Code to compute the FastRCS regression outlyingness index.

Description

Uses the FastRCS algorithm to compute the RCS outlyingness index of regression.

Details

Index:

FastRCS                 Function to compute the FastRCS regression outlyingness
                       index.
FRCSnumStarts                 Internal function used to compute the FastRCS regression
                       outlyingness index.
plot.FastRCS		Robust Diagnostic Plots For FastRCS.
quanf                     Internal function used to compute the FastRCS regression
                       outlyingness index.

Author(s)

Kaveh Vakili [aut, cre], Maintainer: Kaveh Vakili <vakili.kaveh.email@gmail.com>

References

Vakili, K. and Schmitt, E. (2014). Finding Regression Outliers With FastRCS. (http://arxiv.org/abs/1307.4834)

Computes the number of starting p-subsets

Description

Computes the number of starting p-subsets so that the desired probability of selecting at least one clean one is achieved. This is an internal function not intended to be called by the user.

Usage

  FRCSnumStarts(p,gamma=0.99,eps=0.5)

Arguments

Value

An integer number of starting p-subsets.

Author(s)

Kaveh Vakili

Examples

FRCSnumStarts(p=3,gamma=0.99,eps=0.4)

Computes the FastRCS outlyingness index for regression.

Description

Computes a fast and robust regression model for a n by p matrix of multivariate continuous regressors and a single dependent variable.

Usage

  FastRCS(x,y,nSamp,alpha=0.5,seed=1,intercept=1)

Arguments

Details

The current version of FastRCS includes the use of a C-step procedure to improve efficiency (Rousseeuw and van Driessen (1999)). C-steps are taken after the raw subset is found and before reweighting. In experiments, we found that carrying C-Steps starting from the members of $rawBest improves the speed of convergence without increasing the bias of the final estimates. FastRCS is regression and affine equivariant and thus consistent at the elliptical model (Grubel and Rock (1990)).

Value

Author(s)

Kaveh Vakili

References

Grubel, R. and Rocke, D. M. (1990). On the cumulants of affine equivariant estimators in elliptical families. Journal of Multivariate Analysis, Vol. 35, p. 203–222. Journal of Multivariate Analysis

Rousseeuw, P. J., and van Driessen, K. (2006). Computing lts regression for large data sets. Data mining and Knowledge Discovery, 12, 29–45

Vakili, K. and Schmitt, E. (2014). Finding Regression Outliers With FastRCS. (http://arxiv.org/abs/1307.4834)

Examples

## testing outlier detection
set.seed(123)
n<-100
p<-3
x0<-matrix(rnorm(n*p),nc=p)
y0<-rnorm(n)
z<-c(rep(0,30),rep(1,70))
x0[1:30,]<-matrix(rnorm(30*p,5,1/100),nc=p)
y0[1:30]<-rnorm(30,10,1/100)
ns<-FRCSnumStarts(p=p,eps=0.4);
results<-FastRCS(x=x0,y=y0,alpha=0.5,nSamp=ns)
z[results$best]

## testing outlier detection, different value of alpha
set.seed(123)
n<-100
p<-3
x0<-matrix(rnorm(n*p),nc=p)
y0<-rnorm(n)
z<-c(rep(0,20),rep(1,80))
x0[1:20,]<-matrix(rnorm(20*p,5,1/100),nc=p)
y0[1:20]<-rnorm(20,10,1/100)
ns<-FRCSnumStarts(p=p,eps=0.25);
results<-FastRCS(x=x0,y=y0,alpha=0.75,nSamp=ns)
z[results$best]



#testing exact fit
set.seed(123)
n<-100
p<-3
x0<-matrix(rnorm(n*p),nc=p)
y0<-rep(1,n)
z<-c(rep(0,30),rep(1,70))
x0[1:30,]<-matrix(rnorm(30*p,5,1/100),nc=p)
y0[1:30]<-rnorm(30,10,1/100)
ns<-FRCSnumStarts(p=p,eps=0.4);
results<-FastRCS(x=x0,y=y0,alpha=0.5,nSamp=ns,seed=1)
z[results$rawBest]
results$obj

#testing regression equivariance
n<-100
p<-3
x0<-matrix(rnorm(n*(p-1)),nc=p-1)
y0<-rnorm(n)
ns<-FRCSnumStarts(p=p,eps=0.4);
y1<-y0+cbind(1,x0)%*%rep(-1,p)
results1<-FastRCS(y=y0,x=x0,nSamp=ns,seed=1)$coefficients
results2<-FastRCS(y=y1,x=x0,nSamp=ns,seed=1)$coefficients
results1+rep(-1,p)
#should be the same:
results2

Sales Data for the Chrysler Town & Country

Description

Sales data for the Chrysler Town & Country.

Usage

Lemons

Format

VehBCost

Acquisition cost paid for the vehicle at time of purchase.

MMRAcquisitionAuctionAveragePrice

Acquisition price for this vehicle in average condition at time of purchase.

MMRAcquisitonRetailCleanPrice

Acquisition price for this vehicle in the above Average condition at time of purchase.

MMRAcquisitionRetailAveragePrice

Acquisition price for this vehicle in the retail market in average condition at time of purchase.

MMRAcquisitonRetailCleanPrice

Acquisition price for this vehicle in the retail market in above average condition at time of purchase.

MMRCurrentAuctionAveragePrice

Acquisition price for this vehicle in average condition as of current day.

MMRCurrentAuctionCleanPrice

Acquisition price for this vehicle in above condition as of current day.

MMRCurrentRetailAveragePrice

Acquisition price for this vehicle on the retail market in average condition as of current day.

MMRCurrentRetailCleanPrice

Acquisition price for this vehicle on the retail market in above average condition as of current day.

WarrantyCost

Warranty price (term=36month and millage=36K).

VehOdo

The vehicle's odometer reading.

Examples

data(Lemons)
alpha<-0.5
p<-ncol(Lemons)
ns<-FRCSnumStarts(p=p,eps=(1-alpha)*4/5)
Fit<-FastRCS(x=Lemons[,-1],y=Lemons[,1],nSamp=ns,seed=1)
plot(Fit)

Robust Diagnostic Plots For FastRCS

Description

Shows the robust Score distances versus robust Orthogonal distances and their respective cutoffs, for the an object of class FastRCS.

Usage

## S3 method for class 'FastRCS'
plot(x,col="black",pch=16,...)

Arguments

Details

This function produces the robust standardized, residuals as well as an indicative cut-off (under normal model). This tool is a diagnostic plot for robust regression and can be used used to reveal the outliers.

See Also

FastRCS

Examples

set.seed(123)
n<-100
p<-3
x0<-matrix(rnorm(n*p),nc=p)
y0<-rnorm(n)
z<-c(rep(0,30),rep(1,70))
x0[1:30,]<-matrix(rnorm(30*p,5,1/100),nc=p)
y0[1:30]<-rnorm(30,10,1/100)
ns<-FRCSnumStarts(p=p,eps=0.4);
results<-FastRCS(x=x0,y=y0,alpha=0.5,nSamp=ns)
plot(results)

Converts alpha values to h-values

Description

FastRCS selects the subset of size h that minimizes the I-index criterion. The function quanf determines the size of h based on the rate of contamination the user expects is present in the data. This is an internal function not intended to be called by the user.

Usage

  quanf(n,p,alpha)

Arguments

Value

An integer number of the size of the starting p-subsets.

Author(s)

Kaveh Vakili

Examples

quanf(p=3,n=500,alpha=0.5)