2,528 research outputs found
Asymptotic Normality for Deconvolution Estimators of Multivariate Densities of Stationary Processes
AbstractWe consider the estimation of the multivariate probability density functions of stationary random processes from noisy observations. The asymptotic normality of kernel-type deconvolution estimators is established for various classes of mixing processes. Classes of noise characteristic functions both with algebraic and with exponential decay are studied
Nonparametric volatility density estimation for discrete time models
We consider discrete time models for asset prices with a stationary
volatility process. We aim at estimating the multivariate density of this
process at a set of consecutive time instants. A Fourier type deconvolution
kernel density estimator based on the logarithm of the squared process is
proposed to estimate the volatility density. Expansions of the bias and bounds
on the variance are derived
Nonparametric methods for volatility density estimation
Stochastic volatility modelling of financial processes has become
increasingly popular. The proposed models usually contain a stationary
volatility process. We will motivate and review several nonparametric methods
for estimation of the density of the volatility process. Both models based on
discretely sampled continuous time processes and discrete time models will be
discussed.
The key insight for the analysis is a transformation of the volatility
density estimation problem to a deconvolution model for which standard methods
exist. Three type of nonparametric density estimators are reviewed: the
Fourier-type deconvolution kernel density estimator, a wavelet deconvolution
density estimator and a penalized projection estimator. The performance of
these estimators will be compared. Key words: stochastic volatility models,
deconvolution, density estimation, kernel estimator, wavelets, minimum contrast
estimation, mixin
Identifiability and consistent estimation of nonparametric translation hidden Markov models with general state space
This paper considers hidden Markov models where the observations are given as
the sum of a latent state which lies in a general state space and some
independent noise with unknown distribution. It is shown that these fully
nonparametric translation models are identifiable with respect to both the
distribution of the latent variables and the distribution of the noise, under
mostly a light tail assumption on the latent variables. Two nonparametric
estimation methods are proposed and we prove that the corresponding estimators
are consistent for the weak convergence topology. These results are illustrated
with numerical experiments
Nonparametric deconvolution problem for dependent sequences
We consider the nonparametric estimation of the density function of weakly
and strongly dependent processes with noisy observations. We show that in the
ordinary smooth case the optimal bandwidth choice can be influenced by long
range dependence, as opposite to the standard case, when no noise is present.
In particular, if the dependence is moderate the bandwidth, the rates of
mean-square convergence and, additionally, central limit theorem are the same
as in the i.i.d. case. If the dependence is strong enough, then the bandwidth
choice is influenced by the strength of dependence, which is different when
compared to the non-noisy case. Also, central limit theorem are influenced by
the strength of dependence. On the other hand, if the density is supersmooth,
then long range dependence has no effect at all on the optimal bandwidth
choice.Comment: Published in at http://dx.doi.org/10.1214/07-EJS154 the Electronic
Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Adaptive density deconvolution with dependent inputs
In the convolution model , we give a model selection
procedure to estimate the density of the unobserved variables , when the sequence is strictly stationary but
not necessarily independent. This procedure depends on wether the density of
is super smooth or ordinary smooth. The rates of convergence of
the penalized contrast estimators are the same as in the independent framework,
and are minimax over most classes of regularity on . Our results
apply to mixing sequences, but also to many other dependent sequences. When the
errors are super smooth, the condition on the dependence coefficients is the
minimal condition of that type ensuring that the sequence
is not a long-memory process
Nonparametric regression for dependent data in the errors-in-variables problem
We consider the nonparametric estimation of the regression functions for dependent data. Suppose that the covariates are observed with additive errors in the data and we employ nonparametric deconvolution kernel techniques to estimate the regression functions in this paper. We investigate how the strength of time dependence affects the asymptotic properties of the local constant and linear estimators. We treat both short-range dependent and long-range dependent linear processes in a unified way and demonstrate that the long-range dependence (LRD) of the covariates affects the asymptotic properties of the nonparametric estimators as well as the LRD of regression errors does.local polynomial regression, errors-in-variables, deconvolution, ordinary smooth case, supersmooth case, linear processes, long-range dependence
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