# predict.not: Estimate signal for a 'not' object. In not: Narrowest-Over-Threshold Change-Point Detection

 predict.not R Documentation

## Estimate signal for a 'not' object.

### Description

Estimates signal in `object\$x` with change-points at `cpt`. The type of the signal depends on on the value of `contrast` that has been passed to `not` (see details below).

### Usage

```## S3 method for class 'not'
predict(object, cpt, ...)
```

### Arguments

 `object` An object of class 'not', returned by `not`. `cpt` An integer vector with locations of the change-points. If missing, the `features` is called internally to extract the change-points from `object`. `...` Further parameters that can be passed to `predict.not` and `features`.

### Details

The data points provided in `object\$x` are assumed to follow

Y_t= f_t + sigma_t varepsilon_t,

for t=1,...,n, where n is the number of observations in `object\$x`, the signal f_t and the standard deviation sigma_{t} are non-stochastic with change-points at locations given in `cpt` and varepsilon_t is a white-noise. Denote by tau_1, ..., tau_q the elements in `cpt` and set tau_0=0 and tau_q+1=T. Depending on the value of `contrast` that has been passed to `not` to construct `object`, the returned value is calculated as follows.

• For `contrast="pcwsConstantMean"` and `contrast="pcwsConstantMeanHT"`, in each segment (tau_j +1, tau_(j+1)), f_t for t in (tau_j +1, tau_(j+1)) is approximated by the mean of Y_t calculated over t in (tau_j +1, tau_(j+1)).

• For `contrast="pcwsLinContMean"`, f_{t} is approximated by the linear spline fit with knots at tau_1, ..., tau_q minimising the l2 distance between the fit and the data.

• For `contrast="pcwsLinMean"` in each segment (tau_j +1, tau_(j+1)), the signal f_t for t in (tau_j +1, tau_(j+1)) is approximated by the line alpha_j + beta_j j, where the regression coefficients are found using the least squares method.

• For `contrast="pcwsQuad"`, the signal f_t for t in (tau_j +1, tau_(j+1)) is approximated by the curve alpha_j + beta_j j + gamma_j^2, where the regression coefficients are found using the least squares method.

• For `contrast="pcwsConstMeanVar"`, in each segment (tau_j +1, tau_(j+1)), f_t and sigma_t for t in (tau_j +1, tau_(j+1)) are approximated by, respectively, the mean and the standard deviation of Y_t, both calculated over t in (tau_j +1, tau_(j+1)).

### Value

A vector wit the estimated signal or a two-column matrix with the estimated estimated signal and standard deviation if `contrast="pcwsConstMeanVar"` was used to construct `object`.

`not`

### Examples

```# **** Piecewisce-constant mean with Gaussian noise.
x <- c(rep(0, 100), rep(1,100)) + rnorm(100)
# *** identify potential locations of the change-points
w <- not(x, contrast = "pcwsConstMean")
# *** when 'cpt' is omitted, 'features' function is used internally
# to choose change-points locations
signal.est <- predict(w)
# *** estimate the signal specifying the location of the change-point
signal.est.known.cpt <- predict(w, cpt=100)
# *** pass arguments of the 'features' function through 'predict'.
signal.est.aic <- predict(w, penalty.type="aic")

# **** Piecewisce-constant mean and variance with Gaussian noise.
x <- c(rep(0, 100), rep(1,100)) + c(rep(2, 100), rep(1,100)) * rnorm(100)
# *** identify potential locations of the change-points
w <- not(x, contrast = "pcwsConstMeanVar")
# *** here signal is two-dimensional
signal.est <- predict(w)
```

not documentation built on March 18, 2022, 7:24 p.m.