The Statistical Analysis of Compositional Data

成分数据 协方差 单纯形 协方差矩阵 数学 三元图 维数之咒 参数统计 基质(化学分析) 协方差矩阵的估计 统计 计算机科学 组合数学 三元运算 化学 色谱法 程序设计语言
作者
Gregory F. Piepel,J. Aitchison
出处
期刊:Technometrics [Informa]
卷期号:30 (1): 120-120 被引量:3502
标识
DOI:10.2307/1270335
摘要

1 Compositional data: some challenging problems.- 1.1 Introduction.- 1.2 Geochemical compositions of rocks.- 1.3 Sediments at different depths.- 1.4 Ternary diagrams.- 1.5 Partial analyses and subcompositions.- 1.6 Supervisory behaviour.- 1.7 Household budget surveys.- 1.8 Steroid metabolite patterns in adults and children.- 1.9 Activity patterns of a statistician.- 1.10 Calibration of white-cell compositions.- 1.11 Fruit evaluation.- 1.12 Firework mixtures.- 1.13 Clam ecology.- 1.14 Bibliographic notes.- Problems.- 2 The simplex as sample space.- 2.1 Choice of sample space.- 2.2 Compositions and simplexes.- 2.3 Spaces, vectors, matrices.- 2.4 Bases and compositions.- 2.5 Subcompositions.- 2.6 Amalgamations.- 2.7 Partitions.- 2.8 Perturbations.- 2.9 Geometrical representations of compositional data.- 2.10 Bibliographic notes.- Problems.- 3 The special difficulties of compositional data analysis.- 3.1 Introduction.- 3.2 High dimensionality.- 3.3 Absence of an interpretable covariance structure.- 3.4 Difficulty of parametric modelling.- 3.5 The mixture variation difficulty.- 3.6 Bibliographic notes.- Problems.- 4 Covariance structure.- 4.1 Fundamentals.- 4.2 Specification of the covariance structure.- 4.3 The compositional variation array.- 4.4 Recovery of the compositional variation array from the crude mean vector and covariance matrix.- 4.5 Subcompositional analysis.- 4.6 Matrix specifications of covariance structures.- 4.7 Some important elementary matrices.- 4.8 Relationships between the matrix specifications.- 4.9 Estimated matrices for hongite compositions.- 4.10 Logratios and logcontrasts.- 4.11 Covariance structure of a basis.- 4.12 Commentary.- 4.13 Bibliographic notes.- Problems.- 5 Properties of matrix covariance specifications.- 5.1 Logratio notation.- 5.2 Logcontrast variances and covariances.- 5.3 Permutations.- 5.4 Properties of P and QP matrices.- 5.5 Permutation invariants involving ?.- 5.6 Covariance matrix inverses.- 5.7 Subcompositions.- 5.8 Equivalence of characteristics of ?, ?, ?.- 5.9 Logratio-uncorrelated compositions.- 5.10 Isotropic covariance structures.- 5.11 Bibliographic notes.- Problems.- 6 Logistic normal distributions on the simplex.- 6.1 Introduction.- 6.2 The additive logistic normal class.- 6.3 Density function.- 6.4 Moment properties.- 6.5 Composition of a lognormal basis.- 6.6 Class-preserving properties.- 6.7 Conditional subcompositional properties.- 6.8 Perturbation properties.- 6.9 A central limit theorem.- 6.10 A characterization by logcontrasts.- 6.11 Relationships with the Dirichlet class.- 6.12 Potential for statistical analysis.- 6.13 The multiplicative logistic normal class.- 6.14 Partitioned logistic normal classes.- 6.15 Some notation.- 6.16 Bibliographic notes.- Problems.- 7 Logratio analysis of compositions.- 7.1 Introduction.- 7.2 Estimation of ? and ?.- 7.3 Validation: tests of logistic normality.- 7.4 Hypothesis testing strategy and techniques.- 7.5 Testing hypotheses about ? and ?.- 7.6 Logratio linear modelling.- 7.7 Testing logratio linear hypotheses.- 7.8 Further aspects of logratio linear modelling.- 7.9 An application of logratio linear modelling.- 7.10 Predictive distributions, atypicality indices and outliers.- 7.11 Statistical discrimination.- 7.12 Conditional compositional modelling.- 7.13 Bibliographic notes.- Problems.- 8 Dimension-reducing techniques.- 8.1 Introduction.- 8.2 Crude principal component analysis.- 8.3 Logcontrast principal component analysis.- 8.4 Applications of logcontrast principal component analysis.- 8.5 Subcompositional analysis.- 8.6 Applications of subcompositional analysis.- 8.7 Canonical component analysis.- 8.8 Bibliographic notes.- Problems.- 9 Bases and compositions.- 9.1 Fundamentals.- 9.2 Covariance relationships.- 9.3 Principal and canonical component comparisons.- 9.4 Distributional relationships.- 9.5 Compositional invariance.- 9.6 An application to household budget analysis.- 9.7 An application to clinical biochemistry.- 9.8 Reappraisal of an early shape and size analysis.- 9.9 Bibliographic notes.- Problems.- 10 Subcompositions and partitions.- 10.1 Introduction.- 10.2 Complete subcompositional independence.- 10.3 Partitions of order 1.- 10.4 Ordered sequences of partitions.- 10.5 Caveat.- 10.6 Partitions of higher order.- 10.7 Bibliographic notes.- Problems.- 11 Irregular compositional data.- 11.1 Introduction.- 11.2 Modelling imprecision in compositions.- 11.3 Analysis of sources of imprecision.- 11.4 Imprecision and tests of independence.- 11.5 Rounded or trace zeros.- 11.6 Essential zeros.- 11.7 Missing components.- 11.8 Bibliographic notes.- Problems.- 12 Compositions in a covariate role.- 12.1 Introduction.- 12.2 Calibration.- 12.3 A before-and-after treatment problem.- 12.4 Experiments with mixtures.- 12.5 An application to firework mixtures.- 12.6 Classification from compositions.- 12.7 An application to geological classification.- 12.8 Bibliographic notes.- Problems.- 13 Further distributions on the simplex.- 13.1 Some generalizations of the Dirichlet class.- 13.2 Some generalizations of the logistic normal classes.- 13.3 Recapitulation.- 13.4 The Ad(?,B) class.- 13.5 Maximum likelihood estimation.- 13.6 Neutrality and partition independence.- 13.7 Subcompositional independence.- 13.8 A generalized lognormal gamma distribution with compositional in variance.- 13.9 Discussion.- 13.10 Bibliographic notes.- Problems.- 14 Miscellaneous problems.- 14.1 Introduction.- 14.2 Multi-way compositions.- 14.3 Multi-stage compositions.- 14.4 Multiple compositions.- 14.5 Kernel density estimation for compositional data.- 14.6 Compositional stochastic processes.- 14.7 Relation to Bayesian statistical analysis.- 14.8 Compositional and directional data.- Problems.- Appendices.- A Algebraic properties of elementary matrices.- B Bibliography.- C Computer software for compositional data analysis.- D Data sets.- Author index.
最长约 10秒,即可获得该文献文件

科研通智能强力驱动
Strongly Powered by AbleSci AI
更新
大幅提高文件上传限制,最高150M (2024-4-1)

科研通是完全免费的文献互助平台,具备全网最快的应助速度,最高的求助完成率。 对每一个文献求助,科研通都将尽心尽力,给求助人一个满意的交代。
实时播报
刚刚
hello发布了新的文献求助10
1秒前
大胆的静竹完成签到,获得积分10
2秒前
学术小白完成签到 ,获得积分10
2秒前
唐诗阅发布了新的文献求助10
3秒前
项听蓉完成签到,获得积分10
6秒前
舒适映寒完成签到,获得积分10
7秒前
科研通AI2S应助锦铭采纳,获得30
8秒前
七栀完成签到,获得积分10
8秒前
能干的梦岚完成签到,获得积分10
9秒前
9秒前
小栩完成签到 ,获得积分10
9秒前
LYB吕完成签到,获得积分20
9秒前
FashionBoy应助科研通管家采纳,获得10
12秒前
深情安青应助科研通管家采纳,获得30
12秒前
田様应助科研通管家采纳,获得10
12秒前
鄂百川完成签到,获得积分10
12秒前
李健应助科研通管家采纳,获得10
12秒前
Akim应助科研通管家采纳,获得10
12秒前
知性的焦发布了新的文献求助10
12秒前
JamesPei应助科研通管家采纳,获得10
12秒前
13秒前
科研通AI2S应助科研通管家采纳,获得30
13秒前
wanci应助科研通管家采纳,获得10
13秒前
坚强亦丝应助科研通管家采纳,获得10
13秒前
琅伊应助科研通管家采纳,获得30
13秒前
完美世界应助科研通管家采纳,获得10
13秒前
隐形曼青应助科研通管家采纳,获得10
13秒前
13秒前
13秒前
小马甲应助可爱绮采纳,获得10
13秒前
唐诗阅完成签到,获得积分10
13秒前
14秒前
瀚子发布了新的文献求助20
14秒前
15秒前
15秒前
kw完成签到,获得积分10
17秒前
gao完成签到 ,获得积分10
17秒前
Lucas应助知性的焦采纳,获得10
19秒前
天云端完成签到,获得积分20
20秒前
高分求助中
The ACS Guide to Scholarly Communication 2500
Sustainability in Tides Chemistry 2000
Pharmacogenomics: Applications to Patient Care, Third Edition 1000
Studien zur Ideengeschichte der Gesetzgebung 1000
TM 5-855-1(Fundamentals of protective design for conventional weapons) 1000
Threaded Harmony: A Sustainable Approach to Fashion 810
Genera Insectorum: Mantodea, Fam. Mantidæ, Subfam. Hymenopodinæ (Classic Reprint) 800
热门求助领域 (近24小时)
化学 医学 生物 材料科学 工程类 有机化学 生物化学 物理 内科学 纳米技术 计算机科学 化学工程 复合材料 基因 遗传学 催化作用 物理化学 免疫学 量子力学 细胞生物学
热门帖子
关注 科研通微信公众号,转发送积分 3085525
求助须知:如何正确求助?哪些是违规求助? 2738394
关于积分的说明 7549581
捐赠科研通 2388186
什么是DOI,文献DOI怎么找? 1266339
科研通“疑难数据库(出版商)”最低求助积分说明 613430
版权声明 598591