OBRE {OBRE}

Optimal B-Robust Estimator

Description

Function for obtaining the Optimal B-Robust Estimates starting by a vector of data and a two parameters distribution.

Usage

OBRE(
  nvData,
  strDistribution,
  nCParOBRE,
  dfParOBRE = data.frame(nEta = 1e-06, nMaxIterLoopWc = 10, nMaxIterLoopA = 10, nRelTol =
    0.001, nAbsTol = 0.5, stringsAsFactors = FALSE),
  nTheta1Init = NA,
  nTheta2Init = NA,
  eDensityFun = NA
)

Arguments

nvData

The vector of data.

strDistribution

The distribution name between "normal" (Normal distribution), "logNormal" (logNormal distribution), "weibull" (Weibull distribution), "logLogistic" (logLogistic distribution), "gpd2" (Generalized Pareto Distribution with two parameters) or "custom" if the distribution is written by the user as an input of "eDensityFun" parameter. Alternatively, the input of "strDistribution" can be an object of class "OBREdist", obtained using function densityExpressions.

nCParOBRE

OBRE robustness parameter.

dfParOBRE

A data frame containing oprimization parameters, i.e. nEta, the precision between two parameters optimization, nMaxIterLoopWc and nMaxIterLoopA, the number of iterations in the optimization proceture, nRelTol and nAbsTol, the relative and absolute tolerances.

nTheta1Init

First parameter for the beginning of the computation.

nTheta2Init

Second parameter for the beginning of the computation.

eDensityFun

The density of a two parameters distribution. To be inserted if in strDistribution the "custom" option is chosen. This should be an expression object, the two parameters should be called "nTheta1" and "nTheta2", the data "nvData" and its formula should be derivable

Value

A list with the vector containing the final parameters, the exit OBRE message, the values of vector a and matrix A, the OBRE tuning parameter c, the initial values of the parameters (if unspecified by the user, the values of MLE are reported), the vector of data, the density expression.

References

Bellio, R. (2007). Algorithms for bounded-influence estimation. Comput. Stat. Data Anal. 51, 2531-2541.

Hampel F (1968). Contributions to the theory of robust estimation. University of California.

Hampel, F., Ronchetti, E., Rousseeuw, P. & Stahel, W. (1985). Robust Statistics. The approach based on influence function. John Wiley and Sons Ltd., Chichester, UK.

Victoria-Feser, M.P. & Ronchetti, E. (1994). Robust methods for personal-income distribution models. Canadian Journal of Statistics 22, 247-258.

Examples

# Using the densityExpressions function for initialize the distribution
distrForOBRE <- densityExpressions(strDistribution = "normal")
simData = c(rnorm(1000, 12, 2),200,150)
try({estOBRE <- OBRE(nvData = simData, strDistribution = distrForOBRE, nCParOBRE = 3)
# Launching the generation of the density expression directly from OBRE
simData = c(rnorm(1000, 12, 2),200,150)
estOBRE <- OBRE(nvData = simData, strDistribution = "normal", nCParOBRE = 3)
# Using the "custom" option and using the normal distribution
simData = c(rnorm(1000, 12, 2),200,150)
estOBRE <- OBRE(nvData = simData, strDistribution = "custom", nCParOBRE = 3,
eDensityFun = expression((exp( -((nvData - nTheta1)^2) / (2 * nTheta2^2)) /
(sqrt(2 * pi) * nTheta2))))})