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

 PM.matrix R Documentation

## Partial Moment Matrix

### Description

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

### Usage

```PM.matrix(LPM_degree, UPM_degree, target, variable, pop_adj)
```

### Arguments

 `LPM_degree` integer; Degree for `variable` below `target` deviations. `(LPM_degree = 0)` is frequency, `(LPM_degree = 1)` is area. `UPM_degree` integer; Degree for `variable` above `target` deviations. `(UPM_degree = 0)` is frequency, `(UPM_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

```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, target = colMeans(A), pop_adj = TRUE)

## 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, pop_adj = TRUE)

## Calling Individual Partial Moment Quadrants
cov.mtx <- PM.matrix(LPM_degree = 1, UPM_degree = 1, variable = A, target = colMeans(A),