63,780 research outputs found
Adaptive density estimation under dependence
Assume that is a real valued time series admitting a common
marginal density with respect to Lebesgue's measure. Donoho {\it et al.}
(1996) propose a near-minimax method based on thresholding wavelets to estimate
on a compact set in an independent and identically distributed setting. The
aim of the present work is to extend these results to general weak dependent
contexts. Weak dependence assumptions are expressed as decreasing bounds of
covariance terms and are detailed for different examples. The threshold levels
in estimators depend on weak dependence properties of the
sequence through the constant. If these properties are
unknown, we propose cross-validation procedures to get new estimators. These
procedures are illustrated via simulations of dynamical systems and non causal
infinite moving averages. We also discuss the efficiency of our estimators with
respect to the decrease of covariances bounds
Aggregation of predictors for nonstationary sub-linear processes and online adaptive forecasting of time varying autoregressive processes
In this work, we study the problem of aggregating a finite number of
predictors for nonstationary sub-linear processes. We provide oracle
inequalities relying essentially on three ingredients: (1) a uniform bound of
the norm of the time varying sub-linear coefficients, (2) a Lipschitz
assumption on the predictors and (3) moment conditions on the noise appearing
in the linear representation. Two kinds of aggregations are considered giving
rise to different moment conditions on the noise and more or less sharp oracle
inequalities. We apply this approach for deriving an adaptive predictor for
locally stationary time varying autoregressive (TVAR) processes. It is obtained
by aggregating a finite number of well chosen predictors, each of them enjoying
an optimal minimax convergence rate under specific smoothness conditions on the
TVAR coefficients. We show that the obtained aggregated predictor achieves a
minimax rate while adapting to the unknown smoothness. To prove this result, a
lower bound is established for the minimax rate of the prediction risk for the
TVAR process. Numerical experiments complete this study. An important feature
of this approach is that the aggregated predictor can be computed recursively
and is thus applicable in an online prediction context.Comment: Published at http://dx.doi.org/10.1214/15-AOS1345 in the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Semiparametric stationarity and fractional unit roots tests based on data-driven multidimensional increment ratio statistics
In this paper, we show that the central limit theorem (CLT) satisfied by the
data-driven Multidimensional Increment Ratio (MIR) estimator of the memory
parameter d established in Bardet and Dola (2012) for d (--0.5, 0.5) can
be extended to a semiparametric class of Gaussian fractionally integrated
processes with memory parameter d (--0.5, 1.25). Since the asymptotic
variance of this CLT can be estimated, by data-driven MIR tests for the two
cases of stationarity and non-stationarity, so two tests are constructed
distinguishing the hypothesis d \textless{} 0.5 and d 0.5, as well as a
fractional unit roots test distinguishing the case d = 1 from the case d
\textless{} 1. Simulations done on numerous kinds of short-memory, long-memory
and non-stationary processes, show both the high accuracy and robustness of
this MIR estimator compared to those of usual semiparametric estimators. They
also attest of the reasonable efficiency of MIR tests compared to other usual
stationarity tests or fractional unit roots tests. Keywords: Gaussian
fractionally integrated processes; semiparametric estimators of the memory
parameter; test of long-memory; stationarity test; fractional unit roots test.Comment: arXiv admin note: substantial text overlap with arXiv:1207.245
The importance of scale in spatially varying coefficient modeling
While spatially varying coefficient (SVC) models have attracted considerable
attention in applied science, they have been criticized as being unstable. The
objective of this study is to show that capturing the "spatial scale" of each
data relationship is crucially important to make SVC modeling more stable, and
in doing so, adds flexibility. Here, the analytical properties of six SVC
models are summarized in terms of their characterization of scale. Models are
examined through a series of Monte Carlo simulation experiments to assess the
extent to which spatial scale influences model stability and the accuracy of
their SVC estimates. The following models are studied: (i) geographically
weighted regression (GWR) with a fixed distance or (ii) an adaptive distance
bandwidth (GWRa), (iii) flexible bandwidth GWR (FB-GWR) with fixed distance or
(iv) adaptive distance bandwidths (FB-GWRa), (v) eigenvector spatial filtering
(ESF), and (vi) random effects ESF (RE-ESF). Results reveal that the SVC models
designed to capture scale dependencies in local relationships (FB-GWR, FB-GWRa
and RE-ESF) most accurately estimate the simulated SVCs, where RE-ESF is the
most computationally efficient. Conversely GWR and ESF, where SVC estimates are
naively assumed to operate at the same spatial scale for each relationship,
perform poorly. Results also confirm that the adaptive bandwidth GWR models
(GWRa and FB-GWRa) are superior to their fixed bandwidth counterparts (GWR and
FB-GWR)
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