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Institute of Mathematical Statistics and Actuarial Science

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Isotonic and Concave Regression

The programs IsoMeans.m, IsoMeans.R and IsoQuants.m compute isotonic fits to a data vector Y using two variants of the pool-adjacent-violators algorithm. In the first case the fitted vector minimizes the sum of weighted squared residuals using local means. In the second case the fitted vector is based on local quantiles.

For given data vectors X and Y and an optional weight vector W, the program IsoLSRegr.R determines an isotonic function m(.) such that the sum of Wi*(Yi - m(Xi))2 is minimal. The weight vector W defaults to a vector of ones.

Similarly, the program IsoQuantRegr.R computes isotonic regression quantiles by minimizing the sum of ρ(m(Xi) - Yi, β), where ρ(t, β) := (1 - 2β) t + |t|.

Finally, the program IsoCondDistr.R estimates the conditional distribution functions F(r | x) := P(Y ≤ r | X = x) of Y given X under a stochastic order assumption only. (El Barmi and Mukerjee 2005, Dümbgen et al. 2011).

The R-File ConcaveWLS.R may be used to fit a concave regression function to given data vectors X and Y and an optional weight vector W.

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