Robust slope estimator

This is the underlying computing engine called by robslope used to fit robust slopes. It wraps around the individual functions TheilSen, RepeatedMedian or PassingBablok. These should usually not be used directly unless by experienced users.

Usage

robslope.fit(x, y, weights, type, alpha = NULL, beta = NULL, verbose = TRUE)

Arguments

x: design matrix of dimension n * p.
y: vector of observations of length n, or a matrix with n rows.
type: the type of robust slope estimator. Should be one of "TheilSen" (default), "RepeatedMedian" or "PassingBablok".
weights: vector of weights. Currently not in use.
alpha: Determines the order statistic of the target slope. Defaults to the upper median. See below for details.
beta: Determines the inner order statistic. Only used when type = "RepeatedMedian". See below for details.
verbose: Whether or not to print out the progress of the algorithm. Defaults to TRUE.

Details

This function provides a wrapper around the individual functions TheilSen, RepeatedMedian or PassingBablok. The details on changing the parameters alpha and beta can be found in the documentation of those respective functions.

Value

list with components

coefficients: p vector
residuals: n vector or matrix
fitted.values: n vector or matrix

References

Theil, H. (1950), A rank-invariant method of linear and polynomial regression analysis (Parts 1-3), Ned. Akad. Wetensch. Proc. Ser. A, 53, 386-392, 521-525, 1397-1412.

Sen, P. K. (1968). Estimates of the regression coefficient based on Kendall's tau. Journal of the American statistical association, 63(324), 1379-1389.

Dillencourt, M. B., Mount, D. M., & Netanyahu, N. S. (1992). A randomized algorithm for slope selection. International Journal of Computational Geometry & Applications, 2(01), 1-27.

Siegel, A. F. (1982). Robust regression using repeated medians. Biometrika, 69(1), 242-244.

Matousek, J., Mount, D. M., & Netanyahu, N. S. (1998). Efficient randomized algorithms for the repeated median line estimator. Algorithmica, 20(2), 136-150.

Passing, H., Bablok, W. (1983). A new biometrical procedure for testing the equality of measurements from two different analytical methods. Application of linear regression procedures for method comparison studies in clinical chemistry, Part I, Journal of clinical chemistry and clinical biochemistry, 21,709-720.

Bablok, W., Passing, H., Bender, R., Schneider, B. (1988). A general regression procedure for method transformation. Application of linear regression procedures for method comparison studies in clinical chemistry, Part III. Journal of clinical chemistry and clinical biochemistry, 26,783-790.

Raymaekers J., Dufey F. (2022). Equivariant Passing-Bablok regression in quasilinear time. (link to open access pdf)

Raymaekers (2023). "The R Journal: robslopes: Efficient Computation of the (Repeated) Median Slope", The R Journal. (link to open access pdf)

Author

Jakob Raymaekers

Examples

set.seed(123)
x <- rnorm(20)
y <- rnorm(20)

robslope.out <- robslope.fit(x, y, type = "RepeatedMedian", verbose = TRUE)
#> Initialization finished, starting interval contraction.
#> Interval contraction ended after 0 iterations.
#> Now starting brute-force computation.
#> Algorithm finished

coef(robslope.out)
#> (intercept)           x 
#>  0.08928224  0.07688021 
plot(fitted.values(robslope.out))


robslope.out <- robslope.fit(x, y, type = "TheilSen", verbose = TRUE)
#> Initialization finished, starting interval contraction.
#> Interval contraction ended after 0 iterations.
#> Now starting brute-force computation.
#> Algorithm finished

plot(residuals(robslope.out))