Description Usage Arguments Details Value Author(s) References See Also
This function detects outliers by using Cook's distance sequentially, and
fits a linear regression model with outliers removed. The object
returned by this function can be used for valid inference corrected
for outlier removal through generic functions like summary
,
confint
, predict
.
1  outference_seq(formula, data, sigma = NULL, numOfOutlier)

formula, 
an object of class 
data, 
an optional data frame, list or environment containing the variables in the model, the same
syntax as in 
sigma, 
the noise level. Must be one of 
numOfOutlier, 
the number of outliers to be detected. 
This function uses the same syntax as lm
for the formula
and data
arguments.
Users can access the original "lm"
objects through $fit.full
and $fit.rm
.
Common generic functions for lm
, including coef
, confint
,
plot
, predict
and summary
are rewritten so that
they can be used to extract useful features of the object returned by this function.
The ith observation is considered as an outlier when its Cook's distance rank among top k, where k is the userspecified number of outliers to be detected. The outlier detection event can be characterized as a set of quadratic constraints in the response y:
\bigcap_{i \in I} {y^T Q_i y ≥ 0},
where I is a finite index set, and the constraint returned by this function is the list of Q_i matrices.
This function returns an object of class
c("outference_seq", "outference")
.
The function summary
is used to obtain and print a summary (including pvalues)
of the results. The generic functions coef
, confint
, plot
,
predict
are used to extract useful features of the object returned by this function.
An object of class c("outference_seq", "outference")
is a list containing the following components:
fit.full, 
an 
fit.rm, 
an 
method, 
"cook". 
cutoff, 

numOfOutlier, 
the number of outliers to be detected. 
outlier.det, 
indexes of detected outliers. 
magnitude, 
the vector of the Cook's distance for all observations 
constraint, 
the constraint in the response that characterizes the outlier detection event. A list of n by n matrices. 
sigma, 
the noise level used in the fit. 
call, 
the function call. 
Shuxiao Chen <[email protected]>
S. Chen and J. Bien. “Valid Inference Corrected for Outlier Removal”. arXiv preprint arXiv:1711.10635 (2017).
summary.outference
for summaries;
coef.outference
for extracting coefficients;
confint.outference
for confidence intervals of regression coefficients;
plot.outference
for plotting the outlying measure;
predict.outference
for making predictions.
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