Mathematics – Statistics Theory
Scientific paper
2011-12-20
Mathematics
Statistics Theory
Scientific paper
Minimax rates of convergence for the problem of estimation in nonparametric models are often determined by strategically chosen submodels that capture the difficulty of the whole problem. The submodels are constructed to have separation properties, such as those required by Assouad's lemma, while still satisfying the constraints of the model. For the estimation of submodels, even more constraints are imported, which can make the calculation of minimax rates substantially more difficult. This paper illustrates the difficulty for a density estimation problem by means of a normal location mixture model, which actually has the same minimax rates as for a larger family of analytic densities. The analysis exploits a stability property of a two-parameter family of functions under convolution with the standard normal followed by Fourier transformation.
No associations
LandOfFree
Minimax Bounds for Estimation of Normal Mixtures does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Minimax Bounds for Estimation of Normal Mixtures, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Minimax Bounds for Estimation of Normal Mixtures will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-54597