Adaptive Density Estimation on the Circle by Nearly-Tight Frames

This work is concerned with the study of asymptotic properties of nonparametric density estimates in the framework of circular data. The estimation procedure here applied is based on wavelet thresholding methods: the wavelets used are the so-called Mexican needlets, which describe a nearly-tight frame on the circle. We study the asymptotic behaviour of the $L^{2}$-risk function for these estimates, in particular its adaptivity, proving that its rate of convergence is nearly optimal.Comment: 30 pages, 3 figure

SiteSeek: Post-translational modification analysis using adaptive locality-effective kernel methods and new profiles

<p>Abstract</p> <p>Background</p> <p>Post-translational modifications have a substantial influence on the structure and functions of protein. Post-translational phosphorylation is one of the most common modification that occur in intracellular proteins. Accurate prediction of protein phosphorylation sites is of great importance for the understanding of diverse cellular signalling processes in both the human body and in animals. In this study, we propose a new machine learning based protein phosphorylation site predictor, SiteSeek. SiteSeek is trained using a novel compact evolutionary and hydrophobicity profile to detect possible protein phosphorylation sites for a target sequence. The newly proposed method proves to be more accurate and exhibits a much stable predictive performance than currently existing phosphorylation site predictors.</p> <p>Results</p> <p>The performance of the proposed model was compared to nine existing different machine learning models and four widely known phosphorylation site predictors with the newly proposed PS-Benchmark_1 dataset to contrast their accuracy, sensitivity, specificity and correlation coefficient. SiteSeek showed better predictive performance with 86.6% accuracy, 83.8% sensitivity, 92.5% specificity and 0.77 correlation-coefficient on the four main kinase families (CDK, CK2, PKA, and PKC).</p> <p>Conclusion</p> <p>Our newly proposed methods used in SiteSeek were shown to be useful for the identification of protein phosphorylation sites as it performed much better than widely known predictors on the newly built PS-Benchmark_1 dataset.</p

Spectral Density Regression for Bivariate Extremes

We introduce a density regression model for the spectral density of a bivariate extreme value distribution, that allows us to assess how extremal dependence can change over a covariate. Inference is performed through a double kernel estimator, which can be seen as an extension of the Nadaraya–Watson estimator where the usual scalar responses are replaced by mean constrained densities on the unit interval. Numerical experiments with the methods illustrate their resilience in a variety of contexts of practical interest. An extreme temperature dataset is used to illustrate our methods