est_nlin1: Estimation for non-linear AR(1) models by simplicial depth
In ChrisKust/rexpar: Simplicial Depth for Explosive Autoregressive Processes

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

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).

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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)

`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 can be found in Kustosz (2016).

The function returns a list with

`estimate`	Parameter maximising the selected depth notion.
`value`	Depth at the resulting maximum.
`numit`	Number of iterations.

Kustosz, Christoph

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.

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