BOX-COX TRANSFORMATIONS IN THE ANALYSIS OF COMPOSITIONAL DATA

The statistical analysis of compositional data is of fundamental importance to practitioners in generaland to chemists in particular.The existing methodology is principally due to Aitchison,who effectivelyuses two transformations,a ratio followed by the logarithmic,to create a useful,coherent theory thatin principle allows the plethora of normal-based multivariate techniques to be used on the transformeddata.This paper suggests that the well-known class of Box-Cox transformations can be employed inplace of the logarithmic to significantly improve the existing methodology.This is supported in part byshowing that one of the most basic problems that Aitchison managed to overcome,namely thespecification of an interpretable covariance structure for compositional data,can be resolved,or nearlyresolved,once the ratio transformation has been applied.Hence the resolution is not directly dependenton the logarithmic transformation.It is then verified that access to the general Box-Cox family will allowa more accurate use of the normal-based multivariate techniques,simply because better fits to normalitycan be achieved.Finally,maximum likelihood estimation and some associated asymptotics are employedto construct confidence intervals for ratios of the true,unknown compositional constituents.Heretoforethis had not been done even in the context of the logarithmic transformation.Applications to real dataare presented.     

FINDING CAUSES OF OUTLIERS IN MULTIVARIATE ENVIRONMENTAL DATA

Multivariate outliers in environmental data sets are often caused by atypical measurement error in a singlevariable.From a quality assurance perspective it is important to identify these variables efficiently so thatcorrective actions may be performed.We demonstrate a procedure for using two multivariate tests toidentify which variable‘caused’each outlier.The procedure is tested with simulated data sets that havethe same correlation structure as selected water chemistry variables from a survey of lakes in the WesternUnited States.The success rates are evaluated for three of the variables for sample sizes of 50 and 100,significance levels of 0.01 and 0.05 and various amounts of mean shift.The procedure works best forhighly correlated variables.     

SPLITTING OF CALIBRATION DATA BY CLUSTER ANALYSIS

from eorresponding valuesof x.The most eommon aPProaeh to this Problem 15 linear regression(or ealibration),but1 inear methods are usually best suited for quite limited regions alld are not generallyaPPlieable.If a linear fit 15 not satisfactory,alternative aPProaehes are non一linear regression,non一Parametrie regression,transformations and sPlitting of the data into subgrouPs     

地理数据线性回归中的稳健估计方法

在线性回归中，常用最小二乘估计求线性方程的回归系数。但最小二乘估计受异常值影响较大，当样本数据存在异常值时，估计出的回归系数会产生较大偏差。稳健估计是最小二乘估计的改进，能在不排除异常数据的情况下，达到减弱异常数据对结果的影响。利用稳健估计提出黄土地区沟谷密度与侵蚀量的回归方程，并和最小二乘估计得到的回归方程比较，前者具有更回归效果。     

METHODOLOGY: DISCRIMINANT FUNCTION ANALYSIS OF COMPOSITIONAL DATA: AN EXAMPLE FROM HYDRAULIC GEOMETRY

Many of the data sets analyzed by physical geographers are compositional in nature: they have row vectors that add to one (or 100%). These unit-sum constrained data sets should not be analyzed by standard multivariate statistical methods. Significant differences were found in the log-ratio mean vectors of the hydraulic exponents (which are unit-sum constrained) for two classes of streams: those with cohesive, non-vertical banks, and those with one firm and one loose bank. Compositional discriminant function analysis of bank stability on the basis of hydraulic geometry had a success rate of 88%, making routinely archived measurements of stream width, cross-sectional area, mean velocity, and discharge a readily available data base for predicting the stability of stream reaches. [Key words: geomorphology, hydraulic geometry, discriminant function, statistics.]     

A BOOTSTRAP RESAMPLING SCHEME FOR USING THE CANONICAL CORRELATION TECHNIQUE IN RANK ESTIMATION

Rank estimation by canonical correlation analysis in multivariate statistics has been proposed as analternative approach for estimating the number of components in a multicomponent mixture.Amethodological turning point of this new approach is that it focuses on the difference in structure ratherthan in magnitude in characterizing the difference between the signal and the noise.This structuraldifference is quantified through the analysis of canonical correlation,which is a well-established datareduction technique in multivariate statistics.Unfortunately,there is a price to be paid for having thisstructural difference:at least two replicate data matrices are needed to carry out the analysis.In this paper we continue to explore the potential and to extend the scope of the canonical correlationtechnique.In particular,we propose a bootstrap resampling method which makes it possible to performthe canonical correlation analysis on a single data matrix.Since a robust estimator is introduced to makeinference about the rank,the procedure may be applied to a wide range of data without any restrictionon the noise distribution.Results from real as well as simulated mixture samples indicate that when usedin conjunction with this resampling method,canonical correlation analysis of a single data matrix isequally efficient as of replicate data matrices.     

SCALING TECHNIQUES IN THE ANALYSIS OF ENVIRONMENTAL COGNITION DATA *

The utility of nonmetric, multidimensional-scaling techniques is demonstrated for the analysis and collection of environmental-cognition data. By comparing the multidimensional-scaling solutions of a real-setting map to scaling solutions for sketch maps and two psychophysical, distance-scaling procedures, we demonstrate that magnitude estimation of actual interpoint distances is comparable in accuracy to sketch maps when produced without constraints, or when subjects are given a specified list of landmarks to include on their maps. Triadic comparisons of actual interpoint distances were less accurate than the three other techniques.     

CAN IMAGE ANALYSIS PROVIDE INFORMATION USEFUL IN CTTEMISTRY?

Images can contain chemical information and many chemical methods can generate image data. For anefficient extraction of chemical data from images, data analysis techniques are necessary, It is a greatadvantage to be able to work on multivariate images. Many imaging techniques allow the extraction ofchemical information. Inorganic analytical chemistry seems to have the longest tradition here, butorganic chemistry and biochemistry may soon be catching up. Also large data arrays from non-imagingtechniques can be combined with image analysis in a useful way, provided certain conditions are fulfilled.     

TWO STATISTICS FOR THE ANALYSIS OF ORIENTATION DATA IN GEOGRAPHY*

Two versions of the A_n statistic of Ajne and Stephens are introduced, explained, interpreted and evaluated. These statistics possess important advantages over those currently used by geographers for the analysis of orientation data. They are invariant with respect to the point of origin of measurements, do not assume a circular-normal distribution and are not limited by sample size. Used in conjunction, they allow the significance of direction as well as orientation to be determined.     

COMPOSITIONAL GRADIENTS IN MESOPHYTIC FORESTS OF EASTERN NORTH AMERICA

Numerical classification and ordination techniques are used to examine compositional variability in 112 stands of mesophytic upland forest in the eastern United States from data published by Braun (1950). Five forest types are identified and used to interpret ordination results. Two prominent environmental gradients account for much of the compositional variability in the data set: along the first ordination axis a microclimate gradient reflects increasing soil moisture availability and cold stress from dry uplands to northern hardwood sites; along the second ordination axis, a soil fertility gradient segregates hemlock coves and dry uplands, both of which are characteristically found on shallow, nutrient-poor soils, from the other forest types. The efficacy of combining numerical classification and ordination techniques for analyzing and interpreting patterns in ecological data is underscored by these results.     

基于CBERS遥感数据的云南安宁“3．29”火灾面积评估

以中巴资源卫星（CBERS）多波段数据及纹理均匀性指标、图斑变异性指标和地形因子作为森林火灾灾后模式识别指标,提取了云南安宁“3．29”重大森林火灾火烧迹地地图以及受害指标,结合地面样地数据对过火区域的受害程度进行了等级划分。通过对灾前森林分布图和过火程度区划图的叠加分析,统计出了各类林地的受害面积。结果表明“3．29”火灾过火面积1695．4hm^2（25 430．29亩）,重度受害面积为518．6hm^2（7779．42亩）,中度受害面积为508．5hm^2（7627．36亩）,轻度受害积为668．2hm^2（10023．50亩）。地盘松过火面积最大,为796．3hm^2（11944．47亩）,其次为栎类灌木,过火746．4hm^2（11195．43亩）。利用卫星遥感图像的自动识别处理算法,既可识别火场、又可识别森林受害程度,可以替代地面对坡勾绘与目视解译的传统火场调查方法。     

DATA ANALYSIS WITH MINIMAL ASSUMPTIONS

The computer has made it possible to scrutinize data rapidly by means of graphics. This should be doneprior to the application of any model to the data, since the model must be validated before using it asa means of analyzing the data. The procedure is illustrated in terms of two examples of real experimentaldata.     

RAPID ESTIMATION OF THE NUMBER OF COELUTING COMPONENTS IN LIQUID CHROMATOGRAPHY BY FACTOR ANALYSIS

Evaluation of the results of factor analysis of sets of spectroscopically detected chromatograms is carriedout by examining the shapes of the abstract factors.This is done either by visual inspection or by analysisof the power density spectra produced from them.Owing to constraints imposed by the column functionand the spectroscopic instrument function,the information content of the chromatograms necessarilyoccurs at low spatial frequencies.As a consequence,it appears as relatively broad features in the abstractchromatograms and as a peak in the low-frequency region of the corresponding power density plot.Onthe basis of examination of the power density distribution,a well-defined distinction is made betweenprimary and secondary abstract factors.The major uncertainty encountered in determining the numberof chemical components appears to arise from effects of contaminants in reagents.     

EVOLVING FACTOR ANALYSIS APPLIED TO FLOW INJECTION ANALYSIS DATA

Evolving factor analysis is used to estimate the concentration profiles and spectra of Bi~(3 )and the bismuthchloride complexes BiCl~(2 )through BiCl_6~(3-)formed by injection of bismuth percblorate into a flowingstream of 1.0 mol l~(-1) HCl.The estimated spectra compare favorably with previously published spectraof the complexes.     

基于ASCAT散射计数据的2012年南极周边海面风场特征分析

利用2012年全年的ASCAT散射计风场数据,对55°S以南的南极周边海域海面风场开展了时空分布特性统计分析。结果表明:对于南极周边海域,7月平均风速最大,为12 m·s-1,12月平均风速最小,为8 m·s-1,冬季大于夏季;该区域平均风速主要在9—12 m·s-1之间,全年出现的天数280天,约占全年的77%;风速10 m·s-1所占比例也是冬季大于夏季。从全年来看,南极周边海域在冬季(4—6月)和春季(7—9月)风速普遍较大。该区域0°W—60°W海域内风速明显比其他海域要小。     

塔克拉玛干沙漠腹地塔中一井地区起沙风分析和输沙量的估算

本文通过塔克拉玛干沙漠塔中一井地区气象站的一年多野外实地观测，收集了丰富的风的气资料，在此基础上定量化地描了该地区起沙风的分布状况、风沙流的特点和输流量的数值特征。     

喀斯特溶蚀强度分析与估算*

以红水河流域水化学资料推算的溶蚀量为依据,分析降水量、岩性、地貌、气温等因素对溶蚀强度的影响.得出影响喀斯特溶蚀强度的主要因素是岩性,其次是降水量,随着地表起伏度的增加溶蚀强度稍有增加.气温对溶蚀强度的影响在本研究区内没有发现明显的规律.     

新疆耕地资源卫星遥感调查数据分析研究

依据卫星遥感调查结果。分析新疆耕地资源类型（包括现耕地和后备宜耕地类型）的数量、质量、分布组合特点以及中低产田产生的原因及其后备宜耕荒地的限制因素，提出新疆耕地资源合理开发利用与中低产田治理的总体构思与设想。     

COMPRESSION OF nth-ORDER DATA ARRAYS BY B-SPLINES.PART 1:THEORY

For efficient handling of very large data arrays,pretreatment by compression is mandatory.In the presentpaper B-spline methods are described as good candidates for such data array compression.Themathematical relation between the maximum entropy method for compression of data tables andthe B-spline of zeroth degree is described together with the generalization of B-spline compression tonth-order data array tables in matrix and tensor algebra.