median | R Documentation |
Compute the sample projected or geometric median.
## S3 method for class 'SO3' median( x, na.rm = FALSE, type = "projected", epsilon = 1e-05, maxIter = 2000, ... ) ## S3 method for class 'Q4' median( x, na.rm = FALSE, type = "projected", epsilon = 1e-05, maxIter = 2000, ... )
x |
n-by-p matrix where each row corresponds to a random rotation in matrix form (p=9) or quaternion (p=4) form. |
na.rm |
a logical value indicating whether NA values should be stripped before the computation proceeds. |
type |
string indicating "projected" or "geometric" type mean estimator. |
epsilon |
stopping rule. |
maxIter |
maximum number of iterations allowed before returning most recent estimate. |
... |
additional arguments. |
The median-type estimators are defined as
argmin∑ d(Ri,S).
If the choice of distance metric d is Riemannian then the estimator is called the geometric median, and if the distance metric in Euclidean then it is called the projected median. The algorithm used in the geometric case is discussed in hartley11 and the projected case is in stanfill2013.
hartley11 stanfill2013
Estimate of the projected or geometric median in the same parametrization.
mean.SO3
, bayes.mean
,
weighted.mean.SO3
Rs <- ruars(20, rvmises, kappa = 0.01) # Projected median median(Rs) # Geometric median median(Rs, type = "geometric") # Bias of the projected median rot.dist(median(Rs)) # Bias of the geometric median rot.dist(median(Rs, type = "geometric")) Qs <- as.Q4(Rs) # Projected median median(Qs) # Geometric median median(Qs, type = "geometric") # Bias of the projected median rot.dist(median(Qs)) # Bias of the geometric median rot.dist(median(Qs, type = "geometric"))
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