4,478 research outputs found
A partial oracle for uniformity statistics
This paper investigates the problem of testing implementations of uniformity statistics. In this paper we used Metamorphic Testing to address the oracle problem, of checking the output of one or more test executions, for uniformity statistics. We defined a partial oracle that uses regression analysis (a Regression Model based Metamorphic Relation).
We investigated the effectiveness of our partial oracle. We found that the technique can achieve mutation scores ranging from 77.78% to 100%, and tends towards higher mutation scores in this range. These results are promising, and suggest that the Regression Model based Metamorphic Relation approach is a viable method of alleviating the oracle problem in implementations of uniformity statistics, and potentially other classes of statistics e.g. correlation statistics
Inference for High-Dimensional Sparse Econometric Models
This article is about estimation and inference methods for high dimensional
sparse (HDS) regression models in econometrics. High dimensional sparse models
arise in situations where many regressors (or series terms) are available and
the regression function is well-approximated by a parsimonious, yet unknown set
of regressors. The latter condition makes it possible to estimate the entire
regression function effectively by searching for approximately the right set of
regressors. We discuss methods for identifying this set of regressors and
estimating their coefficients based on -penalization and describe key
theoretical results. In order to capture realistic practical situations, we
expressly allow for imperfect selection of regressors and study the impact of
this imperfect selection on estimation and inference results. We focus the main
part of the article on the use of HDS models and methods in the instrumental
variables model and the partially linear model. We present a set of novel
inference results for these models and illustrate their use with applications
to returns to schooling and growth regression
Covariance regularization by thresholding
This paper considers regularizing a covariance matrix of variables
estimated from observations, by hard thresholding. We show that the
thresholded estimate is consistent in the operator norm as long as the true
covariance matrix is sparse in a suitable sense, the variables are Gaussian or
sub-Gaussian, and , and obtain explicit rates. The results are
uniform over families of covariance matrices which satisfy a fairly natural
notion of sparsity. We discuss an intuitive resampling scheme for threshold
selection and prove a general cross-validation result that justifies this
approach. We also compare thresholding to other covariance estimators in
simulations and on an example from climate data.Comment: Published in at http://dx.doi.org/10.1214/08-AOS600 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Pairwise Fused Lasso
In the last decade several estimators have been proposed that enforce the grouping property. A regularized estimate exhibits the grouping property if it selects groups of highly correlated predictor rather than selecting one representative. The pairwise fused lasso is related to fusion methods but does not assume that predictors have to be ordered. By penalizing parameters and differences between pairs of coefficients it selects predictors and enforces the grouping property. Two methods how to obtain estimates are given. The first is based on LARS and works for the linear model, the second is based on quadratic approximations and works in the more general case of generalized linear models. The method is evaluated in simulation studies and applied to real data sets
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