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## Linear Estimator (linear + estimator)
## Selected Abstracts## Computer Algebra Derivation of the Bias of Linear Estimators of Autoregressive Models JOURNAL OF TIME SERIES ANALYSIS, Issue 2 2006Y. ZhangAbstract., A symbolic method which can be used to obtain the asymptotic bias and variance coefficients to order O(1/n) for estimators in stationary time series is discussed. Using this method, the large-sample bias of the Burg estimator in the AR(p) for p = 1, 2, 3 is shown to be equal to that of the least squares estimators in both the known and unknown mean cases. Previous researchers have only been able to obtain simulation results for the Burg estimator's bias because this problem is too intractable without using computer algebra. The asymptotic bias coefficient to O(1/n) of Yule,Walker as well as least squares estimates is also derived in AR(3) models. Our asymptotic results show that for the AR(3), just as in the AR(2), the Yule,Walker estimates have a large bias when the parameters are near the nonstationary boundary. The least squares and Burg estimates are much better in this situation. Simulation results confirm our findings. [source] ## Basin-Scale Transmissivity and Storativity Estimation Using Hydraulic Tomography GROUND WATER, Issue 5 2008Kristopher L KuhlmanWhile tomographic inversion has been successfully applied to laboratory- and field-scale tests, here we address the new issue of scale that arises when extending the method to a basin. Specifically, we apply the hydraulic tomography (HT) concept to jointly interpret four multiwell aquifer tests in a synthetic basin to illustrate the superiority of this approach to a more traditional Theis analysis of the same tests. Transmissivity and storativity are estimated for each element of a regional numerical model using the geostatistically based sequential successive linear estimator (SSLE) inverse solution method. We find that HT inversion is an effective strategy for incorporating data from potentially disparate aquifer tests into a basin-wide aquifer property estimate. The robustness of the SSLE algorithm is investigated by considering the effects of noisy observations, changing the variance of the true aquifer parameters, and supplying incorrect initial and boundary conditions to the inverse model. Ground water flow velocities and total confined storage are used as metrics to compare true and estimated parameter fields; they quantify the effectiveness of HT and SSLE compared to a Theis solution methodology. We discuss alternative software that can be used for implementing tomography inversion. [source] ## Bootstrapping a weighted linear estimator of the ARCH parameters JOURNAL OF TIME SERIES ANALYSIS, Issue 3 2009Arup BoseAbstract., A standard assumption while deriving the asymptotic distribution of the quasi maximum likelihood estimator in ARCH models is that all ARCH parameters must be strictly positive. This assumption is also crucial in deriving the limit distribution of appropriate linear estimators (LE). We propose a weighted linear estimator (WLE) of the ARCH parameters in the classical ARCH model and show that its limit distribution is multivariate normal even when some of the ARCH coefficients are zero. The asymptotic dispersion matrix involves unknown quantities. We consider appropriate bootstrapped version of this WLE and prove that it is asymptotically valid in the sense that the bootstrapped distribution (given the data) is a consistent estimate (in probability) of the distribution of the WLE. Although we do not show theoretically that the bootstrap outperforms the normal approximation, our simulations demonstrate that it yields better approximations than the limiting normal. [source] ## Remote sensing of protected areas to derive baseline vegetation functioning characteristics JOURNAL OF VEGETATION SCIENCE, Issue 5 2004Martín F. GarbulskyAbstract: Question: How can we derive baseline/reference situations to evaluate the impact of global change on terrestrial ecosystem functioning? Location: Main biomes (steppes to rain forests) of Argentina. Methods: We used AVHRR/NOAA satellite data to characterize vegetation functioning. We used the seasonal dynamics of the Normalized Difference Vegetation Index (NDVI), a linear estimator of the fraction of the photosynthetic active radiation intercepted by vegetation (fPAR), and the surface temperature (Ts), for the period 1981,1993. We extracted the following indices: NDVI integral (NDVI -I), NDVI relative range (Rrel), NDVI maximum value (Vmax), date of maximum NDVI (Dmax) and actual evapotranspiration. Results: fPAR varied from 2 to 80%, in relation to changes in net primary production (NPP) from 83 to 1700 g.m- 2.yr -1. NDVI -I, Vmax and fPAR had positive, curvilinear relationships to mean annual precipitation (MAP), NPP was linearly related to MAP. Tropical and subtropical biomes had a significantly lower seasonality (Rrel) than temperate ones. Dmax was not correlated with the defined environmental gradients. Evapotranspiration ranged from 100 to 1100 mm.yr -1. Interannual variability of NDVI attributes varied across the temperature and precipitation gradients. Conclusions: Our results may be used to represent baseline conditions in evaluating the impact of land use changes across environmental gradients. The relationships between functional attributes and environmental variables provide a way to extrapolate ecological patterns from protected areas across modified habitats and to generate maps of ecosystem functioning. [source] ## Corrected local polynomial estimation in varying-coefficient models with measurement errors THE CANADIAN JOURNAL OF STATISTICS, Issue 3 2006Jinhong YouAbstract The authors study a varying-coefficient regression model in which some of the covariates are measured with additive errors. They find that the usual local linear estimator (LLE) of the coefficient functions is biased and that the usual correction for attenuation fails to work. They propose a corrected LLE and show that it is consistent and asymptotically normal, and they also construct a consistent estimator for the model error variance. They then extend the generalized likelihood technique to develop a goodness of fit test for the model. They evaluate these various procedures through simulation studies and use them to analyze data from the Framingham Heart Study. Estimation polynomiale locale corrigée dans les modèles à coefficients variables comportant des erreurs de mesure Les auteurs s'intéressent à un modèle de régression à coefficients variables dont certaines cova-riables sont entachées d'erreurs additives. Ils montrent que l'estimateur localement linéaire (ELL) usuel des coefficients fonctionnels est biaisé et que le facteur de correction habituel du phénomène d'atténuation est inefficace. Ils proposent une version corrigée de l'ELL qui s'avère convergente et asymptotiquement normale; ils suggèrent aussi une estimation convergente de la variance du terme d'erreur du modèle. Une adaptation de la technique de vraisemblance généralisée leur permet en outre d'élaborer un test d'adéquation du modèle. Ils évaluent ces diverses procédures par voie de simulation et s'en servent pour analyser des données issues de l'étude Framingham sur les risques cardiométaboliques. [source] ## Bootstrapping a weighted linear estimator of the ARCH parameters JOURNAL OF TIME SERIES ANALYSIS, Issue 3 2009Arup BoseAbstract., A standard assumption while deriving the asymptotic distribution of the quasi maximum likelihood estimator in ARCH models is that all ARCH parameters must be strictly positive. This assumption is also crucial in deriving the limit distribution of appropriate linear estimators (LE). We propose a weighted linear estimator (WLE) of the ARCH parameters in the classical ARCH model and show that its limit distribution is multivariate normal even when some of the ARCH coefficients are zero. The asymptotic dispersion matrix involves unknown quantities. We consider appropriate bootstrapped version of this WLE and prove that it is asymptotically valid in the sense that the bootstrapped distribution (given the data) is a consistent estimate (in probability) of the distribution of the WLE. Although we do not show theoretically that the bootstrap outperforms the normal approximation, our simulations demonstrate that it yields better approximations than the limiting normal. [source] ## Multi-scale sampling and statistical linear estimators to assess land use status and change APPLIED VEGETATION SCIENCE, Issue 2 2009D. RocchiniAbstract Question: Multi-temporal analysis of remotely sensed imagery has proven to be a powerful tool for assessment and monitoring of landscape diversity. Here the feasibility of assessing land-use diversity and land-use change was tested at multiple scales and over time by means of statistical linear estimators based on a probabilistic sampling design. Location: The study area (the district of Asciano, Tuscany, Italy) is characterized by erosional forms typical of Pliocene claystone (i.e. calanchi and biancane) that have been subject to the phenomenon of biancane reworking over the past 50 years, mainly owing to the expansion of intensive agriculture. Methods: Cells at two different scales (50 m × 50 m and 10 m × 10 m) were classified by two operators according to a multilevel legend, using 1954 and 2000 aerial photographs. Inter-operator agreement and accuracy were tested by Cohen's K coefficient. Total land cover estimation for each class was carried out using a multistage estimator, while the variance was estimated by means of the Wolter estimator. Field-based information on plant species composition was recorded in order to test for a relationship between land use and plant community composition by anova and indicator species analysis. Results: Agreement between photointerpreters and accuracy were significantly higher than those expected by chance, proving that the approach proposed is reproducible, as long as proper quality assurance methods are used. Our data show that, at the two scales considered (50 m × 50 m and 10 m × 10 m), crops have increased against woodlands and semi-natural areas, the latter showing the highest and significantly different mean species richness. Meanwhile, an increase in the coverage of trees and shrubs was found within the semi-natural areas, probably as a result of secondary succession occurring on typical landscape elements such as biancane. Conclusions: Inferential statistics made it possible to acquire quantitative information on the abundance of land cover classes, allowing formal multi-temporal and multi-scale analysis. Sampling design-based statistical linear estimators were found to be a powerful tool for assessing landscape trends considering both time expenditure and other costs. They make it possible to maintain the same scale of analysis over time series data and to detect both coarse- and fine-grained changes in spatial patterns. [source] |