optimization and design of heat compressors, exchangers and other refrigeration equipment. In this study, An optimization algorithm was used to obtain the constant parameters of the new empirical model by fitting them to the source databank. The model was used to calculate the constant coefficients of t...
متن کاملCanonical Analysis of the Relationship between Components of Professional Ethics and Dimensions of Social Responsibility
Background: Today, professional ethics and social responsibility play an important role in organizations. This study aimed canonical analysis of the relationship between components of professional ethics and social responsibility dimensions among the first high school teachers in the Naghadeh province. Method: This study, in terms of purpose is application, and in terms of data collec...
متن کاملConvergence of Density Expansions of Correlation Functions and the Ornstein-zernike Equation
Abstract. We prove convergence of the multi-body correlation function as a power series in the density. We work in the context of the cluster expansion in the canonical ensemble and we obtain bounds uniform in the volume and the number of particles. In the thermodynamic limit, the coefficients are characterized by sums over some class of two-connected graphs. We introduce the “direct correlatio...
متن کامل