predict.not | R Documentation |

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).

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

`object` |
An object of class 'not', returned by |

`cpt` |
An integer vector with locations of the change-points.
If missing, the |

`...` |
Further parameters that can be passed to |

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))*.

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`

# **** 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)

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