est_nlin1: Estimation for non-linear AR(1) models by simplicial depth

Description Usage Arguments Details Value Author(s) References See Also Examples

View source: R/est_nlin1.R

Description

This function implements an algortihm to estimate a non-linear AR(1) model and explosion by simplicial depth or one of the proposed simplified notions in Kustosz, Mueller and Wendler (2016).

Usage

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est_nlin1(y, maxit = 25, candy = FALSE, perc = 0.1, acc = 0.1, plots = FALSE, 
normtype = 1, pv = 2, wgt = c(1, 0.5), unique = TRUE, 
notion = dS3_lin2, optim_rude = FALSE)

Arguments

y

An observed series form an non-linear AR(1) process with intercept.

maxit

A value for the maximal number of iterations of the optimisation algorithm.

candy

A switch (TRUE/FALSE) deciding, if just edges of simplices defined by the residuals shall be evaluated candy = FALSE or if points interior of the simplices should be considered candy = TRUE.

perc

A value in (0,1) definig, how large the search regions around an acual candidate should be. A small value defines a very small region, while the value 1 means, that all potential candidates are considered.

acc

A value in (0,1) defining the search regions in the iteration steps. A value of 1 gives large regions, while a value close to 0 defines small regions, measured by the distance to the actual candidate.

plots

A switch (TRUE/FALSE) which allows plots of the iterations steps.

normtype

A parameter which defines the norm used to define distances to the actual paramter in the optimisation algorithm (see Ele_Norm for details).

pv

A parameter defining the power in the norm to calculate distances (see Ele_Norm).

wgt

A vector of weights used for the norm used to calculate distances (see Ele_Norm).

unique

A switch (TRUE/FALSE) defining, if a unique maximum shall be the result if multiple points with maximal depth exist. In this case the median point is selected.

notion

Here the function which is used for depth calculation is defined. The following notionn are allowed: "dS1_lin2", "dS2_lin2", "dS3_lin2", "dS_lin2". Thereby model = nlinAR1 is used.

optim_rude

This switch allows a rude optimisation by a Nelder-Mead algorithm. This may be more accurate due to the shape of thenon-linear empirical depth function.

Details

Details can be found in Kustosz (2016).

Value

The function returns a list with

estimate

Parameter maximising the selected depth notion.

value

Depth at the resulting maximum.

numit

Number of iterations.

Author(s)

Kustosz, Christoph

References

Kustosz, C. (2016). Depth based estimators and tests for autoregressive processes with application. Ph. D. thesis. TU Dortmund.

Kustosz C., Mueller Ch. H. and Wendler M. (2016). Simplified Simplicial Depth for Regression and Autoregressive Growth Processes. Journal of Statistical Planning and Inference. In press.

See Also

dS1_lin2,dS2_lin2,dS3_lin2,dS_lin2,Tri_Mid_n1,nlin1_theta_f,Ele_Norm

Examples

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y <- RandomARMod_nlin1(200, 1.003, 0.2, 15, 1)
est_nlin1(y)

ChrisKust/rexpar documentation built on May 6, 2019, 11:48 a.m.