-estimation for the partially linear regression model under monotonic constraints

Signed-rank analysis of a partial linear model with B-splines estimated monotone non parametric function

“…The parameter β is an unknown p × 1 vector, and f is an unknown real-valued function defined on the closed interval [0, 1]. As in Lu (2010); Du et al (2013)…”

“…We note that in all our simulations, we used cubic splines. It was already observed in Du et al (2013) that knots selection is a major issue in practice and that the number of knots b n can be determined by a model criterion such as AIC, BIC or cross-validation. Since we were not particularly interested in the convergence rate, the number of interior knots was empirically selected so that b n = O(n ν ) where ν ≤ 1/3.…”

“…As in Du et al (2013) we take p = 2, β 1 = 1 and β 2 = 2. ε i ∼ N(0, 1), ε i ∼ t(3), and ε i ∼ Cauchy(0, 1). We also choose X i ∼ N(0, 1), f (w) = (w/4) 3 − 0.1.…”

“…In this paper, we propose a signed-rank (SR) estimator with B-splines. This estimation approach mirrors that of Du et al (2013). The method has the following advantages:…”

“…The most important result in the application of B-splines in a monotonic context was given by Schumaker (1981) where he argues essentially that monotonic functions on an interval [a, b] can be estimated by monotonic splines under some constraints. This result has been used by Lu (2010), Lu et al (2007Lu et al ( , 2009, Du et al (2013).…”