半参数平差模型估计量的精度评定

将半参数估计理论引入测量数据处理理论中,利用Blight和Ott提出的思想,用多项式函数来表示半参数平差模型中的非参数分量,从而得到了半参数平差模型中参数分量和非参数分量的Bayes估计量,通过理论证明,半参数模型参数分量的Bayes估计为通常意义下高斯马尔可夫模型参数估计值与参数期望的加权平均,是一致、渐近无偏和渐近有效估计量,并且其方差小于参数模型中参数估计量的方差。在一定情况下推广了平差理论,具有一定的理论价值。     

K 近邻非参数回归概率预报技术及其应用

针对参数回归技术制作概率预报存在拟合好、但预报结果不稳定的现象, 提出了用K近邻非参数回归技术制作概率预报的新途径。K 近邻非参数回归技术包括历史样本数据库、近邻子集生成和优化以及预报量估计4 个主要部分。利用该技术进行了单要素概率预报(主要包括云量和降水)和多维联合概率预报(降水、总云量、风速和气温)试验, 并对试验结果进行了检验。实例研究结果表明:该文所给出的计算方案预报稳定性好, 准确率较高,具有良好的业务应用价值。     

Power of the Mann–Whitney test for detecting a shift in median or mean of hydro-meteorological data

 The non-parametric Mann–Whitney (MW) statistic test has been popularly used to assess the significance of a shift in median or mean of hydro-meteorological time series. It has been considered that the test is more suitable for non-normally distributed data and it may be not sensitive to the distribution type of sample data. However, no evidence has been provided to demonstrate these. This study investigates the power of the test in various circumstances by means of Monte Carlo simulation. Simulation results demonstrate that the power of the test is very sensitive to various properties of sample data. The power depends on the pre-assigned significance level, magnitude of a shift, sample size, and its occurrence position within a time series; and it is also strongly affected by the variation, skewness, and distribution type of a time series. The bigger the magnitude of a shift, the more powerful the test is; the larger the sample size, the more powerful the test is; and the bigger the variation within a time series, the less power the test has. The test has the highest power if a shift occurs at the midpoint of a time series. For the samples with different distribution types, the power of the test is dramatically different. The test has the highest power for time series with the extreme value type III (EV3) distribution while it indicates the lowest power for time series with the lognormal distribution.     

Multivariate nonparametric resampling scheme for generation of daily weather variables

A nonparametric resampling technique for generating daily weather variables at a site is presented. The method samples the original data with replacement while smoothing the empirical conditional distribution function. The technique can be thought of as a smoothed conditional Bootstrap and is equivalent to simulation from a kernel density estimate of the multivariate conditional probability density function. This improves on the classical Bootstrap technique by generating values that have not occurred exactly in the original sample and by alleviating the reproduction of fine spurious details in the data. Precipitation is generated from the nonparametric wet/dry spell model as described in Lall et al. [1995]. A vector of other variables (solar radiation, maximum temperature, minimum temperature, average dew point temperature, and average wind speed) is then simulated by conditioning on the vector of these variables on the preceding day and the precipitation amount on the day of interest. An application of the resampling scheme with 30 years of daily weather data at Salt Lake City, Utah, USA, is provided.     

Fitting the Linear Model of Coregionalization by Generalized Least Squares

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.     

Appraisal of regional and index flood quantile estimators

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.     

On the Bayesian analysis of the earthquake hazard in the North-East Indian peninsula

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.     

Comparison between different kriging estimators

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.     

THE QUALITY OF MEAN AND VARIANCE ESTIMATES FOR NORMAL AND LOGNORMAL DATA WHEN THE UNDERLYING DISTRIBUTION IS MISSPECIFIED

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.