ISSN:0886-9383    

DOI:10.1002/cem.1180070302

出版商:John Wiley&Sons, Ltd.    

年代:1993

数据来源: WILEY

摘要:

AbstractThis paper consists of two distinct but related parts. In the first part a geometric theory of generalized inverses is presented and a methodology based on this theory is developed and applied to solve the K‐matrix and P‐matrix forms of Beer's law. It is shown that most currently accepted and practiced methods for solving these forms of Beer's law are just special cases of this geometric theory of generalized inverses. In addition, this geometric theory is used to explain why the current methods work and why they fail.In the second part a general methodology that includes as special cases least squares, principal component regression, partial least squares 1 and 2, continuum regression plus a variety of other described and undescribed methodologies is presented and then applied to solve the P‐matrix formulation of Beer's law. This general methodology, like the first, is also geometric in nature and relies on an understanding of projections.The main emphasis of this paper is one of perspective, which, if understood, provides the proper foundation for answering the general but extremely hard and possibly unanswerable question “what is the best m

ISSN:0886-9383    

DOI:10.1002/cem.1180070303

出版商:John Wiley&Sons, Ltd.    

年代:1993

数据来源: WILEY

摘要:

AbstractEnvironmental data are usually multivariate, with the variables conforming to some correlation structure. Occasionally, measurements which do not conform in structure or magnitude may occur in one or more variables. It is important (1) to characterize these discordancies in terms of the disturbed variables and the direction and magnitude of the anomalous error and (2) to associate each discordant observation with a specific cause of measurement error in order to prevent further mismeasurement. We describe a procedure for identifying suspected causes of discordant observations in otherwise multinormal data sets. Variables are assigned to groups, each of which is associated with a specific cause of measurement error. Discordant observations are identified with the generalized distance test or the multivariate kurtosis test. Suspected causes of measurement error are identified by repeating the tests with one of the groups of variables omitted in each analysis. The procedures are evaluated with simulated data sets having a correlation structure similar to that of a large environmental data set.

ISSN:0886-9383    

DOI:10.1002/cem.1180070304

出版商:John Wiley&Sons, Ltd.    

年代:1993

数据来源: WILEY

摘要:

AbstractA general framework for manipulating spectra as functions in traditional multivariate methods such as PCA and PLS is described. The functional representation is very convenient for compression, ensuring smoothness and continuity. There are two fundamentally different types of representations: (a) by functions and (b) by function coefficients. The use of coefficients is the most practical way of analysis.

ISSN:0886-9383    

DOI:10.1002/cem.1180070305

出版商:John Wiley&Sons, Ltd.    

年代:1993

数据来源: WILEY

摘要:

AbstractA new regression method for non‐linear near‐infrared spectroscopic data is proposed. The technique is based on a model which is linear in the principal components and simple functions (squares and products) of them. Added variable plots are used to determine which squares and products to incorporate into the model. The regression coefficients are estimated by a Stein estimate which shrinks towards the estimate determined by the first several principal components and the selected non‐linear terms. The technique is not computationally intensive and is appropriate for routine predictions of chemical concentrations. The method is tested on three data sets and in all cases gives more accurate predictions than does linear principal components regre

ISSN:0886-9383    

DOI:10.1002/cem.1180070306

出版商:John Wiley&Sons, Ltd.    

年代:1993

数据来源: WILEY

ISSN:0886-9383    

DOI:10.1002/cem.1180070307

出版商:John Wiley&Sons, Ltd.    

年代:1993

数据来源: WILEY

ISSN:0886-9383    

DOI:10.1002/cem.1180070308

出版商:John Wiley&Sons, Ltd.    

年代:1993

数据来源: WILEY

ISSN:0886-9383    

DOI:10.1002/cem.1180070309

出版商:John Wiley&Sons, Ltd.    

年代:1993

数据来源: WILEY

ISSN:0886-9383    

DOI:10.1002/cem.1180070301

出版商:John Wiley&Sons, Ltd.    

年代:1993

数据来源: WILEY