Search results for "probability"

Robust estimation and inference for bivariate line-fitting in allometry.

2011

In allometry, bivariate techniques related to principal component analysis are often used in place of linear regression, and primary interest is in making inferences about the slope. We demonstrate that the current inferential methods are not robust to bivariate contamination, and consider four robust alternatives to the current methods -- a novel sandwich estimator approach, using robust covariance matrices derived via an influence function approach, Huber's M-estimator and the fast-and-robust bootstrap. Simulations demonstrate that Huber's M-estimators are highly efficient and robust against bivariate contamination, and when combined with the fast-and-robust bootstrap, we can make accurat…

On the convenience of heteroscedasticity in highly multivariate disease mapping

2019

Highly multivariate disease mapping has recently been proposed as an enhancement of traditional multivariate studies, making it possible to perform the joint analysis of a large number of diseases. This line of research has an important potential since it integrates the information of many diseases into a single model yielding richer and more accurate risk maps. In this paper we show how some of the proposals already put forward in this area display some particular problems when applied to small regions of study. Specifically, the homoscedasticity of these proposals may produce evident misfits and distorted risk maps. In this paper we propose two new models to deal with the variance-adaptiv…

2019

In the independent component model, the multivariate data are assumed to be a mixture of mutually independent latent components. The independent component analysis (ICA) then aims at estimating these latent components. In this article, we study an ICA method which combines the use of linear and quadratic autocorrelations to enable efficient estimation of various kinds of stationary time series. Statistical properties of the estimator are studied by finding its limiting distribution under general conditions, and the asymptotic variances are derived in the case of ARMA-GARCH model. We use the asymptotic results and a finite sample simulation study to compare different choices of a weight coef…

Statistically validated hierarchical clustering: Nested partitions in hierarchical trees

2022

We develop an algorithm that is fast and scalable in the detection of a nested partition extracted from a dendrogram that is obtained from hierarchical clustering of a multivariate series. Our algorithm provides a -value for each clade observed in the hierarchical tree. The -value is obtained by computing many bootstrap replicas of the dissimilarity matrix and by performing a statistical test on each difference between the dissimilarity associated with a given clade and the dissimilarity of the clade of its parent node. We prove the efficacy of our algorithm with a set of benchmarks generated by a hierarchically nested factor model. We compare results obtained by our algorithm with those of…

A form factor approach to the asymptotic behavior of correlation functions in critical models

2011

We propose a form factor approach for the computation of the large distance asymptotic behavior of correlation functions in quantum critical (integrable) models. In the large distance regime we reduce the summation over all excited states to one over the particle/hole excitations lying on the Fermi surface in the thermodynamic limit. We compute these sums, over the so-called critical form factors, exactly. Thus we obtain the leading large distance behavior of each oscillating harmonic of the correlation function asymptotic expansion, including the corresponding amplitudes. Our method is applicable to a wide variety of integrable models and yields precisely the results stemming from the Lutt…

Form factor approach to dynamical correlation functions in critical models

2012

We develop a form factor approach to the study of dynamical correlation functions of quantum integrable models in the critical regime. As an example, we consider the quantum non-linear Schr\"odinger model. We derive long-distance/long-time asymptotic behavior of various two-point functions of this model. We also compute edge exponents and amplitudes characterizing the power-law behavior of dynamical response functions on the particle/hole excitation thresholds. These last results confirm predictions based on the non-linear Luttinger liquid method. Our results rely on a first principles derivation, based on the microscopic analysis of the model, without invoking, at any stage, some correspon…

Thermal form factors of the XXZ chain and the large-distance asymptotics of its temperature dependent correlation functions

2013

We derive expressions for the form factors of the quantum transfer matrix of the spin-1/2 XXZ chain which are suitable for taking the infinite Trotter number limit. These form factors determine the finitely many amplitudes in the leading asymptotics of the finite-temperature correlation functions of the model. We consider form-factor expansions of the longitudinal and transversal two-point functions. Remarkably, the formulae for the amplitudes are in both cases of the same form. We also explain how to adapt our formulae to the description of ground state correlation functions of the finite chain. The usefulness of our novel formulae is demonstrated by working out explicit results in the hig…

Thermodynamic limit of particle-hole form factors in the massless XXZ Heisenberg chain

2010

We study the thermodynamic limit of the particle-hole form factors of the XXZ Heisenberg chain in the massless regime. We show that, in this limit, such form factors decrease as an explicitly computed power-law in the system-size. Moreover, the corresponding amplitudes can be obtained as a product of a "smooth" and a "discrete" part: the former depends continuously on the rapidities of the particles and holes, whereas the latter has an additional explicit dependence on the set of integer numbers that label each excited state in the associated logarithmic Bethe equations. We also show that special form factors corresponding to zero-energy excitations lying on the Fermi surface decrease as a …

Asymptotics of correlation functions of the Heisenberg-Ising chain in the easy-axis regime

2016

We analyze the long-time large-distance asymptotics of the longitudinal correlation functions of the Heisenberg-Ising chain in the easy-axis regime. We show that in this regime the leading asymptotics of the dynamical two-point functions is entirely determined by the two-spinon contribution to their form factor expansion. Its explicit form is obtained from a saddle-point analysis of the corresponding double integral. It describes the propagation of a wave front with velocity $v_{c_1}$ which is found to be the maximal possible group velocity. Like in wave propagation in dispersive media the wave front is preceded by a precursor running ahead with velocity $v_{c_2}$. As a special case we obta…

Partition function of the trigonometric SOS model with reflecting end

2010

We compute the partition function of the trigonometric SOS model with one reflecting end and domain wall type boundary conditions. We show that in this case, instead of a sum of determinants obtained by Rosengren for the SOS model on a square lattice without reflection, the partition function can be represented as a single Izergin determinant. This result is crucial for the study of the Bethe vectors of the spin chains with non-diagonal boundary terms.