Description Usage Arguments Value References See Also Examples
Consider a linear regression problem for a multivariate stationary time series X_t:
Y_t = P X_t + \varepsilon_t.
Estimator based on formula
EY_0X_0 (EX_0^2)^{-1} = P
is fragile on the eigendirections of EX_0^2 with small eigenvalues.
It is therefore desired to truncate the inversion at a level where eigenvalues are
estimated consistently.
Procedure dim.est
suggest such level by taking only the eigenvalues which are greater
and equal than 1/√{n}K_{const}.
It is designed for √{n} consistent matrix estimator and can serve as one of heuristics
for matrix inverion problems.
1 | reg.dim.est(eigenvalues, n, Kconst = 1)
|
eigenvalues |
vector of eigenvalues |
n |
used for estimation |
Kconst |
parameter for fitting the convergence rate to 1/(Kconst*n^1/2) |
number of 'safe' eigendirections
Siegfried Hormann and Lukasz Kidzinski A note on estimation in Hilbertian linear models Research report, 2012
1 2 3 4 5 6 | n = 100
X = rar(n)
Y = rar(n)
CV = lagged.cov(X,Y)
E = eigen(CV)
K = reg.dim.est(E$values, n)
|
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