An important statistical objective in environmental risk analysis is estimation of minimum exposure levels, called benchmark doses (BMDs), which induce a pre-specified benchmark response in a doseresponse experiment. ...
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An important statistical objective in environmental risk analysis is estimation of minimum exposure levels, called benchmark doses (BMDs), which induce a pre-specified benchmark response in a doseresponse experiment. In such settings, representations of the risk are traditionally based on a parametric doseresponse model. It is a well-known concern, however, that if the chosen parametric form is misspecified, inaccurate and possibly unsafe low-dose inferences can result. We apply a nonparametric approach for calculating BMDs, based on an isotonic doseresponse estimator for quantal-response data. We determine the large-sample properties of the estimator, develop bootstrap-based confidence limits on the BMDs, and explore the confidence limits small-sample properties via a short simulation study. An example from cancer risk assessment illustrates the calculations. Copyright (c) 2012 John Wiley & Sons, Ltd.
Monotonic regression (MR) is an efficient tool for estimating functions that are monotonic with respect to input variables. A fast and highly accurate approximate algorithm called the GPAV was recently developed for e...
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Monotonic regression (MR) is an efficient tool for estimating functions that are monotonic with respect to input variables. A fast and highly accurate approximate algorithm called the GPAV was recently developed for efficient solving large-scale multivariate MR problems. When such problems are too large, the GPAV becomes too demanding in terms of computational time and memory. An approach, that extends the application area of the GPAV to encompass much larger MR problems, is presented. It is based on segmentation of a large-scale MR problem into a set of moderate-scale MR problems, each solved by the GPAV. The major contribution is the development of a computationally efficient strategy that produces a monotonic response using the local solutions. A theoretically motivated trend-following technique is introduced to ensure higher accuracy of the solution. The presented results of extensive simulations on very large data sets demonstrate the high efficiency of the new algorithm. (C) 2011 Elsevier B.V. All rights reserved.
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...
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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, Stat Probab Lett 80: 1947-1953, 2010). It is compared with three other methods, including the leading kernel-based method, called DNP, due to Dette et al. (J Am Stat Assoc 100: 503-510, 2005) and Dette and Scheder (J Stat Comput Simul 80(5): 527-544, 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.
In this paper we describe active set type algorithms for minimization of a smooth function under general order constraints, an important case being functions on the set of bimonotone rxs matrices. These algorithms can...
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In this paper we describe active set type algorithms for minimization of a smooth function under general order constraints, an important case being functions on the set of bimonotone rxs matrices. These algorithms can be used, for instance, to estimate a bimonotone regression function via least squares or (a smooth approximation of) least absolute deviations. Another application is shrinkage estimation in image denoising or, more generally, regression problems with two ordinal factors after representing the data in a suitable basis which is indexed by pairs (i,j)a{1,aEuro broken vertical bar,r}x{1,aEuro broken vertical bar,s}. Various numerical examples illustrate our methods.
Discrimination of time series is an important practical problem with applications in various scientific fields. We propose and study a novel approach to this problem. Our approach is applicable to cases where time ser...
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Discrimination of time series is an important practical problem with applications in various scientific fields. We propose and study a novel approach to this problem. Our approach is applicable to cases where time series in different categories have a different "shape." Although based on the idea of feature extraction, our method is not distance-based, and as such does not require aligning the time series. Instead, features are measured for each time series, and discrimination is based on these individual measures. An AR process with a time-varying variance is used as an underlying model. Our method then uses shape measures or, better, measures of concentration of the variance function, as a criterion for discrimination. It is this concentration aspect or shape aspect that makes the approach intuitively appealing. We provide some mathematical justification for our proposed methodology, as well as a simulation study and an application to the problem of discriminating earthquakes and explosions.
This paper offers a new method for testing one-sided hypotheses in discrete multivariate data models. One-sided alternatives mean that there are restrictions on the multidimensional parameter space. The focus is on mo...
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This paper offers a new method for testing one-sided hypotheses in discrete multivariate data models. One-sided alternatives mean that there are restrictions on the multidimensional parameter space. The focus is on models dealing with ordered categorical data. In particular, applications are concerned with R x C contingency tables. The method has advantages over other general approaches. All tests are exact in the sense that no large sample theory or large sample distribution theory is required. Testing is unconditional although its execution is done conditionally, section by section, where a section is determined by marginal totals. This eliminates any potential nuisance parameter issues. The power of the tests is more robust than the power of the typical linear tests often recommended. Furthermore, computer programs are available to carry out the tests efficiently regardless of the sample sizes or the order of the contingency tables. Both censored data and uncensored data models are discussed.
We consider the problem of optimally quantifying the categories of an ordered response variable under a linear model. The mathematical formulation leads to the maximization of a ratio of quadratic forms subject to lin...
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We consider the problem of optimally quantifying the categories of an ordered response variable under a linear model. The mathematical formulation leads to the maximization of a ratio of quadratic forms subject to linear inequality constraints. The solution is given by a hierarchical active constraints search algorithm. We prove that the algorithm converges to the global optimum.
In the present paper we consider the isotonic regression problem with an arbitrary convex distance function d(.), and the main purpose being to present an algorithm for obtaining all isotonic regressions under this re...
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In the present paper we consider the isotonic regression problem with an arbitrary convex distance function d(.), and the main purpose being to present an algorithm for obtaining all isotonic regressions under this reasonable assumption on d(.). Further, we consider a piece-wise linear distance function d(.) of the type d(t) = C-\t\ for t < 0 and d(t) = C+ \t\ for t greater-than-or-equal-to 0 and get an isotonic pth frctile regression by choosing p = C+ /(C- + C+).
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