José A. Vilar

Size at maturity of Liocarcinus depurator (Brachyura: Portunidae): a reproductive and morphometric study

Sexual maturity in brachyurans is often associated with an allometric change in the relative growth of the animal. Maturity of Liocarcinus depurator was examined by analysing the monthly percentages of mature females (determined by the stage of gonad maturation and the presence of brood and sperm plugs) by size-class and the relative growth of different body parts: length and width of the carapace, length, height and width of the cheliped propodus; width of the abdominal segments in females and length of the first pleopod in males. Using the reproductive criteria the size at the onset of sexual maturity (carapace width at which 50% females are mature) in females of L. depurator is around 30–34 mm cephalothorax width. Principal component analysis (PCA) showed that the main source of morphometric variation for both sexes was due to heterochelia and allometric changes in growth. Morphometric variables were fitted using different regression techniques to one and two-phase growth models. The length of the first pleopod and the propodus of the right cheliped in males, and width of abdominal segments in females showed two clearly differentiated phases. Estimated maturity size (carapace width) corresponding to 50% mature animals was greater in males than in females. In males, size at the onset of maturity ranged between 31.4 and 35.7 mm, depending on the methods and variables used. The size at the onset of maturity in females ranged between 25.5 and 31.5 mm. In the Ria de Arousa, the size at maturity in females of L. depurator estimated using reproductive criteria is considerably greater than the size found based on morphometric criteria. The size at maturity based on morphometric criteria is greater in males than in females.

Comparing Several Parametric and Nonparametric Approaches to Time Series Clustering: A Simulation Study

One key point in cluster analysis is to determine a similarity or dissimilarity measure between data objects. When working with time series, the concept of similarity can be established in different ways. In this paper, several non-parametric statistics originally designed to test the equality of the log-spectra of two stochastic processes are proposed as dissimilarity measures between time series data. Their behavior in time series clustering is analyzed throughout a simulation study, and compared with the performance of several model-free and model-based dissimilarity measures. Up to three different classification settings were considered: (i) to distinguish between stationary and non-stationary time series, (ii) to classify different ARMA processes and (iii) to classify several non-linear time series models. As it was expected, the performance of a particular dissimilarity metric strongly depended on the type of processes subjected to clustering. Among all the measures studied, the nonparametric distances showed the most robust behavior.

Non-linear time series clustering based on non-parametric forecast densities

The problem of clustering time series is studied for a general class of non-parametric autoregressive models. The dissimilarity between two time series is based on comparing their full forecast densities at a given horizon. In particular, two functional distances are considered: L^1 and L^2. As the forecast densities are unknown, they are approximated using a bootstrap procedure that mimics the underlying generating processes without assuming any parametric model for the true autoregressive structure of the series. The estimated forecast densities are then used to construct the dissimilarity matrix and hence to perform clustering. Asymptotic properties of the proposed method are provided and an extensive simulation study is carried out. The results show the good behavior of the procedure for a wide variety of nonlinear autoregressive models and its robustness to non-Gaussian innovations. Finally, the proposed methodology is applied to a real dataset involving economic time series.

Discriminant and cluster analysis for Gaussian stationary processes: local linear fitting approach

This article is concerned with discrimination and clustering of Gaussian stationary processes. The problem of classifying a realization X n  = (X 1, …, X n ) t from a linear Gaussian process X into one of two categories described by their spectral densities f 1 (λ) and f 2 (λ) is considered first. A discrimination rule based on a general disparity measure between every f i (λ), i = 1, 2, and a nonparametric spectral density estimator fˆ n (λ) is studied when local polynomial techniques are used to obtain fˆ n (λ). In particular, three different local linear smoothers are considered. The discriminant statistic proposed here provides a consistent classification criterion for all three smoothers in the sense that the misclassification probabilities tend to zero. A simulation study is performed to confirm in practice the good theoretical behavior of the discriminant rule and to compare the influence of the different smoothers. The disparity measure is also used to carry out cluster analysis of time series and some examples are presented and compared with previous works.

Classifying Time Series Data: A Nonparametric Approach

A general nonparametric approach to identify similarities in a set of simultaneously observed time series is proposed. The trends are estimated via local polynomial regression and classified according to standard clustering procedures. The equality of the trends is checked using several nonparametric test statistics whose asymptotic distributions are approximated by a bootstrap procedure. Once the estimated trends are removed from the model, the residual series are grouped by means of a nonparametric cluster method specifically designed for time series. Such a method is based on a disparity measure between local linear smoothers of the spectra of the series. The performance of the proposed methodology is illustrated by means of its application to a particular financial data example. The dependence of the observations is a crucial factor in this work and is taken into account throughout the study.

Annual trend patterns of phytoplankton species abundance belie homogeneous taxonomical group responses to climate in the NE Atlantic upwelling

Phytoplankton is a sentinel of marine ecosystem change. Composed by many species with different life-history strategies, it rapidly responds to environment changes. An analysis of the abundance of 54 phytoplankton species in Galicia (NW Spain) between 1989 and 2008 to determine the main components of temporal variability in relation to climate and upwelling showed that most of this variability was stochastic, as seasonality and long term trends contributed to relatively small fractions of the series. In general, trends appeared as non linear, and species clustered in 4 groups according to the trend pattern but there was no defined pattern for diatoms, dinoflagellates or other groups. While, in general, total abundance increased, no clear trend was found for 23 species, 14 species decreased, 4 species increased during the early 1990s, and only 13 species showed a general increase through the series. In contrast, series of local environmental conditions (temperature, stratification, nutrients) and climate-related variables (atmospheric pressure indices, upwelling winds) showed a high fraction of their variability in deterministic seasonality and trends. As a result, each species responded independently to environmental and climate variability, measured by generalized additive models. Most species showed a positive relationship with nutrient concentrations but only a few showed a direct relationship with stratification and upwelling. Climate variables had only measurable effects on some species but no common response emerged. Because its adaptation to frequent disturbances, phytoplankton communities in upwelling ecosystems appear less sensitive to changes in regional climate than other communities characterized by short and well defined productive periods.

Functional ANOVA starting from discrete data: an application to air quality data

A nonparametric functional approach is proposed to compare the mean functions of

Finite sample performance of density estimators from unequally spaced data

k