Search results for "Discriminant"
showing 10 items of 344 documents
A Comment on the Coefficient of Determination for Binary Responses
1992
Abstract Linear logistic or probit regression can be closely approximated by an unweighted least squares analysis of the regression linear in the conditional probabilities provided that these probabilities for success and failure are not too extreme. It is shown how this restriction on the probabilities translates into a restriction on the range of the coefficient of determination R 2 so that, as a consequence, R 2 is not suitable to judge the effectiveness of linear regressions with binary responses even if an important relation is present.
The affine equivariant sign covariance matrix: asymptotic behavior and efficiencies
2003
We consider the affine equivariant sign covariance matrix (SCM) introduced by Visuri et al. (J. Statist. Plann. Inference 91 (2000) 557). The population SCM is shown to be proportional to the inverse of the regular covariance matrix. The eigenvectors and standardized eigenvalues of the covariance, matrix can thus be derived from the SCM. We also construct an estimate of the covariance and correlation matrix based on the SCM. The influence functions and limiting distributions of the SCM and its eigenvectors and eigenvalues are found. Limiting efficiencies are given in multivariate normal and t-distribution cases. The estimates are highly efficient in the multivariate normal case and perform …
STATIS and DISTATIS: optimum multitable principal component analysis and three way metric multidimensional scaling
2012
STATIS is an extension of principal component analysis PCA tailored to handle multiple data tables that measure sets of variables collected on the same observations, or, alternatively, as in a variant called dual-STATIS, multiple data tables where the same variables are measured on different sets of observations. STATIS proceeds in two steps: First it analyzes the between data table similarity structure and derives from this analysis an optimal set of weights that are used to compute a linear combination of the data tables called the compromise that best represents the information common to the different data tables; Second, the PCA of this compromise gives an optimal map of the observation…
On the usage of joint diagonalization in multivariate statistics
2022
Scatter matrices generalize the covariance matrix and are useful in many multivariate data analysis methods, including well-known principal component analysis (PCA), which is based on the diagonalization of the covariance matrix. The simultaneous diagonalization of two or more scatter matrices goes beyond PCA and is used more and more often. In this paper, we offer an overview of many methods that are based on a joint diagonalization. These methods range from the unsupervised context with invariant coordinate selection and blind source separation, which includes independent component analysis, to the supervised context with discriminant analysis and sliced inverse regression. They also enco…
Large-sample properties of unsupervised estimation of the linear discriminant using projection pursuit
2021
We study the estimation of the linear discriminant with projection pursuit, a method that is unsupervised in the sense that it does not use the class labels in the estimation. Our viewpoint is asymptotic and, as our main contribution, we derive central limit theorems for estimators based on three different projection indices, skewness, kurtosis, and their convex combination. The results show that in each case the limiting covariance matrix is proportional to that of linear discriminant analysis (LDA), a supervised estimator of the discriminant. An extensive comparative study between the asymptotic variances reveals that projection pursuit gets arbitrarily close in efficiency to LDA when the…
The Development of the Dealing with Challenging Interaction (DCI) Method to Evaluate Teachers’ Social Interaction Skills
2012
The Dealing with Challenging Interaction (DCI) method was developed to measure social interaction skills of teacher study groups. The participants were 70 teachers from three schools. The inter-rater agreement, Cohen’s kappa, varied between 0.57- 1.00. The discriminant validity was supported by a cluster analysis differentiating between the skilful and less skilful teachers. The results of the supplementary instrument were equivalent to the cluster analysis maintaining criterion oriented validity of the method developed. The DCI appeared to be a reliable and valid tool for measuring teachers’ social interaction skills. Peer reviewed
Arithmetic and geometry of a K3 surface emerging from virtual corrections to Drell–Yan scattering
2020
We study a K3 surface, which appears in the two-loop mixed electroweak-quantum chromodynamic virtual corrections to Drell--Yan scattering. A detailed analysis of the geometric Picard lattice is presented, computing its rank and discriminant in two independent ways: first using explicit divisors on the surface and then using an explicit elliptic fibration. We also study in detail the elliptic fibrations of the surface and use them to provide an explicit Shioda--Inose structure. Moreover, we point out the physical relevance of our results.
Use of linear discriminant analysis applied to vibrational spectroscopy data to characterize commercial varnishes employed for art purposes.
2007
An improvement of methodologies for characterising synthetic resins used in varnishes employed for art purposes has been suggested. Several kinds of standard of the most common polymeric resins (acrylic, vinyl, poly(vinyl alcohol), alkyd, cellulose nitrate, latex, polyester, polyurethane, epoxy, organosilicic, and ketonic) were analyzed by Fourier transform infrared (FTIR) spectroscopy. Synthetic resins characterization is based on the mathematical treatment of their whole spectrum, dividing it in 13 sections, avoiding the one-by-one interpretation of the absorption bands. The mathematical model takes as variables the maximal absorbance of each section, and each synthetic standard resin as …
Time, frequency and information domain analysis of short-term heart rate variability before and after focal and generalized seizures in epileptic chi…
2019
OBJECTIVE In this work we explore the potential of combining standard time and frequency domain indexes with novel information measures, to characterize pre- and post-ictal heart rate variability (HRV) in epileptic children, with the aim of differentiating focal and generalized epilepsy regarding the autonomic control mechanisms. APPROACH We analyze short-term HRV in 37 children suffering from generalized or focal epilepsy, monitored 10 s, 300 s, 600 s and 1800 s both before and after seizure episodes. Nine indexes are computed in time (mean, standard deviation of normal-to-normal intervals, root mean square of the successive differences (RMSSD)), frequency (low-to-high frequency power rati…
Assessing the territorial influence of an Iberian worship site. The chemical characterisation of the terracotta from the Iron Age sanctuary of La Ser…
2017
This paper presents the study of the prestigious terracotta votive figurines from the Iberian Iron Age sanctuary of La Serreta (Alicante province, Spain) composed of 174 items. Portable X-ray fluorescence (PXRF) was used to identify elemental markers that permit us to observe the differences between local and non-local terracotta figurines and furthermore to evaluate the geographical influence of the La Serreta sanctuary using Principal Component Analysis (PCA). The Partial Least Squares Discriminant Analysis (PLSDA) statistical method was also used to classify the figurines of uncertain geographical origin. The resulting groups were related to typological and stylistic groups of figurines …