Minimax Rates of Density Estimators for Continuous Time Processes
نویسنده
چکیده
In this paper we investigate the problem of estimating density for continuous time processes when continuous sampling is available. Consider an R-valued stochastic process (Xt, t ∈ R) such that each Xt has the same distribution, say μ, with unknown density, say f . In the following we construct the kernel density estimator fT based upon the data (Xt, 0 ≤ t ≤ T ) and study its asymptotic behaviour as T tends to infinity.
منابع مشابه
On the Minimax Optimality of Block Thresholded Wavelets Estimators for ?-Mixing Process
We propose a wavelet based regression function estimator for the estimation of the regression function for a sequence of ?-missing random variables with a common one-dimensional probability density function. Some asymptotic properties of the proposed estimator based on block thresholding are investigated. It is found that the estimators achieve optimal minimax convergence rates over large class...
متن کاملTruncated Linear Minimax Estimator of a Power of the Scale Parameter in a Lower- Bounded Parameter Space
Minimax estimation problems with restricted parameter space reached increasing interest within the last two decades Some authors derived minimax and admissible estimators of bounded parameters under squared error loss and scale invariant squared error loss In some truncated estimation problems the most natural estimator to be considered is the truncated version of a classic...
متن کاملOptimal rates for k-NN density and mode estimation
We present two related contributions of independent interest: (1) high-probability finite sample rates for k-NN density estimation, and (2) practical mode estimators – based on k-NN – which attain minimax-optimal rates under surprisingly general distributional conditions.
متن کاملOptimal rates for plug-in estimators of density level sets
In the context of density level set estimation, we study the convergence of general plug-in methods under two main assumptions on the density for a given level λ. More precisely, it is assumed that the density (i) is smooth in a neighborhood of λ and (ii) has γ -exponent at level λ. Condition (i) ensures that the density can be estimated at a standard nonparametric rate and condition (ii) is si...
متن کاملFast rates for plug-in estimators of density level sets
In the context of density level set estimation, we study the convergence of general plug-in methods under two main assumptions on the density for a given level λ. More precisely, it is assumed that the density (i) is smooth in a neighborhood of λ and (ii) has γ-exponent at level λ. Condition (i) ensures that the density can be estimated at a standard nonparametric rate and condition (ii) is sim...
متن کامل