Open Access. Powered by Scholars. Published by Universities.®

Digital Commons Network

Open Access. Powered by Scholars. Published by Universities.®

Articles 1 - 5 of 5

Full-Text Articles in Entire DC Network

Information-Theoretic Determination Of Minimax Rates Of Convergence, Yuhong Yang, Andrew Barron Mar 1997

Information-Theoretic Determination Of Minimax Rates Of Convergence, Yuhong Yang, Andrew Barron

Statistics Preprints

We present some general results determining minimax bounds on statistical risk for density estimation based on certain information-theoretic considerations. These bounds depend only on metric entropy conditions and are used to identify the minimax rates of convergence.


The Modified Sudden Death Test: Planning Life Tests With A Limited Number Of Test Positions, Francis G. Pascual, William Q. Meeker Jan 1997

The Modified Sudden Death Test: Planning Life Tests With A Limited Number Of Test Positions, Francis G. Pascual, William Q. Meeker

Statistics Preprints

We present modified sudden death test (MSDT) plans to address the problem of limited testing positions in life tests. A single MSDT involves testing k specimens simultaneously until the rth failure. The traditional sudden death test (SDT) is a special case when r=1. The complete MSDT plan consists of g single MSDTs run in sequence. When r>1, there can be up to r−1 idle test positions at any time. We propose testing “standby” specimens in the idle positions and use simulation to gage the improvement over the basic MSDT plan. We evaluate test plans with respect to ...


Estimating Fatigue Curves With The Random Fatigue-Limit Mode, Francis G. Pascual, William Q. Meeker Jan 1997

Estimating Fatigue Curves With The Random Fatigue-Limit Mode, Francis G. Pascual, William Q. Meeker

Statistics Preprints

In a fatigue-limit model, units tested below the fatigue limit (also known as the threshold stress) theoretically will never fail. This article uses a random fatigue-limit model to describe (a) the dependence of fatigue life on the stress level, (b) the variation in fatigue life, and (c) the unit-tounit variation in the fatigue limit.We fit the model to actual fatigue datasets by maximum likelihood methods and study the fits under different distributional assumptions. Small quantiles of the life distribution are often of interest to designers. Lower confidence bounds based on likelihood ratio methods are obtained for such quantiles. To ...


Nonparametric Regression With Dependent Errors, Yuhong Yang Jan 1997

Nonparametric Regression With Dependent Errors, Yuhong Yang

Statistics Preprints

We study minimax rates of convergence for nonparametric regression under a random design with dependent errors. It is shown that when the errors are independent of the explanatory variables, long-range dependence among the errors does not necessarily hurt regression estimation, which at first glance contradicts with earlier results by Hall and Hart, Wang, and Johnstone and Silverman under a fixed design. In fact we show that, in general, the minimax rate of convergence under the square L2 loss is simply at the worse of two quantities: one determined by the massiveness of the class alone and the other by the ...


Model Selection For Nonparametric Regression, Yuhong Yang Jan 1997

Model Selection For Nonparametric Regression, Yuhong Yang

Statistics Preprints

Risk bounds are derived for regression estimation based on model selection over an unrestricted number of models. While a large list of models provides more flexibility, significant selection bias may occur with model selection criteria like AIC. We incorporate a model complexity penalty term in AIC to handle selection bias. Resulting estimators are shown to achieve a trade-off among approximation error, estimation error and model complexity without prior knowledge about the true regression function. We demonstrate the adaptability of these estimators over full and sparse approximation function classes with different smoothness. For high-dimensional function estimation by tensor product splines we ...