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Causal band-limited approximation and forecasting for discrete time processes
band-limited processes discrete time processes causal filters sampling low-pass filters forecasting.
2012/9/18
We study causal dynamic approximation of non-bandlimited discretetime processes by band-limited discrete time processes such that a part of the historical path of the underlying process is approximate...
Adaptive estimation in regression and complexity of approximation of random fields
regression and complexity approximation random fields
2012/9/17
In this thesis we study adaptive nonparametric regression with noise misspecifi-cation and the complexity of approximation of random fields in dependence of the dimension.
First, we consider the prob...
Scaling of Model Approximation Errors and Expected Entropy Distances
Scaling of Model Approximation Errors Expected Entropy Distances
2012/9/19
We compute the expected value of the Kullback-Leibler divergence to various fundamental statistical models with respect to canonical priors on the probability simplex. This yields information about th...
Scaling of Model Approximation Errors and Expected Entropy Distances
Scaling of Model Approximation Errors Expected Entropy Distances
2012/9/19
We compute the expected value of the Kullback-Leibler divergence to various fundamental statistical models with respect to canonical priors on the probability simplex. This yields information about th...
Asymptotic Normality of Maximum Likelihood and its Variational Approximation for Stochastic Blockmodels
network statistics stochastic blockmodeling, varia-tional methods maximum likelihood
2012/9/18
Variational methods for parameter estimation are an activere-search area, potentially offering computationally tractable heuristics with theoretical performance bounds. We build on recent work that ap...
Stochastic Approximation and Newton's Estimate of a Mixing Distribution
Stochastic approximation empirical Bayes mixture models Lyapunov functions
2011/3/23
Many statistical problems involve mixture models and the need for computationally efficient methods to estimate the mixing distribution has increased dramatically in recent years. Newton [Sankhya Ser....
Functional principal components analysis via penalized rank one approximation
Functional data analysis penalization regularization singular value decomposition
2009/9/16
Two existing approaches to functional principal components analysis (FPCA) are due to Rice and Silverman (1991) and Silverman (1996), both based on maximizing variance but introducing penalization in ...
Quantifying the cost of simultaneous non-parametric approximation of several samples
Modality non-parametric regression penalization regularization total variation
2009/9/16
We consider the standard non-parametric regression model with Gaussian errors but where the data consist of different samples. The question to be answered is whether the samples can be adequately repr...
Testing for independence: Saddlepoint approximation to associated permutation distributions
Independence tests linear rank test permutation distribution saddlepoint approximation
2009/9/16
One of the most popular class of tests for independence between two random variables is the general class of rank statistics which are invariant under permutations. This class contains Spearman's coef...