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1. Inference in finite populations.
a) Inference about the distribution function.
In collaboration with Prof. J. Opsomer (Iowa State University of Science and Technology). Objectives:
a) Estimation of parameters in finite populations, particularly the distribution function or transformations of the distribution function, via model-assisted methods.
b) Tests for the selection of the superpopulation model in the estimation process.
c) Study of resampling techniques in this context.
d) Software development and real data applications.
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b) Mixed models in small areas.
In collaboration with Prof. Domingo Morales (Universidad Miguel Hernández de Elche). Objectives:
a) Nonparametric estimation of the Mean Square Error of several features in small areas and the corresponding estimators (mean, total, etc.), for mixed models with a random factor.
b) Significance tests for the random effect in mixed models.
c) Study of resampling techniques in this context.
d) Software development and real data applications (for instance, estimation of the mean income in several areas in Galicia).
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2. Inference in spatial statistics and spatial-temporal models.
a) Development of estimation and testing for spatial and spatial-temporal models via spectral domain techniques.
b) Tests for spatial models via generalizations of regression empirical processes.
c) Tests for point processes.
d) Software development and applications to environmental and ecological predictions (SO2 maps in the surroundings of power stations, moss concentration maps in Galicia, study of forest species locations).
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3. Modelization and prediction in financial series.
a) Development of models with a trend component (parametric, nonparametric or mixed), such as dynamic partial linear models with volatility modelization.
b) Development of multivariate partial linear regression models. Generalization and extension to models with various error dependence structures.
c) Significance tests about the model or its components, prediction, exogenous variables, trend, etc.
d) Study of resampling techniques to obtain prediction intervals, taking into account the volatility.
e) Applications to portfolio design. Simulations and real data analysis about the profitability of the portfolios (data from Caixa Galicia).
f) Refinement in learning techniques for future predictions: baaging y boosting.
g) Software development for financial active.
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4. Set estimation.
a) Estimation of geometrical features of set boundaries: length, area, fractal dimension, etc.
b) Tests about the support of a distribution.
c) Applications: image analysis, indirect observations from medical trials, etc.
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5. Goodness-of-fit tests.
a) Goodness-of-fit tests and comparison of curves tests in regression, with censored and/or truncated data.
b) Goodness-of-fit tests in regression with missing data.
c) Development of new tests based on empirical likelihood.
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6. Learning techniques.
a) Study of the variogram as the kernel in kernel-type learning techniques, such as support vector machines (SVM), for regression and classification. Other techniques based on the kernel trick, with applications to several contexts. Extension to nonparametric estimation in regression.
b) Development of algorithms for variogram estimation in high dimensionality setups.
c) Development of more stable and more efficient algorithms (for instance, based on genetic algorithms), for the modelization of the conditional distribution and estimation of parameters in ARMA-GARCH and other nonparametric models, in a time-varying context.
d) Development of techniques and algorithms for the modelization of structural nonlinear equations, by using a) kernel trick, b) neuronal networks with an architecture reflecting the postulated model, c) other nonlinear techniques.
e) Applications: management of natural resources and mining, data mining, prediction in financial management, biological applications, quality studies in business sectors, etc.
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7. Inference and prediction with point data and functional data.
a) Extension of learning techniques to a functional data setup.
b) Development of new process control methods based on neuronal networks.
c) Bootstrap inference with functional data.
d) Software development for application in chemical engineering and environmental studies.
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