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Parametric Form (parametric + form)

Distribution by Scientific Domains
Mathematics and Statistics57%

Selected Abstracts

Model updating using noisy response measurements without knowledge of the input spectrum

EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 2 2005
Ka-Veng Yuen
Abstract A new probabilistic model identification methodology is proposed using measured response time histories only. The proposed approach requires that the number of independent measurements is larger than the number of independent excitations. Under this condition, no input measurements or any information regarding the stochastic model of the input is required. Specifically, the method does not require the response to be stationary and does not assume any knowledge of the parametric form of the spectral density of the input. Therefore, the method has very wide applicability. The proposed approach allows one to obtain not only the most probable values of the updated model parameters but also their associated uncertainties using only one set of response data. It is found that the updated probability distribution can be well approximated by a Gaussian distribution centered at the most probable values of the parameters. Examples are presented to illustrate the proposed method. Copyright © 2004 John Wiley & Sons, Ltd. [source]

On the Rank-Size Distribution for Human Settlements

JOURNAL OF REGIONAL SCIENCE, Issue 1 2002
William J. Reed
An explanation for the rank-size distribution for human settlements based on simple stochastic models of settlement formation and growth is presented. Not only does the analysis of the model explain the rank-size phenomenon in the upper tail, it also predicts a reverse rank-size phenomenon in the lower tail. Furthermore it yields a parametric form (the double Pareto-lognormal distribution) for the complete distribution of settlement sizes. Settlement-size data for four regions (two in Spain and two in the U.S.) are used as examples. For these regions the lower tail rank-size property is seen to hold and the double Pareto-lognormal distribution shown to provide an excellent fit, lending support to the model and to the explanation for the rank-size law. [source]

Robust sequential designs for nonlinear regression

THE CANADIAN JOURNAL OF STATISTICS, Issue 4 2002
Sanjoy Sinha
Abstract The authors introduce the formal notion of an approximately specified nonlinear regression model and investigate sequential design methodologies when the fitted model is possibly of an incorrect parametric form. They present small-sample simulation studies which indicate that their new designs can be very successful, relative to some common competitors, in reducing mean squared error due to model misspecifi-cation and to heteroscedastic variation. Their simulations also suggest that standard normal-theory inference procedures remain approximately valid under the sequential sampling schemes. The methods are illustrated both by simulation and in an example using data from an experiment described in the chemical engineering literature. Les auteurs définissent formellement le concept de modéle de régression non linéaire approxima-tif et proposentdes plans d'expérience séquentiels pour les situations o4uG la forme paramétrique du modéle ajusté est inexacte. Ils présentent une étude de simulation qui montre que, pour de petits échantillons, leurs nouveaux plans sont largement préférables aux plans usuels en terme de réduction de I'erreur quadratique moyenne associée à rinadéquation du modéle et à l'hétéroscédasticité. Leurs simulations montrent aussi que les procédures d'inférence classiques associées au paradigme normal restent valables, à peu de choses prés, pour ces plans expéimentaux se'quentiels. La methodologie proposde est illustrée par voie de simulation et au moyen d'une application concréte tirée de la pratique du génie chimique. [source]

NONPARAMETRIC LIKELIHOOD: EFFICIENCY AND ROBUSTNESS,

THE JAPANESE ECONOMIC REVIEW, Issue 1 2007
YUICHI KITAMURAArticle first published online: 8 FEB 200
Nonparametric likelihood is a natural generalization of parametric likelihood and it offers effective methods for analysing economic models with nonparametric components. This is of great interest, since econometric theory rarely suggests a parametric form of the probability law of data. Being a nonparametric method, nonparametric likelihood is robust to misspecification. At the same time, it often achieves good properties that are analogous to those of parametric likelihood. This paper explores various applications of nonparametric likelihood, with some emphasis on the analysis of biased samples and data combination problems. [source]

BOOTSTRAP TESTS FOR THE ERROR DISTRIBUTION IN LINEAR AND NONPARAMETRIC REGRESSION MODELS

AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, Issue 2 2006
Natalie Neumeyer
Summary In this paper we investigate several tests for the hypothesis of a parametric form of the error distribution in the common linear and non-parametric regression model, which are based on empirical processes of residuals. It is well known that tests in this context are not asymptotically distribution-free and the parametric bootstrap is applied to deal with this problem. The performance of the resulting bootstrap test is investigated from an asymptotic point of view and by means of a simulation study. The results demonstrate that even for moderate sample sizes the parametric bootstrap provides a reliable and easy accessible solution to the problem of goodness-of-fit testing of assumptions regarding the error distribution in linear and non-parametric regression models. [source]

An Adaptive Two-stage Design with Treatment Selection Using the Conditional Error Function Approach

BIOMETRICAL JOURNAL, Issue 4 2006
Jixian Wang
Abstract As an approach to combining the phase II dose finding trial and phase III pivotal trials, we propose a two-stage adaptive design that selects the best among several treatments in the first stage and tests significance of the selected treatment in the second stage. The approach controls the type I error defined as the probability of selecting a treatment and claiming its significance when the selected treatment is indifferent from placebo, as considered in Bischoff and Miller (2005). Our approach uses the conditional error function and allows determining the conditional type I error function for the second stage based on information observed at the first stage in a similar way to that for an ordinary adaptive design without treatment selection. We examine properties such as expected sample size and stage-2 power of this design with a given type I error and a maximum stage-2 sample size under different hypothesis configurations. We also propose a method to find the optimal conditional error function of a simple parametric form to improve the performance of the design and have derived optimal designs under some hypothesis configurations. Application of this approach is illustrated by a hypothetical example. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Order-Restricted Semiparametric Inference for the Power Bias Model

BIOMETRICS, Issue 2 2010
Ori Davidov
Summary The power bias model, a generalization of length-biased sampling, is introduced and investigated in detail. In particular, attention is focused on order-restricted inference. We show that the power bias model is an example of the density ratio model, or in other words, it is a semiparametric model that is specified by assuming that the ratio of several unknown probability density functions has a parametric form. Estimation and testing procedures under constraints are developed in detail. It is shown that the power bias model can be used for testing for, or against, the likelihood ratio ordering among multiple populations without resorting to any parametric assumptions. Examples and real data analysis demonstrate the usefulness of this approach. [source]