Parametric and nonparametric estimators of ED100α

Park, Dongryeon; Park, Sangun

doi:10.1080/10629360500279706

Cited by 14 publications

(20 citation statements)

References 14 publications

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“…Throughout this paper we denote the estimate of the effective dose level obtained through the inversion of the PAVA-monotonized estimate byÊD (PP1) α . Park and Park (2006) discussed another method to monotonizep QL (x) proposed by Kappenman (1987) [see also Silvermann (1981)], where the bandwidth h of the weighted quasi-likelihood estimator in (2.3) is increased to determine the smallest h 0 such thatp QL (x) is monotone for all h ≥ h 0 .…”

Section: A Locally Weighted Quasi-likelihood Estimator For Ed αmentioning

confidence: 99%

“…Similarly, Park and Park (2006) proposed a kernel method using the local quasi-likelihood approach. The idea is to maximize the function…”

Section: A Locally Weighted Quasi-likelihood Estimator For Ed αmentioning

confidence: 99%

“…We denote the monotonized estimate byp QL (x). In particular, Park and Park (2006) considered two methods to calculate a monotonized estimate. The first method applies the PAV algorithm discussed in Section 2.1.…”

Section: A Locally Weighted Quasi-likelihood Estimator For Ed αmentioning

confidence: 99%

“…Park and Park (2006) suggest to monotonize this estimate and compute the generalized inverse of the monotonized estimate. We denote the monotonized estimate byp QL (x).…”

Section: A Locally Weighted Quasi-likelihood Estimator For Ed αmentioning

confidence: 99%

“…In such situations parametric models can lead to wrong conclusions about the effective dose level if the underlying parametric model is wrong [see Hamilton (1979) or Dette, Neumeyer and Pilz (2005)]. Therefore several authors proposed nonparametric estimates of the effective dose in the literature [see Müller and Schmitt (1988), Dette et al (2005), Park and Park (2006), Bhattacharya and Kong (2007)]. …”

Section: Introductionmentioning

confidence: 99%

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

Dette

Scheder

2010

Journal of Statistical Computation and Simulation

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To estimate the effective dose level ED α 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 α 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.

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Section: A Locally Weighted Quasi-likelihood Estimator For Ed αmentioning

confidence: 99%

“…Similarly, Park and Park (2006) proposed a kernel method using the local quasi-likelihood approach. The idea is to maximize the function…”

Section: A Locally Weighted Quasi-likelihood Estimator For Ed αmentioning

confidence: 99%

Section: A Locally Weighted Quasi-likelihood Estimator For Ed αmentioning

confidence: 99%

“…Park and Park (2006) suggest to monotonize this estimate and compute the generalized inverse of the monotonized estimate. We denote the monotonized estimate byp QL (x).…”

Section: A Locally Weighted Quasi-likelihood Estimator For Ed αmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Dette

Scheder

2010

Journal of Statistical Computation and Simulation

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Nonparametric benchmark analysis in risk assessment: a comparative study by simulation and data analysis

Bhattacharya

Lin

2011

Sankhya B

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We consider the finite sample performance of a new nonparametric method for bioassay and benchmark analysis in risk assessment, which averages isotonic MLEs based on disjoint subgroups of dosages, and whose asymptotic behavior is essentially optimal (Bhattacharya and Lin (2010)). It is compared with three other methods, including the leading kernel-based method, called DNP, due to Dette et al. (2005) and Dette and Scheder (2010). In simulation studies, the present method, termed NAM, outperforms the DNP in the majority of cases considered, although both methods generally do well. In small samples, NAM and DNP both outperform the MLE.

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Recent progress in the nonparametric estimation of monotone curves—With applications to bioassay and environmental risk assessment

Bhattacharya

Lin

2013

Computational Statistics & Data Analysis

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Three recent nonparametric methodologies for estimating a monotone regression function F and its inverse F−1 are (1) the inverse kernel method DNP (Dette et al. (2005), Dette and Scheder (2010)), (2) the monotone spline (Kong and Eubank (2006)) and (3) the data adaptive method NAM (Bhattacharya and Lin (2010), (2011)), with roots in isotonic regression (Ayer et al. (1955), Bhattacharya and Kong (2007)). All three have asymptotically optimal error rates. In this article their finite sample performances are compared using extensive simulation from diverse models of interest, and by analysis of real data. Let there be m distinct values of the independent variable x among N observations y. The results show that if m is relatively small compared to N then generally the NAM performs best, while the DNP outperforms the other methods when m is O(N) unless there is a substantial clustering of the values of the independent variable x.

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Parametric and nonparametric estimators of ED100α

Cited by 14 publications

References 14 publications

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

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

Nonparametric benchmark analysis in risk assessment: a comparative study by simulation and data analysis

Recent progress in the nonparametric estimation of monotone curves—With applications to bioassay and environmental risk assessment

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