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Anti-Concentration and Honest Adaptive Confidence Bands
Anti-Concentration Honest Adaptive Confidence Bands
2013/4/28
Modern construction of uniform confidence bands for nonparametric densities (and other functions) often relies on the Smirnov-Bickel-Rosenblatt (SBR) condition; see e.g. Gine and Nickl (2010). This co...
Variance estimation and asymptotic confidence bands for the mean estimator of sampled functional data with high entropy unequal probability sampling designs
covariance function finite population Hajek approximation Horvitz-Thompso estimator Kullback-Leibler divergence rejective sampling unequal probability sampling without replacement
2012/11/23
For fixed size sampling designs with high entropy it is well known that the variance of the Horvitz-Thompson estimator can be approximated by the H\'ajek formula. The interest of this asymptotic varia...
Adaptive confidence bands in the nonparametric fixed design regression model
Adaptive confidence bands nonparametric fixed design regression model
2012/9/19
In this note, we consider the problem of existence of adaptive confidence bands in the fixed design regression model, adapting ideas in Hoffmann and Nickl [10] to the present case. In the course of th...
Confidence bands for Horvitz-Thompson estimators using sampled noisy functional data
CLT functional data local polynomial smoothing maximal inequalities space of continuous functions suprema of Gaussian processes survey sampling weighted crossvalidation
2011/6/17
When collections of functional data are too large to be exhaustively observed, survey
sampling techniques provide an e ective way to estimate global quantities such as
the population mean function. ...
Concentration Inequalities and Confidence Bands for Needlet Density Estimators on Compact Homogeneous Manifolds
Concentration Inequalities Confidence Bands Density Estimators
2011/3/21
Let $X_1,...,X_n$ be a random sample from some unknown probability density $f$ defined on a compact homogeneous manifold $\mathbf M$ of dimension $d \ge 1$. Consider a 'needlet frame' $\{\phi_{j \eta}...
Confidence bands in density estimation
Adaptive estimation limit theorem density estimation extremes Gaussian processes wavelet estimators kernel estimators
2010/3/11
we construct adaptive confidence bands that are honest for all densities
in a “generic” subset of the union of t-H¨older balls, 0 < t r,
where r is a fixed but arbitrary integer. The exceptional (...
On Confidence Bands for Time Series Problems in the Time and Frequency Domains
Confidence Bands Time Series Problems Frequency Domains
2009/9/17
On Confidence Bands for Time Series Problems in the Time and Frequency Domains。
Confidence bands for densities, logarithmic point of view
Density Kernel estimator Asymptotic logarithmic level Asymptotic almost sure condence regions Moderate deviations principles
2009/6/12
Confidence bands for densities, logarithmic point of view.
Confidence bands in nonparametric time series regression
Long-range dependence model validation moderate deviation nonlinear time series nonparametric regression short-range dependence
2010/4/30
We consider nonparametric estimation of mean regression and
conditional variance (or volatility) functions in nonlinear stochastic
regression models. Simultaneous confidence bands are constructed
a...
We show that there do not exist adaptive confidence bands for
curve estimation except under very restrictive assumptions. We propose
instead to construct adaptive bands that cover a surrogate functi...