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Robustness of design in dose–response studies
 Journal of the Royal Statistical Society: Series B
"... Summary. We construct experimental designs for dose–response studies. The designs are robust against possibly misspecified link functions; for this they minimize the maximum meansquared error of the estimated dose required to attain a response in 100p % of the target population. Here p might be one ..."
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Summary. We construct experimental designs for dose–response studies. The designs are robust against possibly misspecified link functions; for this they minimize the maximum meansquared error of the estimated dose required to attain a response in 100p % of the target population. Here p might be one particular value—p D0:5 corresponds to ED50estimation—or it might range over an interval of values of interest. The maximum of the meansquared error is evaluated over a Kolmogorov neighbourhood of the fitted link. Both the maximum and the minimum must be evaluated numerically; the former is carried out by quadratic programming and the latter by simulated annealing.
Estimation of smooth regression functions in monotone response models
"... We consider the estimation of smooth regression functions in a class of conditionally parametric covariateresponse models. Independent and identically distributed observations are available from the distribution of (Z,X), where Z is a realvalued covariate with some unknown distribution, and the ..."
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We consider the estimation of smooth regression functions in a class of conditionally parametric covariateresponse models. Independent and identically distributed observations are available from the distribution of (Z,X), where Z is a realvalued covariate with some unknown distribution, and the response X conditional on Z is distributed according to the density p(.,psi(Z)), where p(.,theta) is a oneparameter exponential family. The function psi is a smooth monotone function. Under this formulation, the regression function E(XZ) is monotone in the covariate Z (and can be expressed as a oneone function of psi); hence the term ``monotone response model''. Using a penalized least squares approach that incorporates both monotonicity and smoothness, we develop a scheme for producing smooth monotone estimates of the regression function and also the function psi across this entire class of models. Pointwise asymptotic normality of this estimator is established, with the rate of convergence depending on the smoothing parameter. This enables construction of Waldtype (pointwise) as well as pivotal confidence sets for psi and also the regression function.
Nonparametric quantile regression for twice censored data
, 2009
"... regression for twice censored data D is ..."
Nonparametric quantile regression for twice censored data
"... Abstract We consider the problem of nonparametric quantile regression for twice censored data. Two new estimates are presented, which are constructed by applying concepts of monotone rearrangements to estimates of the conditional distribution function. The proposed methods avoid the problem of cros ..."
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Abstract We consider the problem of nonparametric quantile regression for twice censored data. Two new estimates are presented, which are constructed by applying concepts of monotone rearrangements to estimates of the conditional distribution function. The proposed methods avoid the problem of crossing quantile curves. Weak uniform consistency and weak convergence is established for both estimates and their finite sample properties are investigated by means of a simulation study. As a byproduct, we obtain a new result regarding the weak convergence of the Beran estimator for right censored data on the maximal possible domain, which is of its own interest.
Contents
, 710
"... Regression for partially observed variables and nonparametric quantiles of ..."
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Regression for partially observed variables and nonparametric quantiles of
www.samsi.info Bayesian Isotonic Estimation for Exponential Family and Beyond
, 2008
"... In the restricted parameter estimation, the use of exponential family have been introduced to include applications from several scientific studies. The MLE based approach or the smoothing type estimators have been studied using monotone link functions. In this paper, we introduce Bayesian techniques ..."
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In the restricted parameter estimation, the use of exponential family have been introduced to include applications from several scientific studies. The MLE based approach or the smoothing type estimators have been studied using monotone link functions. In this paper, we introduce Bayesian techniques to investigate such methods in a general scenario, with illustrations to special examples such as binomial, Poisson etc. The conjugate priors in the exponential family problem helps us to obtain posterior distributions with similar expressions. The logconcavity of the posterior densities allow us to use adaptive rejection sampling for the individual draws. An MCMC method involving Gibbs sampler is developed to sample from that posterior which yields credible regions for the parameters. We modify our method to include changepoint estimation as well, where the underlying parameter curve has some known or unknown changepoint. Finally, the method is extended to semiparametric models, where the link function consists of a monotone function of one particular covariate and a linear model on the other covariate. The method is shown to be applicable to some simulated data from the binomial and Poisson family to corroborate our findings. We also apply our technique to estimate the current immunization status for the Rubella virus in a study conducted on Austrian males.
Nonparametric quantile regression for twice censored data
"... We consider the problem of nonparametric quantile regression for twice censored data. Two new estimates are presented, which are constructed by applying concepts of monotone rearrangements to estimates of the conditional distribution function. The proposed methods avoid the problem of crossing quant ..."
Abstract
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We consider the problem of nonparametric quantile regression for twice censored data. Two new estimates are presented, which are constructed by applying concepts of monotone rearrangements to estimates of the conditional distribution function. The proposed methods avoid the problem of crossing quantile curves. Weak uniform consistency and weak convergence is established for both estimates and their finite sample properties are investigated by means of a simulation study. As a byproduct, we obtain a new result regarding the weak convergence of the Beran estimator for right censored data on the maximal possible domain, which is of its own interest.