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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Journal of classification 1 (1984), S. 243-253 
    ISSN: 1432-1343
    Keywords: Distance between groups ; Location model ; Mixed variables ; Monte Carlo methods ; Simulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The location model is a useful tool in parametric analysis of mixed continuous and categorical variables. In this model, the continuous variables are assumed to follow different multivariate normal distributions for each possible combination of categorical variable values. Using this model, a distance between two populations involving mixed variables can be defined. To date, however, no distributional results have been available, against which to assess the outcomes of practical applications of this distance. The null distribution of estimated distance is therefore considered in this paper, for a range of possible situations. No explicit analytical expressions are derived for this distribution, but easily implementable Monte Carlo schemes are described. These are then applied to previously cited examples.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    Journal of Chemometrics 9 (1995), S. 509-520 
    ISSN: 0886-9383
    Keywords: canonical variates ; discriminant analysis ; partial least squares ; principal components ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A new set of derived variables is proposed for exhibiting group separation in multivariate data on for preprocessing such data prior to discriminant analysis. The technique combines optimal features of canonical variate analysis and principal component analysis: the derived variables are linear combinations of the original variables that optimize the canonical variate criterion (ratio of between-group to within-group variance) but subject to the orthogonality constraints of principal components. In this formulation the canonical variates can be derived even when the within-group matrix is singular (i.e. when there are more variables than objects in the data matrix). A simple computational algorithm for extraction of these variables is proposed. The methods are illustrated on several data sets and compared with alternative techniques such as principal component analysis and partial least squares.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Statistics and computing 3 (1993), S. 37-44 
    ISSN: 1573-1375
    Keywords: bootstrapping ; eigenvalues ; eigenvectors ; Monte Carlo methods ; random permutations ; significance levels
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Permutational tests are proposed for the hypotheses that two population correlation matrices have common eigenvectors, and that two population correlation matrices are equal. The only assumption made in these tests is that the distributional form is the same in the two populations; they should be useful as a prelude either to tests of mean differences in grouped standardised data or to principal component investigation of such data. The performance of the permutational tests is subjected to Monte Carlo investigation, and a comparison is made with the performance of the likelihood-ratio test for equality of covariance matrices applied to standardised data. Bootstrapping is considered as an alternative to permutation, but no particular advantages are found for it. The various tests are applied to several data sets.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Statistics and computing 10 (2000), S. 209-229 
    ISSN: 1573-1375
    Keywords: cross-validation ; ridge regression ; partial least squares ; prediction ; assessment of predictive models
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We describe a Monte Carlo investigation of a number of variants of cross-validation for the assessment of performance of predictive models, including different values of k in leave-k-out cross-validation, and implementation either in a one-deep or a two-deep fashion. We assume an underlying linear model that is being fitted using either ridge regression or partial least squares, and vary a number of design factors such as sample size n relative to number of variables p, and error variance. The investigation encompasses both the non-singular (i.e. n 〉 p) and the singular (i.e. n ≤ p) cases. The latter is now common in areas such as chemometrics but has as yet received little rigorous investigation. Results of the experiments enable us to reach some definite conclusions and to make some practical recommendations.
    Type of Medium: Electronic Resource
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