Finds LP moments of a random variable or comoments of two random variables
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.
LP.moment(x, m) LP.comoment(x, y,zero.order = TRUE, m)
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 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)].
A vector of LP moments.
A matrix of LP co-moments between X and Y.
Subhadeep Mukhopadhyay
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.
xdata <- rnorm(100) head(LP.moment(xdata, m =4)) require(stats) data(faithful) head(LP.comoment(faithful$eruptions,faithful$waiting,m=4))
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