A note on modelling cross correlations: hyperbolic secant regression
نویسنده
چکیده
The problem of determining if a bivariate normal correlation changes with respect to time or some other covariate is considered. It is assumed that the means and standard deviations of the normal random variables can be consistently estimated from the entire data run, and do not need to be re-estimated for each covariate value. A new estimator of a bivariate normal correlation is given that has useful performance down to samples of size one. This allows regression type modelling of the correlation without unnecessary loss of resolution. The arc-tanh transformation of this estimator has a symmetric Fisher’s z-distribution about the arc-tanh correlation. A method of smoothing the correlation estimates is given using moving average smoothers of the sufficient statistics from which the correlation estimator is calculated.
منابع مشابه
A meshless technique for nonlinear Volterra-Fredholm integral equations via hybrid of radial basis functions
In this paper, an effective technique is proposed to determine thenumerical solution of nonlinear Volterra-Fredholm integralequations (VFIEs) which is based on interpolation by the hybrid ofradial basis functions (RBFs) including both inverse multiquadrics(IMQs), hyperbolic secant (Sechs) and strictly positive definitefunctions. Zeros of the shifted Legendre polynomial are used asthe collocatio...
متن کاملAll-Optical THz OFDM Communications using Photonic Crystal Fibers
An all-optical Orthogonal Frequency Division Multiplexing communication system at 2 THz is modeled using photonic crystal fiber of length 1km, and the performance of four carrier waveforms hyperbolic secant, square of hyperbolic secant, square and sinusoidal is evaluated using standard metrics such as eye diagram and bit error rate. From the above mentioned valuations, one can deduce the minima...
متن کاملA Distribution Family Bridging the Gaussian and the Laplace Laws, Gram-Charlier Expansions, Kurtosis Behaviour, and Entropy Features
The paper devises a family of leptokurtic bell-shaped distributions which is based on the hyperbolic secant raised to a positive power, and bridges the Laplace and Gaussian laws on asymptotic arguments. Moment and cumulant generating functions are then derived and represented in terms of polygamma functions. The behaviour of shape parameters, namely kurtosis and entropy, is investigated. In add...
متن کاملTwo-sample scale rank procedures optimal for the generalized secant hyperbolic distribution
There are many linear rank tests for the two-sample dispersion problem presented in literature. However just a few of them, the simplest ones, are commonly used. These common tests are not efficient for many practical distributions and thus other simple tests need to be developed to serve a wider range of distributions. The generalized secant hyperbolic distribution, proposed by Vaughan in [9],...
متن کاملINTERPOLATION BY HYPERBOLIC B-SPLINE FUNCTIONS
In this paper we present a new kind of B-splines, called hyperbolic B-splines generated over the space spanned by hyperbolic functions and we use it to interpolate an arbitrary function on a set of points. Numerical tests for illustrating hyperbolic B-spline are presented.
متن کامل