From Minimax Shrinkage Estimation to Minimax Shrinkage Prediction
نویسندگان
چکیده
منابع مشابه
Minimax Estimation via Wavelet Shrinkage
We attempt to recover an unknown function from noisy, sampled data. Using orthonormal bases of compactly supported wavelets we develop a nonlinear method which works in the wavelet domain by simple nonlinear shrinkage of the empirical wavelet coe cients. The shrinkage can be tuned to be nearly minimax over any member of a wide range of Triebeland Besov-type smoothness constraints, and asymptoti...
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The Inverse Gaussian distribution plays an important role in Reliability theory and Life testing problems. It has useful applications in a wide variety of fields such as Biology, Economics, and Medicine. It is used as an important mathematical model for the analysis of positively skewed data. The review article by Folks & Chhikara [1,2] and Seshadri [3] have proposed many interesting properties...
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For independent samples, shrinkage estimation theory has been developed systematically. Although shrinkage estimators are biased, they improve the MSE of unbiased ones. In view of this, we will develop shrinkage estimation theory and prediction for dependent samples. First, we propose a shrinkage estimator for the coefficients of AR model, which improves the MSE of the least squares estimator. ...
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We study a class of quadratic stochastic programs where the distribution of random variables has unknown parameters. A traditional approach is to estimate the parameters using a maximum likelihood estimator (MLE) and to use this as input in the optimization problem. For the unconstrained case, we show that an estimator that shrinks the MLE towards an arbitrary vector yields a uniformly better r...
متن کاملMinimax Time Series Prediction
We consider an adversarial formulation of the problem of predicting a time series with square loss. The aim is to predict an arbitrary sequence of vectors almost as well as the best smooth comparator sequence in retrospect. Our approach allows natural measures of smoothness such as the squared norm of increments. More generally, we consider a linear time series model and penalize the comparator...
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ژورنال
عنوان ژورنال: Statistical Science
سال: 2012
ISSN: 0883-4237
DOI: 10.1214/11-sts383