Nonparametric estimation of a point-spread function in multivariate problems

The removal of blur from a signal, in the presence of noise, is readily accomplished if the blur can be described in precise mathematical terms. However, there is growing interest in problems where the extent of blur is known only approximately, for example in terms of a blur function which depends on unknown parameters that must be computed from data. More challenging still is the case where no parametric assumptions are made about the blur function. There has been a limited amount of work in this setting, but it invariably relies on iterative methods, sometimes under assumptions that are mathematically convenient but physically unrealistic (e.g., that the operator defined by the blur function has an integrable inverse). In this paper we suggest a direct, noniterative approach to nonparametric, blind restoration of a signal. Our method is based on a new, ridge-based method for deconvolution, and requires only mild restrictions on the blur function. We show that the convergence rate of the method is close to optimal, from some viewpoints, and demonstrate its practical performance by applying it to real images.Comment: Published in at http://dx.doi.org/10.1214/009053606000001442 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Distribution-free cumulative sum control charts using bootstrap-based control limits

This paper deals with phase II, univariate, statistical process control when a set of in-control data is available, and when both the in-control and out-of-control distributions of the process are unknown. Existing process control techniques typically require substantial knowledge about the in-control and out-of-control distributions of the process, which is often difficult to obtain in practice. We propose (a) using a sequence of control limits for the cumulative sum (CUSUM) control charts, where the control limits are determined by the conditional distribution of the CUSUM statistic given the last time it was zero, and (b) estimating the control limits by bootstrap. Traditionally, the CUSUM control chart uses a single control limit, which is obtained under the assumption that the in-control and out-of-control distributions of the process are Normal. When the normality assumption is not valid, which is often true in applications, the actual in-control average run length, defined to be the expected time duration before the control chart signals a process change, is quite different from the nominal in-control average run length. This limitation is mostly eliminated in the proposed procedure, which is distribution-free and robust against different choices of the in-control and out-of-control distributions.Comment: Published in at http://dx.doi.org/10.1214/08-AOAS197 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Image Denoising by a Local Clustering Framework

Images often contain noise due to imperfections in various image acquisition techniques. Noise should be removed from images so that the details of image objects (e.g., blood vessels, inner foldings, or tumors in the human brain) can be clearly seen, and the subsequent image analyses are reliable. With broad usage of images in many disciplines—for example, medical science—image denoising has become an important research area. In the literature, there are many different types of image denoising techniques, most of which aim to preserve image features, such as edges and edge structures, by estimating them explicitly or implicitly. Techniques based on explicit edge detection usually require certain assumptions on the smoothness of the image intensity surface and the edge curves which are often invalid especially when the image resolution is low. Methods that are based on implicit edge detection often use multiresolution smoothing, weighted local smoothing, and so forth. For such methods, the task of determining the correct image resolution or choosing a reasonable weight function is challenging. If the edge structure of an image is complicated or the image has many details, then these methods would blur such details. This article presents a novel image denoising framework based on local clustering of image intensities and adaptive smoothing. The new denoising method can preserve complicated edge structures well even if the image resolution is low. Theoretical properties and numerical studies show that it works well in various applications

On Jump Structure Consideration in One-Dimensional Nonparametric Regression

1 online resource (PDF, 20 pages

Identification of shared biological features in four different lung cell lines infected with SARS-CoV-2 virus through RNA-seq analysis

The COVID-19 pandemic caused by SARS-CoV-2 has resulted in millions of confirmed cases and deaths worldwide. Understanding the biological mechanisms of SARS-CoV-2 infection is crucial for the development of effective therapies. This study conducts differential expression (DE) analysis, pathway analysis, and differential network (DN) analysis on RNA-seq data of four lung cell lines, NHBE, A549, A549.ACE2, and Calu3, to identify their common and unique biological features in response to SARS-CoV-2 infection. DE analysis shows that cell line A549.ACE2 has the highest number of DE genes, while cell line NHBE has the lowest. Among the DE genes identified for the four cell lines, 12 genes are overlapped, associated with various health conditions. The most significant signaling pathways varied among the four cell lines. Only one pathway, “cytokine-cytokine receptor interaction”, is found to be significant among all four cell lines and is related to inflammation and immune response. The DN analysis reveals considerable variation in the differential connectivity of the most significant pathway shared among the four lung cell lines. These findings help to elucidate the mechanisms of SARS-CoV-2 infection and potential therapeutic targets

On Nonparametric Profile Monitoring

Quality of a process is often characterized by the functional relationship between a response and one or more predictors. Profile monitoring is for checking the stability of this relationship over time. In the literature, most existing control charts are for monitoring parametric profiles, and they assume that within-profile observations are independent of each other, which is often invalid. This talk presents some of our recent research on nonparametric profile monitoring when within-profile data are correlated. We will also briefly describe the problems of online image monitoring and dynamic disease screening that are closely related to profile monitoring.Non UBCUnreviewedAuthor affiliation: University of FloridaFacult

Estimation Of The Number Of Jumps Of The Jump Regression Functions

This paper suggests an estimator of the number of jumps of the jump regression functions. The estimator is based on the difference between right and left onesided kernel smoothers. It is proved to be a.s. consistent. Some results about its rate of convergence are also provided. 1 Introduction Regression analysis is one of the most mature branches in statistics. For a long time, however, its main theory is about the continuous regression functions (c. f. Draper and Smith (1981), Hardle (1990), etc. ). Recently, discontinuous regression functions have gotten more and more attention from statisticians all over the world. This, we think, is mainly due to their great application background (e. g. Wahba (1986) used the discontinuous regression model to explore the equi-temperature surfaces of the high sky and the deep ocean). By now, we have found that jump regression functions are discussed in two statistical fields. One is the change-point field, in which statisticians discuss the jump r..

The local piecewisely linear kernel smoothing procedure for fitting jump regression surfaces

It is known that a surface fitted by conventional local smoothing procedures is not statistically consistent at the jump locations of the true regression surface. In this paper, a procedure is suggested for modifying conventional local smoothing procedures such that the modified procedures can fit the surface with jumps preserved automatically. Taking the local linear kernel smoothing procedure as an example, in a neighborhood of a given point, we fit a bivariate piecewisely linear function with possible jumps along the boundaries of four quadrants. The fitted function provides four estimators of the surface at the given point, which are constructed from observations in the four quadrants, respectively. When the difference among the four estimators is smaller than a threshold value, the given point is most likely a continuous point and the surface at that point is then estimated by the average of the four estimators. When the difference is larger than the threshold value, the given point is likely a jump point and at least one of the four estimators estimates the surface well under some regularity conditions. By comparing the weighted residual sums of squares of the four estimators, the best one is selected to define the surface estimator at the given point. Like most conventional estimators, the current surface estimator has an explicit mathematical formula. Therefore it is easy to compute and convenient to use. It can be applied directly to image reconstruction problems and other jump surface estimation problems including mine surface estimation in geology and equi-temperature surface estimation in meteorology and oceanography

A jump-preserving curve fitting procedure based on local piecewise-linear kernel estimation

It is known that the fitted regression function based on conventional local smoothing pro-cedures is not statistically consistent at jump positions of the true regression function. In this article, a curve-fitting procedure based on local piecewise-linear kernel estimation is suggested. In a neighborhood of a given point, a piecewise-linear function with a possible jump at the given point is fitted by the weighted least squares procedure with the weights determined by a kernel function. The fitted value of the regression function at this point is then defined by one of the two estimators provided by the two fitted lines (the left and right lines) with the smaller value of the weighted residual sum of squares. It is proved that the fitted curve by this procedure is consistent in the entire design space. In other words, this procedure is jump-preserving. Several numerical examples are presented to evaluate its performance in small-to-moderate sample size cases. Key Words: Jump-preserving curve fitting; Local piecewise-linear kernel estimation; Local smoothing; Nonparametric regression; Strong consistency