LP.moment: Finds LP moments of a random variable or comoments of two...

In LPTime: LP Nonparametric Approach to Non-Gaussian Non-Linear Time Series Modelling

Description

Evaluates m LP moments of a random variable.
Estimates LP-comoment matrix of order m \times m between X and Y , i.e., covariance between the LP transformations of X and Y; where the random variables could be discrete or continuous.

Usage

LP.moment(x, m)
LP.comoment(x, y,zero.order = TRUE, m)

Arguments

x	The observations on the variable X.
y	The observations on the variable Y.
zero.order	Logical argument set to TRUE if zero-order LP comoments are required.
m	The number of LP moments to be found using LP.moment; or The order of LP - comoment matrix.

Details

LP moments of a general random variable (discrete or continuous) is defined as

\mbox{LP}[j;\, X] = \mbox{LP}[j, 0; X, X] = \mbox{E}[X \; T_{j}(X; X)].

LP comoments are the cross-covariance between higher-order orthonormal LP score functions T_j(X; X) and T_k(Y ; Y )

\mbox{LP}[j, k; X, Y ] = \mbox{E}[T_j(X; X)\,T_k(Y ; Y )].

Zero-order LP-comoments are defined as

\mbox{LP}[j, 0; X, Y] = \mbox{E}[T_j(X; X)\,Y],

and

\mbox{LP}[0, k; X, Y] = \mbox{E}[X\, T_k(Y; Y)].

Value

A vector of LP moments.
A matrix of LP co-moments between X and Y.

Author(s)

Subhadeep Mukhopadhyay

References

Mukhopadhyay S. and Parzen E. (2014). LP approach to statistical modeling.arXiv:1405.2601.

Parzen E. and Mukhopadhyay S. (2013a). LP Mixed Data Science:Outline of Theory. arXiv:1311.0562.

See Also

LPTrans

Examples

xdata <- rnorm(100)
head(LP.moment(xdata, m =4))

require(stats)
data(faithful)
head(LP.comoment(faithful$eruptions,faithful$waiting,m=4))

LPTime documentation built on May 2, 2019, 7:18 a.m.