6,309 research outputs found
Semiparametric Multivariate Accelerated Failure Time Model with Generalized Estimating Equations
The semiparametric accelerated failure time model is not as widely used as
the Cox relative risk model mainly due to computational difficulties. Recent
developments in least squares estimation and induced smoothing estimating
equations provide promising tools to make the accelerate failure time models
more attractive in practice. For semiparametric multivariate accelerated
failure time models, we propose a generalized estimating equation approach to
account for the multivariate dependence through working correlation structures.
The marginal error distributions can be either identical as in sequential event
settings or different as in parallel event settings. Some regression
coefficients can be shared across margins as needed. The initial estimator is a
rank-based estimator with Gehan's weight, but obtained from an induced
smoothing approach with computation ease. The resulting estimator is consistent
and asymptotically normal, with a variance estimated through a multiplier
resampling method. In a simulation study, our estimator was up to three times
as efficient as the initial estimator, especially with stronger multivariate
dependence and heavier censoring percentage. Two real examples demonstrate the
utility of the proposed method
Inference on the tail process with application to financial time series modelling
To draw inference on serial extremal dependence within heavy-tailed Markov
chains, Drees, Segers and Warcho{\l} [Extremes (2015) 18, 369--402] proposed
nonparametric estimators of the spectral tail process. The methodology can be
extended to the more general setting of a stationary, regularly varying time
series. The large-sample distribution of the estimators is derived via
empirical process theory for cluster functionals. The finite-sample performance
of these estimators is evaluated via Monte Carlo simulations. Moreover, two
different bootstrap schemes are employed which yield confidence intervals for
the pre-asymptotic spectral tail process: the stationary bootstrap and the
multiplier block bootstrap. The estimators are applied to stock price data to
study the persistence of positive and negative shocks.Comment: 22 page
A conformal bootstrap approach to critical percolation in two dimensions
We study four-point functions of critical percolation in two dimensions, and
more generally of the Potts model. We propose an exact ansatz for the spectrum:
an infinite, discrete and non-diagonal combination of representations of the
Virasoro algebra. Based on this ansatz, we compute four-point functions using a
numerical conformal bootstrap approach. The results agree with Monte-Carlo
computations of connectivities of random clusters.Comment: 16 pages, Python code available at
https://github.com/ribault/bootstrap-2d-Python, v2: some clarifications and
minor improvement
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