Evaluation of the predictive performance of biased regression estimators

Regression models are widely used in forecasting, either directly as prediction equations, or indirectly as the basis of other procedures. The predictive performance of a regression model can be adversely affected by both multicollinearity and high-leverage data points. Although biased estimation procedures have been proposed as an alternative to least squares, there has been little analysis of the predictive performance of the resulting equations. This paper discusses the predictive performance of various biased estimators, emphasizing the concept that the predictive region, as well as the strength of the multicollinearity, dictates the choice of appropriate coefficient estimators.     

解放天空

新技术能改变日渐拥挤的空中交通环境吗 ?     

三维多项式系统焦点量的计算

Fix a collection of polynomial vector fields on R3with a singularity at the origin,for every one of which the linear part at the origin has two pure imaginary and one non-zero eigenvalue. Some such systems admit a local analytic first integral,which then defines a local center manifold of the system. Conditions for existence of a first integral are given by the vanishing certain polynomial or rational functions in the coefficients of the system called focus quantities. In this paper we prove that the focus quantities have a structure analogous to that in the two-dimensional case and use it to formulate an efficient algorithm for computing them.     

Melanoma genome sequencing reveals frequent PREX2 mutations

Melanoma is notable for its metastatic propensity, lethality in the advanced setting and association with ultraviolet exposure early in life. To obtain a comprehensive genomic view of melanoma in humans, we sequenced the genomes of 25 metastatic melanomas and matched germline DNA. A wide range of point mutation rates was observed: lowest in melanomas whose primaries arose on non-ultraviolet-exposed hairless skin of the extremities (3 and 14 per megabase (Mb) of genome), intermediate in those originating from hair-bearing skin of the trunk (5-55 per Mb), and highest in a patient with a documented history of chronic sun exposure (111 per Mb). Analysis of whole-genome sequence data identified PREX2 (phosphatidylinositol-3,4,5-trisphosphate-dependent Rac exchange factor 2)--a PTEN-interacting protein and negative regulator of PTEN in breast cancer--as a significantly mutated gene with a mutation frequency of approximately 14% in an independent extension cohort of 107 human melanomas. PREX2 mutations are biologically relevant, as ectopic expression of mutant PREX2 accelerated tumour formation of immortalized human melanocytes in vivo. Thus, whole-genome sequencing of human melanoma tumours revealed genomic evidence of ultraviolet pathogenesis and discovered a new recurrently mutated gene in melanoma.