Nonparametric Inference via Bootstrapping the Debiased Estimator

In this paper, we propose to construct confidence bands by bootstrapping the debiased kernel density estimator (for density estimation) and the debiased local polynomial regression estimator (for regression analysis). The idea of using a debiased estimator was recently employed by Calonico et al. (2018b) to construct a confidence interval of the density function (and regression function) at a given point by explicitly estimating stochastic variations. We extend their ideas of using the debiased estimator and further propose a bootstrap approach for constructing simultaneous confidence bands. This modified method has an advantage that we can easily choose the smoothing bandwidth from conventional bandwidth selectors and the confidence band will be asymptotically valid. We prove the validity of the bootstrap confidence band and generalize it to density level sets and inverse regression problems. Simulation studies confirm the validity of the proposed confidence bands/sets. We apply our approach to an Astronomy dataset to show its applicabilityComment: Accepted to the Electronic Journal of Statistics. 64 pages, 6 tables, 11 figure

Enhancing Image Quality of Photographs Taken by Portable Devices by Matching Images to High Quality Reference Images Using Machine Learning and Camera Orientation and Other Image Metadata

This publication describes systems and techniques to enhance an image quality of a photograph taken by a portable device using a collection of images to find a replacement object. Although the intrinsic image quality of photographs taken by portable devices, such as a smartphone, continues to improve, many pictures still lack detail or have blurriness. Consequently, a photograph, or “original image,” can include an object having a poor quality, such as blurriness or an inaccurate reproduction of a texture. To enhance the original image, a machine-learned model detects in the original image the object having poor quality. A collection of images is searched to find a reference image having another version of the object with a superior quality. Metadata for the images can be used to find a matching reference image. Metadata can include positioning, distance to subject, tilt angle, and so forth. An object enhancement module replaces at least a portion of the poor-quality object in the original image with the superior quality object from the reference image to produce an enhanced image. The image collection with reference images can be stored in the cloud or locally on the portable device. In these manners, the image quality of a photograph taken by a portable device can be enhanced

New Constructions of Zero-Correlation Zone Sequences

In this paper, we propose three classes of systematic approaches for constructing zero correlation zone (ZCZ) sequence families. In most cases, these approaches are capable of generating sequence families that achieve the upper bounds on the family size ($K$) and the ZCZ width ($T$) for a given sequence period ($N$). Our approaches can produce various binary and polyphase ZCZ families with desired parameters $(N,K,T)$ and alphabet size. They also provide additional tradeoffs amongst the above four system parameters and are less constrained by the alphabet size. Furthermore, the constructed families have nested-like property that can be either decomposed or combined to constitute smaller or larger ZCZ sequence sets. We make detailed comparisons with related works and present some extended properties. For each approach, we provide examples to numerically illustrate the proposed construction procedure.Comment: 37 pages, submitted to IEEE Transactions on Information Theor

Deepen the understanding for school bully-victims : the reasons for bully-victims' role formations, role transitions, and role terminations

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