Strictly monotone and smooth nonparametric regression for two or more variables

In this article a new monotone nonparametric estimate for a regression function of two or more variables is proposed. The method starts with an unconstrained nonparametric regression estimate and uses successively one-dimensional isotonization procedures. In the case of a strictly monotone regression function, it is shown that the new estimate is first order asymptotic equivalent to the unconstrained estimate, and asymptotic normality of an appropriate standardization of the estimate is established. Moreover, if the regression function is not monotone in one of its arguments, the constructed estimate has approximately the same Lp-norm as the initial unconstrained estimate. The methodology is also illustrated by means of a simulation study, and two data examples are analyzed. --multivariate nonparametric regression,isotonic regression,order restricted inference,nondecreasing rearrangement

A finite sample comparison of nonparametric estimates of the effective dose in quantal bioassay

To estimate the effective dose level ED a in the common binary response model, several parametric and nonparametric estimators have been proposed in the literature. In the present paper, we focus on nonparametric methods and present a detailed numerical comparison of four different approaches to estimate the ED a nonparametrically. The methods are briefly reviewed and their finite sample properties are studied by means of a detailed simulation study. Moreover, a data example is presented to illustrate the different concepts. --Binary response model,effective dose level,nonparametric regression,isotonic regression,order restricted inference,local linear regression

A finite sample comparison of nonparametric estimates of the effective dose in quantal bioassay

To estimate the effective dose level ED in the common binary response model, several parametric and nonparametric estimators have been proposed in the literature. In the present paper, we focus on nonparametric methods and present a detailed numerical comparison of four different approaches to estimate the ED nonparametrically. The methods are briefly reviewed and their finite sample properties are studied by means of a detailed simulation study. Moreover, a data example is presented to illustrate the different concepts

Strictly monotone and smooth nonparametric regression for two or more variables

In this article a new monotone nonparametric estimate for a regression function of two or more variables is proposed. The method starts with an unconstrained nonparametric regression estimate and uses successively one-dimensional isotonization procedures. In the case of a strictly monotone regression function, it is shown that the new estimate is first order asymptotic equivalent to the unconstrained estimate, and asymptotic normality of an appropriate standardization of the estimate is established. Moreover, if the regression function is not monotone in one of its arguments, the constructed estimate has approximately the same Lp-norm as the initial unconstrained estimate. The methodology is also illustrated by means of a simulation study, and two data examples are analyzed. AMS Subject Classification: 62G05, 62G2

Shape constraints in multivariate regression

In der vorliegenden Arbeit werden Regressionsschätzer unter Strukturannahmen in höheren Dimensionen entwickelt. In vielen Anwendungsbeispielen müssen mehrere Einflussgrößen berücksichtig werden. Häufig ist auch eine Struktur der Regressionsfunktion bekannt. Im ersten Teil wird ein Schätzer für eine streng monotone Regressionsfunktion in mehreren Variablen eingeführt und analysiert. Der zweite Teil beschäftigt sich mit bedingten additiven Quantilsmodellen. Das asymptotische Verhalten der Schätzer wird untersucht. Zusätzlich wird mit einer Simulationsstudie das Verhalten für eine endliche Stichprobe überprüft

Estimation of additive quantile regression

Conditional quantiles, Additive models, Marginal integration, Non-increasing rearrangements,