Источники (цит. литература)

My articles:

 

Источник

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E. Shekhter, Industrial Laboratory, 1986, v. 52, Nr. 5, p.p. 445-449
E. Shekhter, G. Edelstein, Industrial Laboratory, 1991, v. 57, Nr. 5, p.p. 536-545
Eduard Shekhter «Theoretical Limit of Accuracy and the Best Estimator for Concentrations by Multielement Matrix Correction in EPMA.» PDF-> The base work containing the basic results for the least squares estimations with restrictions and investigation of the solution accuracy for the matrix correction in EPMA

 

— The mathematical literature: About Restricted Least Square Estimator

 

Classical theory (nonsingular case)

 

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D.C. Montgomery, E.A. Peck, G. G. Vining, Introduction to Linear Regression Analysis, 3 ed., J.W.&S., N.Y., 2001 Very precise and comprehensive classical theory of the regression analysis for the nonsingular matrix of plan.
G. A. F. Seber, A.J. Lee, Linear Regression Analysis, 2. ed., J.W. & S. (2003) Exhaustive statement of the classical theory of regression. For the first acquaintance it is too theoretical. The case of the singular matrix of the plan is considered by means of projective matrices and the geometrical approach that is not simple for the first acquaintance. The first edition was translated into Russian.
Juan M. Rodriguwz-Poo, Computer-aided Introduction to Econometrics, edited by Springer (2002), 350 p., SBN:354044114X PDF, 2395 kb Ideal statement for first acquaintance with the statistical theory of estimation. The broad area of questions is considered, including Cramer’s -Рао inequality and estimations with restrictions on parameters.
Y. Bard, Nonlinear Parameter Estimation, A.P., N.Y. (1974) The statement as theories, and computing methods. A little bit obsoletely. It was translated into Russian
Engineering Statistics Extremely useful internet — source on mathematical statistics. A content for engineers.

General case (singular matrix)

 

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A.Albert, Regression and the Moor-Penrose Pseudoinverse, A.P., N.Y.(1972) The basic source to which I refer. A precise statement of the theory of pseudo-inversion of matrices and on its basis of the generalized method of the linear least squares for singular matrices of the plan. It was translated into Russian.
C.R. Rao, Linear Statistical Inference and Its Application, 2. ed., J.W., N.Y., (1973) Fundamental book about the theory of linear estimation. It was translated into Russian
G. A. F. Seber, C.J. Wild, Nonlinear Regression, J.W., N.Y., (1989) Modern statement of the theory of nonlinear estimation. It is a little bit concise. Contains references to results G. A. F. Seber, A.J. Lee, Linear Regression Analysis, 1. ed.
H. R. Van Trees, Detection, Estimation, and Modulation Theory, part 1, J.W., N.Y., (1968) Precise and clear statement of the statistical theory of detection of signals on a background of noise and an estimation of their parameters. The textbook for university. It was translated into Russian.
D. Kahaner, C.B. Moller, S. Nash, Numerical methods and software, Prentice-Hall, (1989) The description of the basic computing algorithms and programs on Fortran. The algorithm of the pseudo-inverse of matrices (SVD) is resulted. All programs occur in the Internet on a Fortran, library LAPACK. I have translated for the own purposes algorithm on VB

— The physical literature:

 

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J.L. Lábár, Quantitative electron microprobe analysis of homogeneous bulk samples, EMAS-2002, Szczyrk (Poland) The precise critical consideration of axiomatics of equations of the Quantitative X-ray Microanalysis
B. I. Kitov, X-Ray Spectrometry, 2000; 29: 285–290 Unique attempt that I know to obtain the theoretically proved solution for the  quantitative fluorescent analysis equations with the proof of the existence and uniqueness of the solution.
Ziebold T.O., Anal. Chem. 1967, v.39, Nr. 8, p.86 Formulas for a theoretical limit of detection and sensitivity of the x-ray microanalysis for the case of the binary sample are resulted. Formulas consider both errors of measurements, and errors of factors of the equations. The unique result used everywhere already for 40 years, even for the multivariate case.
Ziebold T.O., Ogilvie R.E., Anal. Chem. 1964, v.36, p.322-327
H. J. Beattie and R. M. Brissey, Analytical Chemistry 26 (1954) 980–983.
Bence, A. E. & Albee, A. L., 1968, Journal of Geology, 76, 382 – 403
D.R. Biemen, J.A. Jsasi, Anal. Chem. 1970, v.42, p.p. 1540-1568
Handbook of Spectrometry: 2. ed., edited by R.E. Van Grieken and A.A. Marcowicz, M.D. Inc., (2002)
M Mantler, N. Kawahara; The Rigaku Journal, v.21, Nr. 2, (2004), 17-25
Goldstein JI, Newbury DE, Echlin P, Joy DC, Romig AD Jr, Lyman CE, Fiori C, Lifshin E (1992) Scanning Electron Microscopy and X-ray Microanalysis, 2nd ed. New York: Plenum Press
Quantitative X-ray fluorescence analysis of geological materials using partial least-squares regression Adams, M. J., Allen, J., (School Appl. Sci., Univ.Wolverhampton, W. Midlands, UK WV1 1SB).Presented at XXX Colloquium W. Midlands, UK WV1 1SB Spectroscopicum Internationale (CSI), Melbourne, Australia, September 21–26, 1997
IUPAC, Compendium of Chemical Terminology, 2nd Edition (1997)
International Standard, ISO 3534-1, Statistics-Vocabulary and symbols, (1993)
R. M. Rousseau, The Rigaku Journal, v. 18, Nr. 2, 2001, PDF,
Lifshin E, Doganaksoy N, Sirois, J, Gauvin R (1999) Statistical
considerations in microanalysis by energy-dispersive spectrometry.
Microsc Microanal 4:598–604 , 1999
John Donovan, Center for Advanced Materials Characterization in Oregon (Facilities), Electron Beam Micro Analysis- Lecture Notes (Geol 619), Сhapter 7 (Statistics).
J.I. Goldstein, H. Yakowitz, Practical Scanning Electron Microscopy, P.P., N.Y., (1975)
G. Springer, X-Ray Spectrometry, 1976, v. 5, p.p. 88-91
S. J. B. Reed, Electron Microprobe Analysis. Cambridge University Press, 1975. 400 pp.
Steinbrecher, Stefan. A unified Monte Carlo approach for quantitative standardless x-ray fluorescence and electron probe microanalysis inside the scanning electron microscope. Dissertation, 2004ebook
«Uncertainties in electron probe microanalysis» R B Marinenko and S Leigh, 11th European Workshop on Modern Developments and Applications in Microbeam Analysis IOP Publishing, IOP Conf. Series: Materials Science and Engineering 7 (2010) 012017 doi:10.1088/1757-899X/7/1/012017

 

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