Abstract

Abstract
Here we obtain difference equations for the higher order moments and cumulants of a time series {X-t} satisfying an INAR(p) model. These equations are similar to the difference equations for the higher order moments and cumulants of the bilinear time series model. We obtain the spectral and bispectral density functions for the INAR(p) process in state-space form, thus characterizing it in the frequency domain. We consider a frequency domain method - the Whittle criterion - to estimate the parameters of the INAR(p) model and illustrate it with the series of the number of epilepsy seizures of a patient.

Abstract
Muscle relaxant drugs are currently given during surgical operations. The design of controllers for the automatic control of neuromuscular blockade benefits from an individual tuning of the controller to the characteristics of the patient. A novel approach to the characterization of the neuromuscular blockade response induced by an initial bolus at the beginning of anaesthesia is proposed. This approach is based on the statistical analysis of the data using principal components and Walsh-Fourier spectral analysis. These methods provide information about the patients dynamics, allowing the on-line autocalibration of the controller, using multiple linear regression techniques. Observed and simulated data are used to compare different approaches to the characterization of the bolus response.

Abstract
Replicated time series are a particular type of repeated measures, which consist of time-sequences of measurements taken from several subjects (experimental units). We consider independent replications of count time series that are modelled by first-order integer-valued autoregressive processes, INAR(1). In this work, we propose several estimation methods using the classical and the Bayesian approaches and both in time and frequency domains. Furthermore, we study the asymptotic properties of the estimators. The methods are illustrated and their performance is compared in a simulation study. Finally, the methods are applied to a set of observations concerning sunspot data.

Abstract
Spatial and temporal sea level variability in the North Atlantic is investigated from Topex/Poseidon (T/P) altimetry data. Time series of sea level anomalies on a regular 5 degrees grid are analysed. Non-linear denoising through thresholding in the wavelet transform domain is carried out for each series in order to remove noise while preserving non-smooth features. Principal Component Analysis (PCA) is used to obtain a spatio-temporal description of the sea level field, To avoid modal mixing and improve interpretation of the principal modes, PCA is implemented separately for seasonal and trend components of the sea level field obtained from a wavelet-based multiresolution analysis. The leading pattern of the seasonal field reflects the dominance of a stable annual cycle over the study area and the change in the seasonal regime approaching the equator with contribution of the semi-annual cycle and phase-shift in the annual cycle in the tropical Atlantic. The leading pattern of the trend field is a broad spatial pattern associated with North Atlantic Oscillation (NAO), reflecting the influence of atmospheric conditions on interannual sea level variability.

Abstract
In this paper we propose a method for grouping and summarizing large sets of association rules according to the items contained in each rule. We use hierarchical clustering to partition the initial rule set into thematically coherent subsets. This enables the summarization of the rule set by adequately choosing a representative rule for each subset, and helps in the interactive exploration of the rule model by the user. We define the requirements of our approach, and formally show the adequacy of the chosen approach to our aims. Rule clusters can also be used to infer novel interest measures for the rules. Such measures are based on the lexicon of the rules and are complementary to measures based on statistical properties, such as confidence, lift and conviction. We show examples of the application of the proposed techniques.