changepoint (version 0.3)

single.mean.norm: Single Change in Mean - Normal Data

Description

Calculates the scaled log-likelihood (assuming the data is normally distributed) for all possible changepoint locations and returns the single most probable (max).

Usage

single.mean.norm(data, penalty="SIC",value=0,class=TRUE,param.estimates=TRUE)

Arguments

data

A vector or matrix containing the data within which you wish to find a changepoint. If data is a matrix, each row is considered a separate dataset.

penalty

Choice of "None", "SIC", "BIC", "AIC", "Hannan-Quinn", "Asymptotic" and "Manual" penalties. If Manual is specified, the manual penalty is contained in the value parameter. If Asymptotic is specified, the theoretical type I error is contained in the value

value

The theoretical type I error e.g.0.05 when using the Asymptotic penalty. The value of the penalty when using the Manual penalty option. This can be a numeric value or text giving the formula to use. Available variables are, n=length of original data, n

class

Logical. If TRUE then an object of class cpt is returned. If FALSE a vector is returned.

param.estimates

Logical. If TRUE and class=TRUE then parameter estimates are returned. If FALSE or class=FALSE no parameter estimates are returned.

Value

• If class=TRUE then an object of S4 class "cpt" is returned. The slot cpts contains the changepoints that are solely returned if class=FALSE. The structure of cpts is as follows.

  If data is a vector (single dataset) then a single value is returned:

• cpt
  The most probable location of a changepoint if H0 was rejected or NA if H1 was rejected.
• If data is an mxn matrix (multiple datasets) then a vector is returned:
• cpt
  Vector of length m containing where each element is the result of the test for data[m,]. If cpt[m] is a number then it is the most probable location of a changepoint under H1. Otherwise cpt[m] has the value NA and indicates that H1 was rejected.

Details

This function is used to find a single change in mean for data that is assumed to be normally distributed. The value returned is the result of testing H0:no change in mean against H1: single change in mean using the log of the likelihood ratio statistic coupled with the penalty supplied.

References

Change in Normal mean: Hinkley, D. V. (1970) Inference About the Change-Point in a Sequence of Random Variables, Biometrika 57, 1--17

See Also

cpt.mean,single.meanvar.norm,single.var.norm,cpt

Examples

# Example of a change in mean at 100 in simulated normal data
set.seed(1)
x=c(rnorm(100,0,1),rnorm(100,10,1))
single.mean.norm(x,penalty="SIC",class=FALSE) # returns 100 to show that the null hypothesis was rejected and the change in mean is at 100
ans=single.mean.norm(x,penalty="Asymptotic",value=0.01) 
cpts(ans) # returns 100 to show that the null hypothesis was rejected, the change in mean is at 100 and we are 99% confident of this result


# Example of a data matrix containing 2 rows, row 1 has a change in mean and row 2 had no change in mean
set.seed(1)
x=c(rnorm(100,0,1),rnorm(100,10,1))
y=rnorm(200,0,1)
z=rbind(x,y)
single.mean.norm(z,penalty="SIC",class=FALSE) # returns vector c(100,200) which shows that the first dataset has a change in mean at 100 and the second dataset rejected H1 and has no change in mean
ans=single.mean.norm(z,penalty="Manual",value="log(n)") 
cpts(ans[[1]]) # test using a manual penalty which is the same as the SIC penalty for this example 
cpts(ans[[2]]) # result is the same as above, c(100, 200)