Kernel Estimates of Dose Response

Staniswalis, Joan G.; Cooper, Vanessa

doi:10.2307/2531739

Cited by 26 publications

(14 citation statements)

References 16 publications

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“…which was proposed in Müller (1985), and Staniswalis and Cooper (1988) [Ruppert and Wand (1994)],p NW is characterized as the minimizer of…”

Section: Weighted Kernel Estimatorsmentioning

confidence: 99%

“…These include kernel methods, smoothing splines and local likelihood methods, among which local logistic regression [Fan et al(1995)] is specifically intended for binary response variable. Nonparametric approaches to binary data were considered by Copas (1983), Staniswalis and Cooper (1988) and Müller and Schmit (1988). Copas (1983) first suggested the use of Nadaraya-Watson estimator [Nadaraya (1964), Watson (1964)] in the binary setting.…”

Section: Introductionmentioning

confidence: 99%

“…Copas (1983) first suggested the use of Nadaraya-Watson estimator [Nadaraya (1964), Watson (1964)] in the binary setting. Various parametric and nonparametric techniques for estimation of the functional of p have been reported in Müller and Schmit (1988) and Staniswalis and Cooper (1988) in conjunction with the practical applications. In this paper, we propose two kernel-based estimators for binomial regression.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we propose two kernel-based estimators for binomial regression. Our estimators are motivated by the kernel-based estimator such as Nadaraya-Watson type suggested and discussed by Staniswalis and Cooper (1988), and are obtained by smoothing the observed proportions at each covariate through the use of the kernel weighted by the inverse of variance of the observed proportion at each covariate.…”

Section: Introductionmentioning

confidence: 99%

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Weighted kernel estimators in nonparametric binomial regression

Okumura¹,

Naito²

2004

Journal of Nonparametric Statistics

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This paper is concerned with nonparametric binomial regression. Two kernel-based binomial regression estimators and their bias-adjusted versions are proposed, whose kernels are weighted by the inverses of variance estimators of the observed proportion at each covariate. Asymptotic theories for deriving asymptotic mean squared errors (AMSEs) of proposed estimators are developed. Comparisons with other estimators discussed by several authors are implemented through the AMSEs. From these considerations, together with the simulation results, the advantages of our weighting scheme are reported.

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“…which was proposed in Müller (1985), and Staniswalis and Cooper (1988) [Ruppert and Wand (1994)],p NW is characterized as the minimizer of…”

Section: Weighted Kernel Estimatorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Weighted kernel estimators in nonparametric binomial regression

Okumura¹,

Naito²

2004

Journal of Nonparametric Statistics

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“…Various nonparametric approaches for the estimation of p(x) can be applied. In particular, Staniswalis and Cooper [1] and Müller and Schmitt [2] discussed nonparametric kernel approaches for the estimation of p(x) and an effective dose in binary *Corresponding author. Email: okumura@cjc.ac.jp 344 H. Okumura and K. Naito settings with fixed design.…”

Section: Introductionmentioning

confidence: 99%

Bandwidth selection for kernel binomial regression

Okumura

Naito

2006

Journal of Nonparametric Statistics

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In nonparametric binomial regression, the weighted kernel estimator of the regression function and its efficient bias-adjusted version have been proposed by Okumura and Naito (2004) with consideration to differences of variances of observed response proportions at covariates. The aim of this article is to propose an effective data-based method for bandwidth selection of the bias-adjusted estimator. The proposed method is developed through three steps: the plug-in method by Ruppert et al. (1995), a scale adjustment suggested by Yang and Tschernig (1999), and an effective use of the approach discussed by Grizzel et al. (1969) for the rule-of-thumb part. Theoretical considerations on the asymptotic performance of the selected bandwidth are given under the situation where the numbers of covariates and responses observed at each covariate increase.

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A semiparametric approach to analysing dose-response data

Nottingham

Birch

2000

Statist. Med.

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In the analysis of a quantal dose‐response experiment with grouped data, the most commonly used parametric procedure is logistic regression, commonly referred to as ‘logit analysis’. The adequacy of the fit by the logistic regression curve is tested using the chi‐square lack‐of‐fit test. If the lack‐of‐fit test is not significant, then the logistic model is assumed to be adequate and estimation of effective doses and confidence intervals on the effective doses can be made. When the tolerance distribution of the dose–response data is not known and cannot be assumed by the user, one can use non‐parametric methods, such as kernel regression or local linear regression, to estimate the dose–response curve, effective doses and confidence intervals. This research proposes another alternative based on semi‐parametric regression to analysing quantal dose–response data called model‐robust quantal regression (MRQR). MRQR linearly combines the parametric and non‐parametric predictions with the use of a mixing parameter. MRQR uses logistic regression as the parametric portion of the model and local linear regression as the non‐parametric portion of the model. Our research has shown that the MRQR procedure can improve the fit of the dose–response curve by producing narrower confidence intervals for predictions while providing improved precision of estimates of the effective doses with respect to either logistic or local linear regression results. Copyright © 2000 John Wiley & Sons, Ltd.

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Kernel Estimates of Dose Response

Cited by 26 publications

References 16 publications

Weighted kernel estimators in nonparametric binomial regression

Weighted kernel estimators in nonparametric binomial regression

Bandwidth selection for kernel binomial regression

A semiparametric approach to analysing dose-response data

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