Tests Based on Regression Rank Scores in Nonlinear Models and Their Computation
نویسنده
چکیده
We consider a nonlinear regression model introduced in Jurečková [2006], where concept of regression rank scores was generalized to nonlinear models. We try to support by simulations the results (asymptotic properties under some regularity conditions) proven in that article and apply them to a set of real data. We test a two sample problem under nuisance nonlinear regression pointing out some difficulties with computation. Introduction The notion of regression quantiles for a linear regression model was first introduced in Koenker and Bassett [1978]. They defined the regression α-th quantile θ̂nα by θ̂nα = arg min t∈Rp n
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Regression rank scores in nonlinear models
with xi ∈ Rk, θ = (θ0, θ1, . . . , θp)′ ∈ Θ (compact in Rp+1), where g(x, θ) = θ0 + g̃(x, θ1, . . . , θp) is continuous, twice differentiable in θ and monotone in components of θ. Following Gutenbrunner and Jurečková (1992) and Jurečková and Procházka (1994), we introduce regression rank scores for model (1), and prove their asymptotic properties under some regularity conditions. As an applicati...
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