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Parametric statistics

About: Parametric statistics is a research topic. Over the lifetime, 39200 publications have been published within this topic receiving 765761 citations.


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Journal ArticleDOI
TL;DR: In this paper, a nine-story steel moment-resisting frame is used as a testbed, employing parameterized moment-rotation relationships with non-deterministic quadrilinear backbones for the beam plastic-hinges.
Abstract: SUMMARY Incremental Dynamic Analysis (IDA) is presented as a powerful tool to evaluate the variability in the seismic demand and capacity of non-deterministic structural models, building upon existing methodologies of Monte Carlo simulation and approximate moment-estimation. A nine-story steel moment-resisting frame is used as a testbed, employing parameterized moment-rotation relationships with non-deterministic quadrilinear backbones for the beam plastic-hinges. The uncertain properties of the backbones include the yield moment, the post-yield hardening ratio, the end-of-hardening rotation, the slope of the descending branch, the residual moment capacity and the ultimate rotation reached. IDA is employed to accurately assess the seismic performance of the model for any combination of the parameters by performing multiple nonlinear timehistory analyses for a suite of ground motion records. Sensitivity analyses on both the IDA and the static pushover level reveal the yield moment and the two rotational-ductility parameters to be the most in∞uential for the frame behavior. To propagate the parametric uncertainty to the actual seismic performance we employ a) Monte Carlo simulation with latin hypercube sampling, b) point-estimate and c) flrst-order second-moment techniques, thus ofiering competing methods that represent difierent compromises between speed and accuracy. The flnal results provide flrm ground for challenging current assumptions in seismic guidelines on using a median-parameter model to estimate the median seismic performance and employing the well-known square-root-sum-of-squares rule to combine aleatory randomness and epistemic uncertainty. Copyright c ∞ 2009 John Wiley & Sons, Ltd.

277 citations

Journal ArticleDOI
TL;DR: A novel multivariate exponentially weighted moving average monitoring scheme for a general linear profile, which fits a quadratic polynomial regression model well and is introduced to improve the performance of the proposed scheme.
Abstract: We propose a statistical process control scheme that can be implemented in industrial practice, in which the quality of a process can be characterized by a general linear profile. We start by reviewing the general linear profile model and the existing monitoring methods. Based on this, we propose a novel multivariate exponentially weighted moving average monitoring scheme for such a profile. We introduce two other enhancement features, the variable sampling interval and the parametric diagnostic approach, to further improve the performance of the proposed scheme. Throughout the article, we use a deep reactive ion etching example from semiconductor manufacturing, which has a profile that fits a quadratic polynomial regression model well, to illustrate the implementation of the proposed approach.

277 citations

Journal ArticleDOI
TL;DR: The main result is that a minimal confidence ellipsoid for the state, consistent with the measured output and the uncertainty description, may be recursively computed in polynomial time, using interior-point methods for convex optimization.
Abstract: This note presents a new approach to finite-horizon guaranteed state prediction for discrete-time systems affected by bounded noise and unknown-but-bounded parameter uncertainty. Our framework handles possibly nonlinear dependence of the state-space matrices on the uncertain parameters. The main result is that a minimal confidence ellipsoid for the state, consistent with the measured output and the uncertainty description, may be recursively computed in polynomial time, using interior-point methods for convex optimization. With n states, l uncertain parameters appearing linearly in the state-space matrices, with rank-one matrix coefficients, the worst-case complexity grows as O(l(n + l)/sup 3.5/) With unstructured uncertainty in all system matrices, the worst-case complexity reduces to O(n/sup 3.5/).

277 citations

Journal ArticleDOI
TL;DR: A related linear dynamic system (RLDS) approximation to the nonlinear system (NLS) is defined, and it is shown that the differences between the NLS and the RLDS can be modeled as stochastic variables with known properties.
Abstract: This paper studies the asymptotic behavior of nonparametric and parametric frequency domain identification methods to model linear dynamic systems in the presence of nonlinear distortions under some general conditions for random multisine excitations. In the first part, a related linear dynamic system (RLDS) approximation to the nonlinear system (NLS) is defined, and it is shown that the differences between the NLS and the RLDS can be modeled as stochastic variables with known properties. In the second part a parametric model for the RLDS is identified. Convergence in probability of this model to the RLDS is proven. A function of dependency is defined to detect and separate the presence of unmodeled dynamics and nonlinear distortions and to bound the bias error on the transfer function estimate.

276 citations

Journal ArticleDOI
TL;DR: In this paper, a conditional Kolmogorov test of model specification for parametric models with covariates (regressors) is proposed, based on the goodness-of-fit test for distribution functions.
Abstract: This paper introduces a conditional Kolmogorov test of model specification for parametric models with covariates (regressors). The test is an extension of the Kolmogorov test of goodness-of-fit for distribution functions. The test is shown to have power against 1/√n local alternatives and all fixed alternatives to the null hypothesis. A parametric bootstrap procedure is used to obtain critical values for the test.

276 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20252
20242
20233,966
20227,822
20211,968
20202,033