# Robust SNHT

### Description

This function performs a standard normal homogeneity test using a robust estimator of the mean and standard deviation. It also allows for a user- defined definition of these statistics.

### Usage

1 2 3 4 5 6 7 8 9 10 | ```
robustSNHT(data, period, scaled=TRUE, rmSeasonalPeriod=Inf
,estimator=function(x, minObs=5){
x = x[!is.na(x)]
if(length(x)<minObs) #Too many NA values, don't return a result
return(c(NA,NA))
if(max(table(x))>length(x)/2) #Too many duplicate values, MAD will be 0
return(c(NA,NA))
fit = MASS::huber(x)
return(c(fit[[1]], fit[[2]]))
})
``` |

### Arguments

`data` |
The data to be analyzed for changepoints. |

`period` |
The SNHT works by calculating the mean of the data on the previous period observations and the following period observations. Thus, this argument controls the window size for the test statistics. |

`scaled` |
See ?snht. |

`rmSeasonalPeriod` |
See ?snht. |

`estimator` |
A custom function may be supplied to this function which computes estimates for the mean and standard deviation. The function should only take one argument (a numeric vector of data) and should return a vector of length two: the estimated center and spread. The huber function from MASS is implemented for the robust SNHT by default (along with some data quality checks). |

### Details

The SNHT works by calculating the mean of the data on the previous period and on the following period. The test statistic at each observation is then computed as described in Haimberger (2007). Essentially, though, it just compares the means of these two periods and normalizes by the standard deviation.

Note: if there are not enough observations both before and after the current observation, no test is performed.

Large values of the test statistic suggests the presence of a changepoint. Haimberger (see references) suggests values larger than 100 should be considered changepoints. However, this does not apply if scaled = TRUE.

### Value

Returns a data.frame, with columns score, leftMean, and rightMean, and time. Statistic is the SNHT test statistic described above, and leftMean (rightMean) are the means to the left (right) of the current observation.

Note that new (missing) observations were introduced to the dataset to ensure the same number of observations occur per day.

### Author(s)

Josh Browning (jbrownin@mines.edu)

### References

L. Haimberger. Homogenization of radiosonde temperature time series using innovation statistics. Journal of Climate, 20(7): 1377-1403, 2007.

### See Also

`huber`

Other snht.functions: `robustSNHTunequal`

,
`snht`