131,960 research outputs found
A new adaptive response surface method for reliability analysis
Response surface method is a convenient tool to assess reliability for a wide range of structural mechanical problems. More specifically, adaptive schemes which consist in iteratively refine the experimental design close to the limit state have received much attention. However, it is generally difficult to take into account a lot of variables and to well handle approximation error. The method, proposed in this paper, addresses these points using sparse response surface and a relevant criterion for results accuracy. For this purpose, a response surface is built from an initial Latin Hypercube Sampling (LHS) where the most significant terms are chosen from statistical criteria and cross-validation method. At each step, LHS is refined in a region of interest defined with respect to an importance level on probability density in the design point. Two convergence criteria are used in the procedure: The first one concerns localization of the region and the second one the response surface quality. Finally, a bootstrap method is used to determine the influence of the response error on the estimated probability of failure. This method is applied to several examples and results are discussed
Density estimation for grouped data with application to line transect sampling
Line transect sampling is a method used to estimate wildlife populations,
with the resulting data often grouped in intervals. Estimating the density from
grouped data can be challenging. In this paper we propose a kernel density
estimator of wildlife population density for such grouped data. Our method uses
a combined cross-validation and smoothed bootstrap approach to select the
optimal bandwidth for grouped data. Our simulation study shows that with the
smoothing parameter selected with this method, the estimated density from
grouped data matches the true density more closely than with other approaches.
Using smoothed bootstrap, we also construct bias-adjusted confidence intervals
for the value of the density at the boundary. We apply the proposed method to
two grouped data sets, one from a wooden stake study where the true density is
known, and the other from a survey of kangaroos in Australia.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS307 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
A Bootstrap Lasso + Partial Ridge Method to Construct Confidence Intervals for Parameters in High-dimensional Sparse Linear Models
Constructing confidence intervals for the coefficients of high-dimensional
sparse linear models remains a challenge, mainly because of the complicated
limiting distributions of the widely used estimators, such as the lasso.
Several methods have been developed for constructing such intervals. Bootstrap
lasso+ols is notable for its technical simplicity, good interpretability, and
performance that is comparable with that of other more complicated methods.
However, bootstrap lasso+ols depends on the beta-min assumption, a theoretic
criterion that is often violated in practice. Thus, we introduce a new method,
called bootstrap lasso+partial ridge, to relax this assumption. Lasso+partial
ridge is a two-stage estimator. First, the lasso is used to select features.
Then, the partial ridge is used to refit the coefficients. Simulation results
show that bootstrap lasso+partial ridge outperforms bootstrap lasso+ols when
there exist small, but nonzero coefficients, a common situation that violates
the beta-min assumption. For such coefficients, the confidence intervals
constructed using bootstrap lasso+partial ridge have, on average, larger
coverage probabilities than those of bootstrap lasso+ols. Bootstrap
lasso+partial ridge also has, on average, shorter confidence interval
lengths than those of the de-sparsified lasso methods, regardless of whether
the linear models are misspecified. Additionally, we provide theoretical
guarantees for bootstrap lasso+partial ridge under appropriate conditions, and
implement it in the R package "HDCI.
- …