Analyzing the probabilities of ordinal patterns is a recent approach to quantifying the complexity of time series and detecting structural changes in the underlying dynamics. The present paper investigates statistical properties of estimators of ordinal pattern probabilities in discrete-time...

This work extends the circle fitting method of Rangarajan and Kanatani (2009) to accommodate ellipse fitting. Our method, which we call HyperLS, relies on algebraic distance minimization with a carefully chosen scale normalization. The normalization is derived using a rigorous error analysis...

Many volatility models used in financial research belong to a class of hierarchical generalized linear models with random effects in the dispersion. Therefore, the hierarchical-likelihood (h-likelihood) approach can be used. However, the dimension of the Hessian matrix is often large, so...

Principal components analysis (PCA) is a popular descriptive multivariate method for handling quantitative data and it can be extended to deal with qualitative data and mixed measurement level data. The existing algorithms for extended PCA are PRINCIPALS of Young et al. (1978) and PRINCALS of...

The Birnbaum-Saunders distribution has been used quite effectively to model times to failure for materials subject to fatigue and for modeling lifetime data. In this paper we obtain asymptotic expansions, up to order n-1/2 and under a sequence of Pitman alternatives, for the non-null...

One way to model a dependence structure is through the copula function which is a mean to capture the dependence structure in the joint distribution of variables. Association measures such as Kendall's tau or Spearman's rho can be expressed as functionals of the copula. The dependence structure...

In this paper, a data-driven test is proposed to compare two independent or dependent stationary time series, in terms of the second order dynamics. We show that the problem of time series comparison is equivalent to a goodness-of-fit test checking if a constant model is adequate. Using the same...

The Birnbaum-Saunders distribution has recently received considerable attention in the statistical literature, including some applications in the environmental sciences. Several authors have generalized this distribution, but these generalizations are still inadequate for predicting extreme...

A model is introduced for measurements obtained in collaborative interlaboratory studies, comprising measurement errors and random laboratory effects that have Laplace distributions, possibly with heterogeneous, laboratory-specific variances. Estimators are suggested for the common median and...

This paper investigates the equality test of risk ratios in multiple 2x2 tables with structural zero, which is formed by a confounding factor such as age, gender, severity of disease, region or other variables of interest. Score statistic, Wald statistic and likelihood ratio statistic for...