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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.


Papers
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Journal ArticleDOI
TL;DR: In this article, the authors derived the asymptotic distribution of the maximum partial likelihood estimator β for the vector of regression coefficients β under a possibly misspecified Cox proportional hazards model.
Abstract: We derive the asymptotic distribution of the maximum partial likelihood estimator β for the vector of regression coefficients β under a possibly misspecified Cox proportional hazards model. As in the parametric setting, this estimator β converges to a well-defined constant vector β*. In addition, the random vector n 1/2(β – β*) is asymptotically normal with mean 0 and with a covariance matrix that can be consistently estimated. The newly proposed robust covariance matrix estimator is similar to the so-called “sandwich” variance estimators that have been extensively studied for parametric cases. For many misspecified Cox models, the asymptotic limit β* or part of it can be interpreted meaningfully. In those circumstances, valid statistical inferences about the corresponding covariate effects can be drawn based on the aforementioned asymptotic theory of β and the related results for the score statistics. Extensive studies demonstrate that the proposed robust tests and interval estimation procedures...

2,466 citations

Book
24 Jul 1998
TL;DR: In this paper, the use of Bayesian methods for reliability data is discussed and a detailed discussion of the application of these methods in the context of automated life test planning is presented.
Abstract: Partial table of contents: Reliability Concepts and Reliability Data. Nonparametric Estimation. Other Parametric Distributions. Probability Plotting. Bootstrap Confidence Intervals. Planning Life Tests. Degradation Data, Models, and Data Analysis. Introduction to the Use of Bayesian Methods for Reliability Data. Failure--Time Regression Analysis. Accelerated Test Models. Accelerated Life Tests. Case Studies and Further Applications. Epilogue. Appendices. References. Indexes.

2,341 citations

Book
01 Jan 1998
TL;DR: In this article, a fault detection and diagnosis framework for discrete linear systems with residual generators and residual generator parameters is presented for additive and multiplicative faults by parameter estimation using a parity equation.
Abstract: Introduction to fault detection and diagnosis discrete linear systems random variables parameter estimation fundamentals analytical redundancy concepts parity equation implementation of residual generators design for structured residuals design for directional residuals residual generation for parametric faults robustness in residual generation statistical testing of residuals model identification for the diagnosis of additive faults diagnosing multiplicative faults by parameter estimation

2,188 citations

Journal ArticleDOI
TL;DR: The novelty of the approach is that it does not use a model selection criterion to choose one among a set of preestimated candidate models; instead, it seamlessly integrate estimation and model selection in a single algorithm.
Abstract: This paper proposes an unsupervised algorithm for learning a finite mixture model from multivariate data. The adjective "unsupervised" is justified by two properties of the algorithm: 1) it is capable of selecting the number of components and 2) unlike the standard expectation-maximization (EM) algorithm, it does not require careful initialization. The proposed method also avoids another drawback of EM for mixture fitting: the possibility of convergence toward a singular estimate at the boundary of the parameter space. The novelty of our approach is that we do not use a model selection criterion to choose one among a set of preestimated candidate models; instead, we seamlessly integrate estimation and model selection in a single algorithm. Our technique can be applied to any type of parametric mixture model for which it is possible to write an EM algorithm; in this paper, we illustrate it with experiments involving Gaussian mixtures. These experiments testify for the good performance of our approach.

2,182 citations

Journal ArticleDOI
TL;DR: FCS is a semi-parametric and flexible alternative that specifies the multivariate model by a series of conditional models, one for each incomplete variable, but its statistical properties are difficult to establish.
Abstract: The goal of multiple imputation is to provide valid inferences for statistical estimates from incomplete data. To achieve that goal, imputed values should preserve the structure in the data, as well as the uncertainty about this structure, and include any knowledge about the process that generated the missing data. Two approaches for imputing multivariate data exist: joint modeling (JM) and fully conditional specification (FCS). JM is based on parametric statistical theory, and leads to imputation procedures whose statistical properties are known. JM is theoretically sound, but the joint model may lack flexibility needed to represent typical data features, potentially leading to bias. FCS is a semi-parametric and flexible alternative that specifies the multivariate model by a series of conditional models, one for each incomplete variable. FCS provides tremendous flexibility and is easy to apply, but its statistical properties are difficult to establish. Simulation work shows that FCS behaves very well in ...

2,119 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