Description Usage Arguments Details Value Note Author(s) References See Also Examples
This function calculates the simplicial depth for explosive AR(1) processes with two parameters. Thereby the parameter θ and the process y are fixed. The assumed model given by the argument model. Further the kernel is replaced by a symmetrised version. This in particular allows the application of standard limit theorems for U-Statistics.
1 2 | dS_lin2_sym(theta, resy, y, ncores = 1,
model = c("linAR1", "nlinAR1", "linARc"), cpow = 1)
|
theta |
θ, parameter (vector) to evaluate dS1 in. |
resy |
Instead of a model and a parameter theta, residuals can be plugged in directly. Then just the sign changes are calculated and the statistic is evaluated |
y |
y = (y_0,...,y_N), oberserved process to evaluate dS1 in. |
ncores |
This value allows the usage of multiple cores to calculate the statistic |
model |
Here the model for the calculation of the underlying residuals is specified. currently the following
models are available Y_n = θ_1 Y_{n-1} θ_0 + E_n "nlinAR1" = linear AR(1) model without intercept but with power parameter Y_n = Y_{n-1} + θ_1 Y_{n-1}^{θ_3} + E_n "linARc" = linear AR(1) model with intercept and fixed and knwon power cpow Y_n = θ_1 Y_{n-1}^{cpow} + θ_0 + E_n |
cpow |
fixed and known power parameter for the y(n) = theta2*y(n)^cpow + theta1 model |
The theoretical details can be found in Kustosz, M\"uller and Wendler (2016). The computational details are in Kustosz (2016).
Result is a real number which gives the depth of theta based on the obervation y.
This expression is a simplification of dS, which is the full simplicial depth for explosive AR(1) processes
Kustosz, Christoph
Kustosz, C. (2016). Depth based estimators and tests for
autoregressive processes with application. Ph. D. thesis. TU Dortmund.
Kustosz C., M\"uller Ch. H. and Wendler M. (2016). Simplified Simplicial Depth for Regression and
Autoregressive Growth Processes. Journal of Statistical Planning and Inference. In press.
resARMod_lin2
, dS_lin2
,dS1_lin2
, dS2_lin2
, dS3_lin2
1 2 3 4 | y <- RandomARMod_lin2(100, 0.2, 1.01, 15, "0")
theta <- c(0.2, 1.01)
dS_lin2_sym(theta = theta, y = y, model = "linAR1")
dS_lin2_sym(theta = theta+0.1, y = y, model = "linAR1")
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