A Reproducing Kernel Perspective of Smoothing Spline Estimators

Spline functions have a long history as smoothers of noisy time series data, and several equivalent kernel representations have been proposed in terms of the Green's function solving the related boundary value problem. In this study we make use of the reproducing kernel property of the Green's function to obtain an hierarchy of time-invariant spline kernels of different order. The reproducing kernels give a good representation of smoothing splines for medium and long length filters, with a better performance of the asymmetric weights in terms of signal passing, noise suppression and revisions. Empirical comparisons of time-invariant filters are made with the classical non linear ones. The former are shown to loose part of their optimal properties when we fixed the length of the filter according to the noise to signal ratio as done in nonparametric seasonal adjustment procedures.equivalent kernels, nonparametric regression, Hilbert spaces, time series filtering, spectral properties

Approximate likelihood inference in generalized linear latent variable models based on integral dimension reduction

Latent variable models represent a useful tool for the analysis of complex data when the constructs of interest are not observable. A problem related to these models is that the integrals involved in the likelihood function cannot be solved analytically. We propose a computational approach, referred to as Dimension Reduction Method (DRM), that consists of a dimension reduction of the multidimensional integral that makes the computation feasible in situations in which the quadrature based methods are not applicable. We discuss the advantages of DRM compared with other existing approximation procedures in terms of both computational feasibility of the method and asymptotic properties of the resulting estimators.Comment: 28 pages, 3 figures, 7 table

A Reproducing Kernel Perspective of Smoothing Spline Estimators

Spline functions have a long history as smoothers of noisy time series data, and several equivalent kernel representations have been proposed in terms of the Green's function solving the related boundary value problem. In this study we make use of the reproducing kernel property of the Green's function to obtain an hierarchy of time-invariant spline kernels of different order. The reproducing kernels give a good representation of smoothing splines for medium and long length filters, with a better performance of the asymmetric weights in terms of signal passing, noise suppression and revisions. Empirical comparisons of time-invariant filters are made with the classical non linear ones. The former are shown to loose part of their optimal properties when we fixed the length of the filter according to the noise to signal ratio as done in nonparametric seasonal adjustment procedures

A general multivariate latent growth model with applications in student careers Data warehouses

The evaluation of the formative process in the University system has been assuming an ever increasing importance in the European countries. Within this context the analysis of student performance and capabilities plays a fundamental role. In this work we propose a multivariate latent growth model for studying the performances of a cohort of students of the University of Bologna. The model proposed is innovative since it is composed by: (1) multivariate growth models that allow to capture the different dynamics of student performance indicators over time and (2) a factor model that allows to measure the general latent student capability. The flexibility of the model proposed allows its applications in several fields such as socio-economic settings in which personal behaviours are studied by using panel data.Comment: 20 page

Asymptotic properties of adaptive maximum likelihood estimators in latent variable models

Latent variable models have been widely applied in different fields of research in which the constructs of interest are not directly observable, so that one or more latent variables are required to reduce the complexity of the data. In these cases, problems related to the integration of the likelihood function of the model arise since analytical solutions do not exist. In the recent literature, a numerical technique that has been extensively applied to estimate latent variable models is the adaptive Gauss-Hermite quadrature. It provides a good approximation of the integral, and it is more feasible than classical numerical techniques in presence of many latent variables and/or random effects. In this paper, we formally investigate the properties of maximum likelihood estimators based on adaptive quadratures used to perform inference in generalized linear latent variable models.Comment: Published in at http://dx.doi.org/10.3150/13-BEJ531 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Approximate likelihood inference in generalized linear latent variable models based on the dimension-wise quadrature

We propose a new method to perform approximate likelihood inference in latent variable models. Our approach provides an approximation of the integrals involved in the likelihood function through a reduction of their dimension that makes the computation feasible in situations in which classical and adaptive quadrature based methods are not applicable. We derive new theoretical results on the accuracy of the obtained estimators. We show that the proposed approximation outperforms several existing methods in simulations, and it can be successfully applied in presence of multidimensional longitudinal data when standard techniques are not applicable or feasible

Industrial carbon emission intensity: a comprehensive dataset of European regions.

The dataset has been developed within the framework of the EU EIT-Climate Kic Flagship Project “Re-Industrialise” and it includes data of Carbon Emission Intensity (CEI) from industrial sources for the European Regions. CEI is considered as a proxy for analysing the Industrial Sustainability Transition pathways and is calculated as the ratio between CO2 equivalent emissions (CO2e) and Gross Domestic Product (GDP) of the industrial sector over a nine-year timespan, i.e. from 2008 to 2016. CO2e data at plant level have been retrieved from EU Emission Trading System (EU ETS) register and aggregated at different geographical scales, corresponding to the nested structure of NUTS (Nomenclature of Territorial Units for Statistics), proposed by EUROSTAT. Industrial GDP data have been selected from EUROSTAT database to match the industrial sectors covered by EU ETS

Multilevel-growth modeling for the study of sustainability transitions.

Sustainability Transitions (ST) is a complex phenomenon, encompassing environmental, societal and economic aspects. Its study requires a proper investigation, with the identification of a robust indicator and the definition of a suitable method of analysis. To identify the most informative geographical boundaries for analysing ST pathways, we consider the Carbon Emission Intensity (CEI) and estimate a four-level growth model to study its pattern over time for all the EU regions. We apply this model to a novel longitudinal dataset that covers CEI data of European regions at four different geographical scales (state, areas, regions, and provinces) over a nine-year timespan. This approach aims at supporting the decision-makers in developing more effective sustainability transitions policies across Europe, especially focusing on regions and overcoming the well-known “one-size fits all” approach. • The unconditional growth model has been applied to a multi-level structure considering four levels, defined by three geographical scales and time. • The ideal structure of the model would have required five levels, but the sample size of the dataset made the application computationally unfeasible; • The application of the model allowed to identify patterns of stability and change over time of the variable amongst different geographical units

Estimation of latent variable models for ordinal data via fully exponential Laplace approximation

Latent variable models for ordinal data represent a useful tool in different fields of research in which the constructs of interest are not directly observable. In such models, problems related to the integration of the likelihood function can arise since analytical solutions do not exist. Numerical approximations, like the widely used Gauss Hermite (GH) quadrature, are generally applied to solve these problems. However, GH becomes unfeasible as the number of latent variables increases. Thus, alternative solutions have to be found. In this paper, we propose an extended version of the Laplace method for approximating the integrals, known as fully exponential Laplace approximation. It is computational feasible also in presence of many latent variables, and it is more accurate than the classical Laplace method