Resampling

About: Resampling is a research topic. Over the lifetime, 5428 publications have been published within this topic receiving 242291 citations.

Smooth motion vector resampling for standard compatible video post-processing

Abstract: This paper presents a smooth motion vector resampling method that operates on a given motion vector field for video coding applications such as resolution change in transcoding or concealment of lost motion vectors. We formulate the motion resampling problem as an optimization problem, where the proposed algorithm obtains the optimal solution by minimizing a smoothness criteria imposed between adjacent motion vectors. The problem is formulated in the most general case, which enables us to explain some other resampling methods such as motion vector averaging, or linear interpolation as special cases. The simulation results show that the proposed algorithm can efficiently improve the visual quality of the video.

Statistical tests of molecular phylogenies.

Abstract: Publisher Summary This chapter provides a summary of methods for testing the significance of inferred phylogenies. In terms of parsimony a nucleotide site is informative (useful) for choosing among the three trees only if it is in the same state in two of the four species and in another state in the other two species. Under the assumption of rate constancy, an informative site has a higher probability of supporting the true tree and a lower probability of supporting each of the two other trees. Instead of testing the significance of an inferred phylogeny, it is simpler to test the significance of estimated intemodal distances. Like the jackknife, the bootstrap is a method of resampling the data under study to infer the variability of the estimate. This method was introduced into phylogenetic studies by Felsenstein. It is not a tree-making method but a statistical method that can be used to evaluate the confidence level of a phylogenetic estimate obtained from a data set by a tree-making method.

Minimax optimality of permutation tests

Abstract: Permutation tests are widely used in statistics, providing a finite-sample guarantee on the type I error rate whenever the distribution of the samples under the null hypothesis is invariant to some rearrangement. Despite its increasing popularity and empirical success, theoretical properties of the permutation test, especially its power, have not been fully explored beyond simple cases. In this paper, we attempt to fill this gap by presenting a general non-asymptotic framework for analyzing the power of the permutation test. The utility of our proposed framework is illustrated in the context of two-sample and independence testing under both discrete and continuous settings. In each setting, we introduce permutation tests based on U-statistics and study their minimax performance. We also develop exponential concentration bounds for permuted U-statistics based on a novel coupling idea, which may be of independent interest. Building on these exponential bounds, we introduce permutation tests which are adaptive to unknown smoothness parameters without losing much power. The proposed framework is further illustrated using more sophisticated test statistics including weighted U-statistics for multinomial testing and Gaussian kernel-based statistics for density testing. Finally, we provide some simulation results that further justify the permutation approach.