# selectPoints: A point selection procedure for multivariate data In npcp: Some Nonparametric CUSUM Tests for Change-Point Detection in Possibly Multivariate Observations

 selectPoints R Documentation

## A point selection procedure for multivariate data

### Description

Returns a matrix of ‘representative’ points.

### Usage

```selectPoints(x, r, kappa = 1.5, plot = FALSE)
```

### Arguments

 `x` a numeric matrix with `d` columns whose rows represent multivariate observations. `r` integer specifying the size of an initial uniformly-spaced grid ‘on the probability scale’; an upper bound for the number of selected points is `r^d`. `kappa` numeric constant required to be strictly greater than one involved in the point selection procedure. `plot` logical used only if `d = 2` specifying whether a plot should be produced.

### Details

The selection procedure is described in detail in Section 3.2 of the reference below. Set `plot = TRUE` for visual feedback and information on the minimum number of ‘surrounding’ observations required for a grid point to be selected. The initial grid 'on the probability scale' is in blue, while the points selected by the procedure are in red.

### Value

a matrix with `d` columns whose rows are the selected points.

### References

M. Holmes, I. Kojadinovic, and A. Verhoijsen, Multi-purpose open-end monitoring procedures for multivariate observations based on the empirical distribution function, 45 pages, https://arxiv.org/abs/2201.10311.

`selectPoints()` is used in `detOpenEndCpDist()`.

### Examples

```## Generate data
set.seed(123)
x1 <- rnorm(1000, 0, 1)
x2 <- rnorm(1000, 0.7 * x1, sqrt((1 - 0.7^2)))
x <- cbind(x1, x2)

## Point selection
selectPoints(x, r = 3, kappa = 1.5, plot = TRUE)
selectPoints(x, r = 3, kappa = 4, plot = TRUE)

selectPoints(x, r = 5, kappa = 1.5, plot = TRUE)
selectPoints(x, r = 5, kappa = 4, plot = TRUE)
```

npcp documentation built on Feb. 16, 2023, 6:04 p.m.