139 research outputs found
Modelling and Forecasting of Realized Covariance Matrices
In this thesis, we use observation-driven models for time-series of daily RCs. That is, we assume a matrix-variate probability distribution for the daily RCs, whose parameters are updated based on the RC realizations from previous days.
In particular, Chapter 2 looks at different matrix-variate probability distributions for the RCs and their theoretical and empirical properties. Chapter 3 proposes a flexible observation-driven model to update all distribution-specific time-varying parameters, not just the expected value matrix as is done in the literature so far. Chapter 4 introduces an observation-driven updating mechanism that is applicable to high-dimensional time-series of RCs. Each of these three chapters is a self-contained paper
Valid Heteroskedasticity Robust Testing
Tests based on heteroskedasticity robust standard errors are an important
technique in econometric practice. Choosing the right critical value, however,
is not simple at all: conventional critical values based on asymptotics often
lead to severe size distortions; and so do existing adjustments including the
bootstrap. To avoid these issues, we suggest to use smallest size-controlling
critical values, the generic existence of which we prove in this article for
the commonly used test statistics. Furthermore, sufficient and often also
necessary conditions for their existence are given that are easy to check.
Granted their existence, these critical values are the canonical choice: larger
critical values result in unnecessary power loss, whereas smaller critical
values lead to over-rejections under the null hypothesis, make spurious
discoveries more likely, and thus are invalid. We suggest algorithms to
numerically determine the proposed critical values and provide implementations
in accompanying software. Finally, we numerically study the behavior of the
proposed testing procedures, including their power properties.Comment: Minor changes; some references added; some minor errors correcte
Modelling multivariate extremes through angular-radial decomposition of the density function
We present a new framework for modelling multivariate extremes, based on an
angular-radial representation of the probability density function. Under this
representation, the problem of modelling multivariate extremes is transformed
to that of modelling an angular density and the tail of the radial variable,
conditional on angle. Motivated by univariate theory, we assume that the tail
of the conditional radial distribution converges to a generalised Pareto (GP)
distribution. To simplify inference, we also assume that the angular density is
continuous and finite and the GP parameter functions are continuous with angle.
We refer to the resulting model as the semi-parametric angular-radial (SPAR)
model for multivariate extremes. We consider the effect of the choice of polar
coordinate system and introduce generalised concepts of angular-radial
coordinate systems and generalised scalar angles in two dimensions. We show
that under certain conditions, the choice of polar coordinate system does not
affect the validity of the SPAR assumptions. However, some choices of
coordinate system lead to simpler representations. In contrast, we show that
the choice of margin does affect whether the model assumptions are satisfied.
In particular, the use of Laplace margins results in a form of the density
function for which the SPAR assumptions are satisfied for many common families
of copula, with various dependence classes. We show that the SPAR model
provides a more versatile framework for characterising multivariate extremes
than provided by existing approaches, and that several commonly-used approaches
are special cases of the SPAR model. Moreover, the SPAR framework provides a
means of characterising all `extreme regions' of a joint distribution using a
single inference. Applications in which this is useful are discussed
Parameter estimation with gravitational waves
The new era of gravitational wave astronomy truly began on September 14, 2015
with the detection of GW150914, the sensational first direct observation of
gravitational waves from the inspiral and merger of two black holes by the two
Advanced LIGO detectors. In the subsequent first three observing runs of the
LIGO/Virgo network, gravitational waves from compact binary mergers
have been announced, with more results to come. The events have mostly been
produced by binary black holes, but two binary neutron star mergers have so far
been observed, as well as the mergers of two neutron star - black hole systems.
Furthermore, gravitational waves emitted by core-collapse supernovae, pulsars
and the stochastic gravitational wave background are within the
LIGO/Virgo/KAGRA sensitivity band and are likely to be observed in future
observation runs. Beyond signal detection, a major challenge has been the
development of statistical and computational methodology for estimating the
physical waveform parameters and quantifying their uncertainties in order to
accurately characterise the emitting system. These methods depend on the
sources of the gravitational waves and the gravitational waveform model that is
used. This article reviews the main waveform models and parameter estimation
methods used to extract physical parameters from gravitational wave signals
detected to date by LIGO and Virgo and from those expected to be observed in
the future, which will include KAGRA, and how these methods interface with
various aspects of LIGO/Virgo/KAGRA science. Also presented are the statistical
methods used by LIGO and Virgo to estimate detector noise, test general
relativity, and draw conclusions about the rates of compact binary mergers in
the universe. Furthermore, a summary of major publicly available gravitational
wave parameter estimation software packages is given
SIS 2017. Statistics and Data Science: new challenges, new generations
The 2017 SIS Conference aims to highlight the crucial role of the Statistics in Data Science. In this new domain of ‘meaning’ extracted from the data, the increasing amount of produced and available data in databases, nowadays, has brought new challenges. That involves different fields of statistics, machine learning, information and computer science, optimization, pattern recognition. These afford together a considerable contribute in the analysis of ‘Big data’, open data, relational and complex data, structured and no-structured. The interest is to collect the contributes which provide from the different domains of Statistics, in the high dimensional data quality validation, sampling extraction, dimensional reduction, pattern selection, data modelling, testing hypotheses and confirming conclusions drawn from the data
Towards an Occam Factor for Random Graphs
The increasing ubiquity of network data in the digital age has demonstrated the necessity of statistical tools designed to estimate and infer from appropriate random graph models. We seek the eventual development of a model selection criterion --- the eponymous Occam factor --- for random graphs founded upon the evidence/flexibility paradigm due to Rougier and Priebe; such choice of model permits one to implement methods and procedures appropriate to that model as determined by its analytical properties. We demonstrate, in particular, how theoretical results for the stochastic blockmodel (SBM) lead to Expectation-Solution algorithms which take explicit advantage of the curved-Gaussian mixture limiting distributions of an observed graph's adjacency and Laplacian spectral embeddings; this method demonstrates improved clustering performance over established methods. We next demonstrate how the evidence/flexibility paradigm may be used to perform model selection in an idealized exponential family setting. Results therein motivate the development of a closed-form conjugate prior distribution for Gaussian models with compound-symmetric variance-covariance. We conclude with a prescripted means of extending the evidence/flexibility paradigm to random graphs
CLADAG 2021 BOOK OF ABSTRACTS AND SHORT PAPERS
The book collects the short papers presented at the 13th Scientific Meeting of the Classification and Data Analysis Group (CLADAG) of the Italian Statistical Society (SIS). The meeting has been organized by the Department of Statistics, Computer Science and Applications of the University of Florence, under the auspices of the Italian Statistical Society and the International Federation of Classification Societies (IFCS). CLADAG is a member of the IFCS, a federation of national, regional, and linguistically-based classification societies. It is a non-profit, non-political scientific organization, whose aims are to further classification research
Nonparametric Statistical Inference with an Emphasis on Information-Theoretic Methods
This book addresses contemporary statistical inference issues when no or minimal assumptions on the nature of studied phenomenon are imposed. Information theory methods play an important role in such scenarios. The approaches discussed include various high-dimensional regression problems, time series and dependence analyses
Model selection and the vectorial misspecification-resistant information criterion in multivariate time series
The thesis deals with the problem of Model Selection (MS) motivated by information and prediction theory, focusing on parametric time series (TS) models. The main contribution of the thesis is the extension to the multivariate case of the Misspecification-Resistant Information Criterion (MRIC), a criterion introduced recently that solves Akaike’s original research problem posed 50 years ago, which led to the definition of the AIC. The importance of MS is witnessed by the huge amount of literature devoted to it and published in scientific journals of many different disciplines. Despite such a widespread treatment, the contributions that adopt a mathematically rigorous approach are not so numerous and one of the aims of this project is to review and assess them. Chapter 2 discusses methodological aspects of MS from information theory. Information criteria (IC) for the i.i.d. setting are surveyed along with their asymptotic properties; and the cases of small samples, misspecification, further estimators. Chapter 3 surveys criteria for TS. IC and prediction criteria are considered for: univariate models (AR, ARMA) in the time and frequency domain, parametric multivariate (VARMA, VAR); nonparametric nonlinear (NAR); and high-dimensional models. The MRIC answers Akaike’s original question on efficient criteria, for possibly-misspecified (PM) univariate TS models in multi-step prediction with high-dimensional data and nonlinear models. Chapter 4 extends the MRIC to PM multivariate TS models for multi-step prediction introducing the Vectorial MRIC (VMRIC). We show that the VMRIC is asymptotically efficient by proving the decomposition of the MSPE matrix and the consistency of its Method-of-Moments Estimator (MoME), for Least Squares multi-step prediction with univariate regressor. Chapter 5 extends the VMRIC to the general multiple regressor case, by showing that the MSPE matrix decomposition holds, obtaining consistency for its MoME, and proving its efficiency. The chapter concludes with a digression on the conditions for PM VARX models
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