# PM.matrix: Partial Moment Matrix In NNS: Nonlinear Nonparametric Statistics

## Description

This function generates a co-partial moment matrix for the specified co-partial moment.

## Usage

 `1` ```PM.matrix(LPM.degree, UPM.degree, target = NULL, variable, pop.adj = FALSE) ```

## Arguments

 `LPM.degree` integer; Degree for `variable` below `target` deviations. `(degree = 0)` is frequency, `(degree = 1)` is area. `UPM.degree` integer; Degree for `variable` above `target` deviations. `(degree = 0)` is frequency, `(degree = 1)` is area. `target` numeric; Typically the mean of Variable X for classical statistics equivalences, but does not have to be. (Vectorized) `(target = NULL)` (default) will set the target as the mean of every variable. `variable` a numeric matrix or data.frame. `pop.adj` logical; `FALSE` (default) Adjusts the sample co-partial moment matrices for population statistics.

## Value

Matrix of partial moment quadrant values (CUPM, DUPM, DLPM, CLPM), and overall covariance matrix. Uncalled quadrants will return a matrix of zeros.

## Note

For divergent asymmetical `"D.LPM" and "D.UPM"` matrices, matrix is `D.LPM(column,row,...)`.

## Author(s)

Fred Viole, OVVO Financial Systems

## References

Viole, F. and Nawrocki, D. (2013) "Nonlinear Nonparametric Statistics: Using Partial Moments" https://www.amazon.com/dp/1490523995/ref=cm_sw_su_dp

Viole, F. (2017) "Bayes' Theorem From Partial Moments" https://www.ssrn.com/abstract=3457377

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14``` ```set.seed(123) x <- rnorm(100) ; y <- rnorm(100) ; z <- rnorm(100) A <- cbind(x,y,z) PM.matrix(LPM.degree = 1, UPM.degree = 1, variable = A) ## Use of vectorized numeric targets (target_x, target_y, target_z) PM.matrix(LPM.degree = 1, UPM.degree = 1, target = c(0, 0.15, .25), variable = A) ## Calling Individual Partial Moment Quadrants cov.mtx <- PM.matrix(LPM.degree = 1, UPM.degree = 1, variable = A) cov.mtx\$cupm ## Full covariance matrix cov.mtx\$cov.matrix ```

NNS documentation built on June 26, 2021, 1:07 a.m.