Browsing by Author "Meloun, Milan"
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- ItemComputer estimation of dissociation constants. Part 6. Diagnostics in regression analysis of absorbance-pH curve(Springer-Verlag, 1994) Meloun, Milan; Militký, JiříNonlinear regression program DCMINOPT is introduced for numerical analysis of a set of {A, pH} data expressing a dependence of absorbance of a mixture of variously protonated light-absorbing species L, LH,..., LHR on pH. Efficiency of the program has been examined on simulated A-pH data corrupted with artificial (generated) errors namely for a case of closely overlapping protonation equilibria. An accuracy and precision of parameters estimates have been examined and compared with those determined by another three standard algorithms DCFIT, DCMINUIT and PSEQUAD. Goodness-of-fit test brings various regression diagnostics, 3D-plots and statistical measures enabling to test and prove a reliability of a regression process and accuracy and precision of parameter estimates. © 1993 Springer-Verlag.
- ItemComputer Estimation Of Dissociation-Constants 5. Regression-Analysis Of Extended Debye-Huckel Law(Springer-Verlag Wien, 1992) Meloun, Milan; Javůrek, Milan; Militký, JiříNonlinear regression program DHMINOPT has been used for an analysis of a set of values expressing the dependence of mixed dissociation constant on ionic strength according to the extended Debye-Hueckel law. Efficiency of program has been examined on simulated data loaded with generated random errors. Goodness-of-fit brings various regression diagnostics enabling to prove a reliability of a regression process and parameter estimates. For five selected sulphonephtalein indicators, i.e. Bromocresol Green, Bromophenol Red, Bromocresol Purple, Bromothymol Blue and Phenol Red, the thermodynamic dissociation constant has been determined at 25-degrees-C together with the ion-size parameter and the salting-out coefficient.
- ItemData analysis in the chemical laboratory Part 1. Analysis of indirect measurements(1994) Meloun, Milan; Militký, JiříResponse quantities of analytical chemistry investigations of, for instance, concentration or content of substances, viscosity, stability constants or solubility, can be obtained as a non-linear transformation of directly measured quantities or signals. The goal of the indirect mesurements analysis is estimation of basic statistical parameters of analytical results from the known non-linear transformation and from the statistical parameters of measured variables. The analysis is based on Taylor series expansion, two-point approximation and Monte Carlo simulation. An algorithm may be applied on any chemical, physical, biological or medical result. © 1994.
- ItemDetection of single influential points in OLS regression model building(2001) Meloun, Milan; Militký, JiříIdentifying outliers and high-leverage points is a fundamental step in the least-squares regression model building process. Various influence measures based on different motivational arguments, and designed to measure the influence of observations on different aspects of various regression results, are elucidated and critiqued here. On the basis of a statistical analysis of the residuals (classical, normalized, standardized, jackknife, predicted and recursive) and diagonal elements of a projection matrix, diagnostic plots for influential points indication are formed. Regression diagnostics do not require a knowledge of an alternative hypothesis for testing, or the fulfillment of the other assumptions of classical statistical tests. In the interactive, PC-assisted diagnosis of data, models and estimation methods, the examination of data quality involves the detection of influential points, outliers and high-leverages, which cause many problems in regression analysis. This paper provides a basic survey of the influence statistics of single cases combining exploratory analysis of all variables. The graphical aids to the identification of outliers and high-leverage points are combined with graphs for the identification of influence type based on the likelihood distance. All these graphically oriented techniques are suitable for the rapid estimation of influential points, but are generally incapable of solving problems with masking and swamping. The powerful procedure for the computation of influential points characteristics has been written in Matlab 5.3 and is available from authors. © 2001 Elsevier Science B.V.
- ItemMultiparametric Curve Fitting 14. Modus-Operandi Of The Least-Squares Algorithm Minopt(Elsevier Science Bv, 1993) Militký, Jiří; Meloun, MilanHybrid least-squares algorithm MINOPT for a nonlinear regression is introduced. MINOPT from CHEMSTAT package combines fast convergence of the Gauss-Newton method in a vicinity of minimum with good convergence of gradient methods for location far from a minimum. Quality of minimization and an accuracy of parameter estimates for six selected models are examined and compared with different derivative least-squares methods of five commercial regression packages.
- ItemMultiparametric Curve Fitting 15. Statistical-Analysis And Goodness-Of-Fit Test By The Least-Squares Algorithm Minopt(Elsevier Science Bv, 1993) Militký, Jiří; Meloun, MilanEstimation of nonlinear regression quality leads to examination of quality of parameter estimates, a degree of fit, a prediction ability of model proposed and quality of experimental data. Statistical analysis serves for computation of confidence intervals of parameters and confidence bands, the bias of parameters and bias of residuals. Goodness-of-fit test examines classical residuals using various diagnostics and identifies influential points. Mentioned topics of nonlinear model building and testing contained in MINOPT program from CHEMSTAT package are illustrated.
- ItemSome graphical aids for univariate exploratory data analysis(Elsevier Science Bv, 1993) Militký, Jiří; Meloun, MilanThe main parts of exploratory data analysis (EDA) are discussed. For data presentation the quantile plot and quantile-box plot are proposed. Special techniques for empirical probability density construction and empirical quantile-quantile plot creation are described. Some graphically oriented methods for selection of optimum power transformations are presented. These graphical aids in EDA are demonstrated on Hinkley's well known data. © 1993.
- ItemStatistical data analysis: A practical guide(Woodhead Publishing Limited, 2011) Meloun, Milan; Militký, JiříOver the past decade, computer supported data analysis by statistical methods has been one of the fastest growth areas in chemometrics, biometrics and other related branches of natural, technical and social sciences. This has been strongly supported by the development of exploratory data analysis, testing assumptions about data, model and statistical methods and computer intensive techniques. This book presents a combination of individual topics with solved problems and a collection of experimental tasks. Methods suitable for extreme or small and large datasets are described. © 2011 Woodhead Publishing Limited.
- ItemUse of the mean quadratic error of prediction for the construction of biased linear models(Elsevier Science Bv, 1993) Militký, Jiří; Meloun, MilanThe main practical problems caused by multi-collinearity are reviewed. The biased estimators based on the generalization of principal components for avoiding multi-collinearity problems are described. The mean quadratic error of prediction criterion is used for the selection of suitable bias. Some advantages of biased regression are demostrated on the problem of intercept estimation in a polynomial model. © 1993.
- ItemUse Of The Mean Quadratic Error Of Prediction For The Construction Of Biased Linear-Models(Elsevier Science Bv, 1993) Militký, Jiří; Meloun, MilanThe main practical problems caused by multi-collinearity are reviewed. The biased estimators based on the generalization of principal components for avoiding multi-collinearity problems are described. The mean quadratic error of prediction criterion is used for the selection of suitable bias. Some advantages of biased regression are demonstrated on the problem of intercept estimation in a polynomial model.