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Bernard Pelletier Pierre Dutilleul Guillaume Larocque James W. Fyles 《Mathematical Geology》2004,36(3):323-343
In geostatistical studies, the fitting of the linear model of coregionalization (LMC) to direct and cross experimental semivariograms is usually performed with a weighted least-squares (WLS) procedure based on the number of pairs of observations at each lag. So far, no study has investigated the efficiency of other least-squares procedures, such as ordinary least squares (OLS), generalized least squares (GLS), and WLS with other weighing functions, in the context of the LMC. In this article, we compare the statistical properties of the sill estimators obtained with eight least-squares procedures for fitting the LMC: OLS, four WLS, and three GLS. The WLS procedures are based on approximations of the variance of semivariogram estimates at each distance lag. The GLS procedures use a variance–covariance matrix of semivariogram estimates that is (i) estimated using the fourth-order moments with sill estimates (GLS1), (ii) calculated using the fourth-order moments with the theoretical sills (GLS2), and (iii) based on an approximation using the correlation between semivariogram estimates in the case of spatial independence of the observations (GLS3). The current algorithm for fitting the LMC by WLS while ensuring the positive semidefiniteness of sill matrix estimates is modified to include any least-squares procedure. A Monte Carlo study is performed for 16 scenarios corresponding to different combinations of the number of variables, number of spatial structures, values of ranges, and scale dependence of the correlations among variables. Simulation results show that the mean square error is accounted for mostly by the variance of the sill estimators instead of their squared bias. Overall, the estimated GLS1 and theoretical GLS2 are the most efficient, followed by the WLS procedure that is based on the number of pairs of observations and the average distance at each lag. On that basis, GLS1 can be recommended for future studies using the LMC. 相似文献
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Our results illustrate the performance of at-site and regional GEV/PWM flood quantile estimators in regions with different coefficients of variation, degrees of regional heterogeneity, record lengths, and number of sites. Analytic approximations of bias and variance are employed. For realistic GEV distributions and short records, the index-flood quantile estimator performs better than a 2-parameter GEV/PWM quantile estimator with a regional shape parameter, or a 3-parameter at-site GEV/PWM quantile estimator, in both humid and especially in arid regions, as long as the degree of regional heterogeneity is moderate. As regional heterogeneity or record lengths increases, 2-parameter estimators quickly dominate. Flood frequency models that assign probabilities larger than 2% to negative flows are unrealistic; experiments employing such distributions provide questionable results. This appraisal generally demonstrates the value of regionalizing estimators of the shape of a flood distribution, and sometimes the coefficient of variation. 相似文献
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Imtiyaz A. Parvez 《Natural Hazards》2007,40(2):397-412
The Bayesian extreme-value distribution of earthquake occurrences has been used to estimate the seismic hazard in 12 seismogenic
zones of the North-East Indian peninsula. The Bayesian approach has been used very efficiently to combine the prior information
on seismicity obtained from geological data with historical observations in many seismogenic zones of the world. The basic
parameters to obtain the prior estimate of seismicity are the seismic moment, slip rate, earthquake recurrence rate and magnitude.
These estimates are then updated in terms of Bayes’ theorem and historical evaluations of seismicity associated with each
zone. From the Bayesian analysis of extreme earthquake occurrences for North-East Indian peninsula, it is found that for T = 5 years, the probability of occurrences of magnitude (M
w = 5.0–5.5) is greater than 0.9 for all zones. For M
w = 6.0, four zones namely Z1 (Central Himalayas), Z5 (Indo-Burma border), Z7 (Burmese arc) and Z8 (Burma region) exhibit high
probabilities. Lower probability is shown by some zones namely␣Z4, Z12, and rest of the zones Z2, Z3, Z6, Z9, Z10 and Z11
show moderate probabilities. 相似文献
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Six different geostatistical estimators (linear kriging, lognormal kriging, and disjunctive kriging, each with and without a nonbias, i.e., universality condition) were compared using data from a polymetallic deposit in Algeria. The differences between estimators with and without the nonbias condition were far more pronounced than between the different kriging methods. This highlights the importance of choosing an appropriate stationarity model for the data. The criterion concerning kriging weight of the mean in simple kriging, proposed by Remacre (1984, 1987) and Rivoirard (1984) was found to be helpful for determining blocks where the choice of the stationarity hypothesis was critical. 相似文献
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《地理学报(英文版)》1991,(3)
Theoretical and simulation results are employed to evaluate mean and variance estimaies for normal datawhen a lognormal distribution is assumed and for lognormal data when a normal distribution is assumed.Misspecifying the distribution leads to the use of suboptimal estimation methods.However,the resultsshow that the suboptimal methods still produce estimators of good quality(low bias and variance)relativeto the minimum variance unbiased estimators for each distribution,at least when practical efficiency isconsidered. 相似文献
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Evaluation and comparison of spatial interpolators 总被引：16，自引：0，他引：16
This study evaluates 15 different estimators to determine their relative merits in estimating block concentrations at contaminant waste sites. The evaluation was based on 54 subsets of data drawn from an exhaustive set of 19,800 data. For each subset, 198 block estimates were made with each estimator. The measurements of estimation quality were a linear loss function and a more standard statistic, the mean square error. The linear loss function showed that seven of the estimators produced scores close enough to be within the same statistical population. Results based on the mean square error were similar. The surprising results of this study were that inverse distance and inverse distance squared both produced better scores than kriging. 相似文献
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The key problem in nonparametric frequency analysis of flood and droughts is the estimation of the bandwidth parameter which defines the degree of smoothing. Most of the proposed bandwidth estimators have been based on the density function rather than the cumulative distribution function or the quantile that are the primary interest in frequency analysis. We propose a new bandwidth estimator derived from properties of quantile estimators. The estimator builds on work by Altman and Léger (1995). The estimator is compared to the well-known method of least squares cross-validation (LSCV) using synthetic data generated from various parametric distributions used in hydrologic frequency analysis. Simulations suggest that our estimator performs at least as well as, and in many cases better than, the method of LSCV. In particular, the use of the proposed plug-in estimator reduces bias in the estimation as compared to LSCV. When applied to data sets containing observations with identical values, typically the result of rounding or truncation, the LSCV and most other techniques generally underestimates the bandwidth. The proposed technique performs very well in such situations. 相似文献