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Robust Estimator (robust + estimator)
Selected AbstractsOnline process mean estimation using L1 norm exponential smoothingNAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 5 2009Wei Jiang Abstract A basic assumption in process mean estimation is that all process data are clean. However, many sensor system measurements are often corrupted with outliers. Outliers are observations that do not follow the statistical distribution of the bulk of the data and consequently may lead to erroneous results with respect to statistical analysis and process control. Robust estimators of the current process mean are crucial to outlier detection, data cleaning, process monitoring, and other process features. This article proposes an outlier-resistant mean estimator based on the L1 norm exponential smoothing (L1 -ES) method. The L1 -ES statistic is essentially model-free and demonstrably superior to existing estimators. It has the following advantages: (1) it captures process dynamics (e.g., autocorrelation), (2) it is resistant to outliers, and (3) it is easy to implement. © 2009 Wiley Periodicals, Inc. Naval Research Logistics 2009 [source] Robust Kalman filtering for uncertain discrete-time linear systemsINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 13 2003Germain Garcia Abstract This paper presents a steady-state robust state estimator for a class of uncertain discrete-time linear systems with norm-bounded uncertainty. It is shown that if the system satisfies some particular structural conditions and if the uncertainty has a specific structure, the gain of the robust estimator (which assures a guaranteed cost) can be calculated using a formula only involving the original system matrices. Among the conditions the system has to satisfy, the strongest one relies on a minimum phase argument. It is also shown that under the assumptions considered, the robust estimator is in fact the Kalman filter for the nominal system. Copyright © 2003 John Wiley & Sons, Ltd. [source] Highly Robust Estimation of the Autocovariance FunctionJOURNAL OF TIME SERIES ANALYSIS, Issue 6 2000Yanyuan Ma In this paper, the problem of the robustness of the sample autocovariance function is addressed. We propose a new autocovariance estimator, based on a highly robust estimator of scale. Its robustness properties are studied by means of the influence function, and a new concept of temporal breakdown point. As the theoretical variance of the estimator does not have a closed form, we perform a simulation study. Situations with various size of outliers are tested. They confirm the robustness properties of the new estimator. An S-Plus function for the highly robust autocovariance estimator is made available on the Web at http://www-math.mit.edu/~yanyuan/Genton/Time/time.html. At the end, we analyze a time series of monthly interest rates of an Austrian bank. [source] Bitumen content estimation of Athabasca oil sand from broad band infrared reflectance spectraTHE CANADIAN JOURNAL OF CHEMICAL ENGINEERING, Issue 5 2010B. Rivard Abstract Oil sand is a mixture of quartz grains, clay minerals, bitumen, water, and minor accessory minerals. There is a need in oil sands mining operations for a robust method to estimate total bitumen content in real time; and so modelling of the total bitumen content (TBC) in Athabasca oil sands of Western Canada was undertaken on the basis of hyperspectral reflectance spectra. A selection of different bitumen, water, and clay mineral spectral features (3.0,30.0,µm) was used to develop broad-band TBC predictive models that have good accuracy, with less than 1.5% error with respect to laboratory methods of bitumen assay. These models are also robust, in that they are independent of mine location. Simple broad band models, based upon previously identified Gaussian features or wavelet features, provide an incremental improvement over the currently deployed industry two-band ratio model. An improved two-band model was also developed, which makes use of a combination of the same two bands but normalised to their mean. A wavelet-based, broad-band model comprised of indices and five bands, where the bands are normalised to the mean of the bands, adequately addresses the influence of water, clay, and textural variation on selected bitumen features. This five-band model appears to produce the most robust estimator of TBC, with a dispersion of ,1.1,1.5%, which can be applied to different sites within a mine and to different mines without additional tuning or calibration, as evidenced by regression slopes of 0.99,1.0 for modelling, validation, and blind data sets. [source] Robust Estimation and Outlier Detection for Overdispersed Multinomial Models of Count DataAMERICAN JOURNAL OF POLITICAL SCIENCE, Issue 2 2004Walter R. Mebane Jr. We develop a robust estimator,the hyperbolic tangent (tanh) estimator,for overdispersed multinomial regression models of count data. The tanh estimator provides accurate estimates and reliable inferences even when the specified model is not good for as much as half of the data. Seriously ill-fitted counts,outliers,are identified as part of the estimation. A Monte Carlo sampling experiment shows that the tanh estimator produces good results at practical sample sizes even when ten percent of the data are generated by a significantly different process. The experiment shows that, with contaminated data, estimation fails using four other estimators: the nonrobust maximum likelihood estimator, the additive logistic model and two SUR models. Using the tanh estimator to analyze data from Florida for the 2000 presidential election matches well-known features of the election that the other four estimators fail to capture. In an analysis of data from the 1993 Polish parliamentary election, the tanh estimator gives sharper inferences than does a previously proposed heteroskedastic SUR model. [source] Causal inference with generalized structural mean modelsJOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 4 2003S. Vansteelandt Summary., We estimate cause,effect relationships in empirical research where exposures are not completely controlled, as in observational studies or with patient non-compliance and self-selected treatment switches in randomized clinical trials. Additive and multiplicative structural mean models have proved useful for this but suffer from the classical limitations of linear and log-linear models when accommodating binary data. We propose the generalized structural mean model to overcome these limitations. This is a semiparametric two-stage model which extends the structural mean model to handle non-linear average exposure effects. The first-stage structural model describes the causal effect of received exposure by contrasting the means of observed and potential exposure-free outcomes in exposed subsets of the population. For identification of the structural parameters, a second stage ,nuisance' model is introduced. This takes the form of a classical association model for expected outcomes given observed exposure. Under the model, we derive estimating equations which yield consistent, asymptotically normal and efficient estimators of the structural effects. We examine their robustness to model misspecification and construct robust estimators in the absence of any exposure effect. The double-logistic structural mean model is developed in more detail to estimate the effect of observed exposure on the success of treatment in a randomized controlled blood pressure reduction trial with self-selected non-compliance. [source] Robust Estimation For Periodic Autoregressive Time SeriesJOURNAL OF TIME SERIES ANALYSIS, Issue 2 2008Q. Shao Abstract., A robust estimation procedure for periodic autoregressive (PAR) time series is introduced. The asymptotic properties and the asymptotic relative efficiency are discussed by the estimating equation approach. The performance of the robust estimators for PAR time-series models with order one is illustrated by a simulation study. The technique is applied to a real data analysis. [source] Omitted variables in longitudinal data modelsTHE CANADIAN JOURNAL OF STATISTICS, Issue 4 2001Edward W. Frees Abstract The omission of important variables is a well-known model specification issue in regression analysis and mixed linear models. The author considers longitudinal data models that are special cases of the mixed linear models; in particular, they are linear models of repeated observations on a subject. Models of omitted variables have origins in both the econometrics and biostatistics literatures. The author describes regression coefficient estimators that are robust to and that provide the basis for detecting the influence of certain types of omitted variables. New robust estimators and omitted variable tests are introduced and illustrated with a case study that investigates the determinants of tax liability. [source] Robustified Maximum Likelihood Estimation in Generalized Partial Linear Mixed Model for Longitudinal DataBIOMETRICS, Issue 1 2009Guo You Qin Summary In this article, we study the robust estimation of both mean and variance components in generalized partial linear mixed models based on the construction of robustified likelihood function. Under some regularity conditions, the asymptotic properties of the proposed robust estimators are shown. Some simulations are carried out to investigate the performance of the proposed robust estimators. Just as expected, the proposed robust estimators perform better than those resulting from robust estimating equations involving conditional expectation like Sinha (2004, Journal of the American Statistical Association99, 451,460) and Qin and Zhu (2007, Journal of Multivariate Analysis98, 1658,1683). In the end, the proposed robust method is illustrated by the analysis of a real data set. [source] |