In this paper, individual differences scaling (INDSCAL) is revisited, considering INDSCAL as being embedded within a hierarchy of individual difference scaling models. We explore the members of this family, distinguishing (i) models, (ii) the role of identification and substantive constraints, (iii) criteria for fitting models and (iv) algorithms to optimise the criteria. Model formulations may...

We define generalized Frobenius-Schur indicators for objects in a linear pivotal category C. An equivariant indicator of an object is defined as a functional on the Grothendieck algebra of the quantum double Z(C) of C using the values of the generalized Frobenius-Schur indicators. In a spherical fusion category C with Frobenius-Schur exponent N , we prove that the set of all equivariant indicat...

In this paper, by using the notions of ”not belonging” (∈) and ”non quasi-k-coincidence” (qk) of a fuzzy point with a fuzzy set, we define the notion of (∈,∈ ∨ qk)-fuzzy subgroups of a group which is a generalization of fuzzy subgroups and (∈,∈ ∨ q)-fuzzy subgroups. Aslo, we generalized the concept of ∈-level set, (∈ ∨ q)-level set and (∈,∈ ∨ q)level set by using ”not belonging” (∈) and ”non qu...

Extreme temperature of several stations in Malaysia is modelled by fitting the monthly maximum to the Generalized Extreme Value (GEV) distribution. The Mann-Kendall (MK) test suggests a non-stationary model. Two models are considered for stations with trend and the Likelihood Ratio test is used to determine the best-fitting model. Results show that half of the stations favour a model which is l...

Ordinary least squares (OLS) is the default method for fitting linear models, but is not applicable for problems with dimensionality larger than the sample size. For these problems, we advocate the use of a generalized version of OLS motivated by ridge regression, and propose two novel three-step algorithms involving least squares fitting and hard thresholding. The algorithms are methodological...

We present a statistical perspective on boosting. Special emphasis is given to estimating potentially complex parametric or nonparametric models, including generalized linear and additive models as well as regression models for survival analysis. Concepts of degrees of freedom and corresponding Akaike or Bayesian information criteria, particularly useful for regularization and variable selectio...

The paper presents the results of a case study fitting the generalized Pareto distribution to insurance industry claims data. Besides classical parametric procedures, robust statistical concepts are considered. The latter provide instruments to assess the characteristics of estimators also in the neighborhood of parametric models. A demand for robust methods may arise in cases of fitting distri...

We derive explicit dimension formulas for irreducible MF-spherical KF-representations where KF is the maximal compact subgroup of the general linear group GLd(F) over a local field F and MF is a closed subgroup of KF such that KF/MF realizes the Grassmannian of n-dimensional F-subspaces of F. We explore the fact that (KF,MF) is a Gelfand pair whose associated zonal spherical functions identify ...

After diagnose the model and something was detected, there needs an adjustment for model fitting. For example, if non-equal variance happens, either use the transformation of response or other choices. If there are influential points in the dataset, we may try to avoid its influence by different fitting method (Robust Methods). If the relation between response and predictors are absolute not li...