Home  About us  Contact
 

Mean Estimation (mean + estimation)

Distribution by Scientific Domains
Mathematics and Statistics80%

Selected Abstracts

Online process mean estimation using L1 norm exponential smoothing

NAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 5 2009
Wei 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]

Specification Testing of Markov Switching Models*

OXFORD BULLETIN OF ECONOMICS & STATISTICS, Issue 2003
Robert Breunig
Abstract This paper proposes a set of formal tests to address the goodness-of-fit of Markov switching models. These formal tests are constructed as tests of model consistency and of both parametric and non-parametric encompassing. The formal tests are then combined with informal tests using simulation in combination with non-parametric density and conditional mean estimation. The informal tests are shown to be useful in shedding light on the failure (or success) of the encompassing tests. Several examples are provided. [source]

Efficiency measure, modelling and estimation in combined array designs

APPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, Issue 4 2003
Tak Mak
Abstract In off-line quality control, the settings that minimize the variance of a quality characteristic are unknown and must be determined based on an estimated dual response model of mean and variance. The present paper proposes a direct measure of the efficiency of any given design-estimation procedure for variance minimization. This not only facilitates the comparison of different design-estimation procedures, but may also provide a guideline for choosing a better solution when the estimated dual response model suggests multiple solutions. Motivated by the analysis of an industrial experiment on spray painting, the present paper also applies a class of link functions to model process variances in off-line quality control. For model fitting, a parametric distribution is employed in updating the variance estimates used in an iteratively weighted least squares procedure for mean estimation. In analysing combined array experiments, Engel and Huele (Technometrics, 1996; 39:365) used log-link to model process variances and considered an iteratively weighted least squares leading to the pseudo-likelihood estimates of variances as discussed in Carroll and Ruppert (Transformation and Weighting in Regression, Chapman & Hall: New York). Their method is a special case of the approach considered in this paper. It is seen for the spray paint data that the log-link may not be satisfactory and the class of link functions considered here improves substantially the fit to process variances. This conclusion is reached with a suggested method of comparing ,empirical variances' with the ,theoretical variances' based on the assumed model. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Youden Index and Optimal Cut-Point Estimated from Observations Affected by a Lower Limit of Detection

BIOMETRICAL JOURNAL, Issue 3 2008
Marcus D. Ruopp
Abstract The receiver operating characteristic (ROC) curve is used to evaluate a biomarker's ability for classifying disease status. The Youden Index (J), the maximum potential effectiveness of a biomarker, is a common summary measure of the ROC curve. In biomarker development, levels may be unquantifiable below a limit of detection (LOD) and missing from the overall dataset. Disregarding these observations may negatively bias the ROC curve and thus J. Several correction methods have been suggested for mean estimation and testing; however, little has been written about the ROC curve or its summary measures. We adapt non-parametric (empirical) and semi-parametric (ROC-GLM [generalized linear model]) methods and propose parametric methods (maximum likelihood (ML)) to estimate J and the optimal cut-point (c *) for a biomarker affected by a LOD. We develop unbiased estimators of J and c * via ML for normally and gamma distributed biomarkers. Alpha level confidence intervals are proposed using delta and bootstrap methods for the ML, semi-parametric, and non-parametric approaches respectively. Simulation studies are conducted over a range of distributional scenarios and sample sizes evaluating estimators' bias, root-mean square error, and coverage probability; the average bias was less than one percent for ML and GLM methods across scenarios and decreases with increased sample size. An example using polychlorinated biphenyl levels to classify women with and without endometriosis illustrates the potential benefits of these methods. We address the limitations and usefulness of each method in order to give researchers guidance in constructing appropriate estimates of biomarkers' true discriminating capabilities. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]