634 research outputs found
On the Bahadur representation of sample quantiles for dependent sequences
We establish the Bahadur representation of sample quantiles for linear and
some widely used nonlinear processes. Local fluctuations of empirical processes
are discussed. Applications to the trimmed and Winsorized means are given. Our
results extend previous ones by establishing sharper bounds under milder
conditions and thus provide new insight into the theory of empirical processes
for dependent random variables.Comment: Published at http://dx.doi.org/10.1214/009053605000000291 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
M-estimation of linear models with dependent errors
We study asymptotic properties of -estimates of regression parameters in
linear models in which errors are dependent. Weak and strong Bahadur
representations of the -estimates are derived and a central limit theorem is
established. The results are applied to linear models with errors being
short-range dependent linear processes, heavy-tailed linear processes and some
widely used nonlinear time series.Comment: Published at http://dx.doi.org/10.1214/009053606000001406 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Covariance matrix estimation for stationary time series
We obtain a sharp convergence rate for banded covariance matrix estimates of
stationary processes. A precise order of magnitude is derived for spectral
radius of sample covariance matrices. We also consider a thresholded covariance
matrix estimator that can better characterize sparsity if the true covariance
matrix is sparse. As our main tool, we implement Toeplitz [Math. Ann. 70 (1911)
351-376] idea and relate eigenvalues of covariance matrices to the spectral
densities or Fourier transforms of the covariances. We develop a large
deviation result for quadratic forms of stationary processes using m-dependence
approximation, under the framework of causal representation and physical
dependence measures.Comment: Published in at http://dx.doi.org/10.1214/11-AOS967 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Confidence bands in nonparametric time series regression
We consider nonparametric estimation of mean regression and conditional
variance (or volatility) functions in nonlinear stochastic regression models.
Simultaneous confidence bands are constructed and the coverage probabilities
are shown to be asymptotically correct. The imposed dependence structure allows
applications in many linear and nonlinear auto-regressive processes. The
results are applied to the S&P 500 Index data.Comment: Published in at http://dx.doi.org/10.1214/07-AOS533 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Asymptotic spectral theory for nonlinear time series
We consider asymptotic problems in spectral analysis of stationary causal
processes. Limiting distributions of periodograms and smoothed periodogram
spectral density estimates are obtained and applications to the spectral domain
bootstrap are given. Instead of the commonly used strong mixing conditions, in
our asymptotic spectral theory we impose conditions only involving
(conditional) moments, which are easily verifiable for a variety of nonlinear
time series.Comment: Published in at http://dx.doi.org/10.1214/009053606000001479 the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
- …