A commonly used paradigm for representing graphs is to use a vector that contains normalized frequencies of occurrence of certain motifs or sub-graphs. This vector representation can be used in a variety of applications, such as, for computing similarity between graphs. The graphlet kernel of Shervashidze et al. [32] uses induced sub-graphs of k nodes (christened as graphlets by Przulj [28]) as...

This paper presents a unified image processing and analysis framework for cortical thickness in characterizing a clinical population. The emphasis is placed on the development of data smoothing and analysis framework. The human brain cortex is a highly convoluted surface. Due to the convoluted non-Euclidean surface geometry, data smoothing and analysis on the cortex are inherently difficult. Wh...

SUMMARY The estimation of population quantiles is of great interest when one is not prepared to assume a parametric form for the u.nderlying distribution. In addition, quantiles often arise as the natural thing to estimate when the underlying distribution is skewed. The sample quantile is a popular nonparametric estimator of the corresponding population quantile. Being a function of at most two...

An important problem for tting local linear regression is the choice of the smoothing parameter. As the smoothing parameter becomes large, the estimator tends to a straight line, which is the least squares t in the ordinary linear regression setting. This property may be used to assess the adequacy of a simple linear model. Motivated by Silverman's (1981) work for testing multimodality in kerne...

Surface estimation is important in many applications. When conventional smoothing procedures, such as the running averages, local polynomial kernel smoothing procedures, and smoothing spline procedures, etc., are used for estimating jump surfaces from noisy data, jumps would be blurred at the same time when noise is removed. In recent years, new smoothing methodologies have been proposed in the...

Maximum likelihood estimation and likelihood ratio tests for nonlinear, non-Gaussian state-space models require numerical integration for likelihood calculations. Several methods, including Monte Carlo (MC) expectation maximization, MC likelihood ratios, direct MC integration, and particle Ž lter likelihoods, are inefŽ cient for the motivating problem of stage-structured population dynamics mod...

BACKGROUND Kernel smoothing method is a non-parametric or graphical method for statistical estimation. In the present study was used a kernel smoothing method for finding the death hazard rates of patients with acute myocardial infarction. METHODS By employing non-parametric regression methods, the curve estimation, may have some complexity. In this article, four indices of Epanechnikov, Biqu...

Fixed kernel density analysis with least squares cross-validation (LSCVh) choice of the smoothing parameter is currently recommended for home-range estimation. However, LSCVh has several drawbacks, including high variability, a tendency to undersmooth data, and multiple local minima in the LSCVh function. An alternative to LSCVh is likelihood cross-validation (CVh). We used computer simulations...

of the Thesis High Performance Kernel Smoothing Library For Biomedical Imaging by Haofu Liao Master of Science in Electrical and Computer Engineering Northeastern University, May 2015 Dr. Deniz Erdogmus, Adviser The estimation of probability density and probability density derivatives has full potential for applications. In biomedical imaging, the estimation of the first and second derivatives ...

This article presents the first comprehensive studies on the local and global inferences for the smoothing spline estimate in a unified asymptotic framework. The novel functional Bahadur representation is developed as the theoretical foundation of this article, and is also of independent interest. Based on that, we establish four interconnected inference procedures: (i) Point-wise Confidence In...