D-optimal Design for Polynomial Regression: Choice of Degree and Robustness

In this paper we show that for D-optimal design, departures from the design are much less important than a depar-ture from a model. As a consequence, we propose, based on D-optimality, a rule for choosing the regression degree. We also study different types of departures from the model to define a new class of D-optimal designs, which is robust and more efficient than the uniform oneD-optimal design; regression degree; polynomial regression

Graphical Methods of Structural Relations between Variables and their Application to Russian Regions (Part Two)

The second part of the article continues studying the structure of a set of variables. It consists of two pieces: (1) de-scription of a modification of Dempster covariance selection algorithm based on its combination with that of tree dependence structures construction, simulation results, methods of representation of the graphical model on the plane, and different methods of results interpretation; (2) application of the method to studying and comparing Russian regionscovariance selection algorithm; Russian regions

Graphical Models of Structural Relations between Variables and their Application to Russian Regions (Part One)

The article deals with variables structure. A summary of dependence trees and graphical models with a special em-phasis on Dempster covariance selection method in part one is followed in the second part by a description of a modi-fication of the latter developed by the author. An application of the obtained results to comparative study of Russian regions will be also given in part twocovariance selection algorithm; Russian regions

Structural Properties of Central Galaxies in Groups and Clusters

Using a representative sample of 911 central galaxies (CENs) from the SDSS DR4 group catalogue, we study how the structure of the most massive members in groups and clusters depend on (1) galaxy stellar mass (Mstar), (2) dark matter halo mass of the host group (Mhalo), and (3) their halo-centric position. We establish and thoroughly test a GALFIT-based pipeline to fit 2D Sersic models to SDSS data. We find that the fitting results are most sensitive to the background sky level determination and strongly recommend using the SDSS global value. We find that uncertainties in the background translate into a strong covariance between the total magnitude, half-light size (r50), and Sersic index (n), especially for bright/massive galaxies. We find that n depends strongly on Mstar for CENs, but only weakly or not at all on Mhalo. Less (more) massive CENs tend to be disk (spheroid)-like over the full Mhalo range. Likewise, there is a clear r50-Mstar relation for CENs, with separate slopes for disks and spheroids. When comparing CENs with satellite galaxies (SATs), we find that low mass (<10e10.75 Msun/h^2) SATs have larger median n than CENs of similar Mstar. Low mass, late-type SATs have moderately smaller r50 than late-type CENs of the same Mstar. However, we find no size differences between spheroid-like CENs and SATs, and no structural differences between CENs and SATs matched in both mass and colour. The similarity of massive SATs and CENs shows that this distinction has no significant impact on the structure of spheroids. We conclude that Mstar is the most fundamental property determining the basic structure of a galaxy. The lack of a clear n-Mhalo relation rules out a distinct group mass for producing spheroids, and the responsible morphological transformation processes must occur at the centres of groups spanning a wide range of masses. (abridged)Comment: 22 pages, 14 figures, submitted to MNRA

Polygenic Risk Scores for Prediction of Breast Cancer and Breast Cancer Subtypes

Stratification of women according to their risk of breast cancer based on polygenic risk scores (PRSs) could improve screening and prevention strategies. Our aim was to develop PRSs, optimized for prediction of estrogen receptor (ER)-specific disease, from the largest available genome-wide association dataset and to empirically validate the PRSs in prospective studies. The development dataset comprised 94,075 case subjects and 75,017 control subjects of European ancestry from 69 studies, divided into training and validation sets. Samples were genotyped using genome-wide arrays, and single-nucleotide polymorphisms (SNPs) were selected by stepwise regression or lasso penalized regression. The best performing PRSs were validated in an independent test set comprising 11,428 case subjects and 18,323 control subjects from 10 prospective studies and 190,040 women from UK Biobank (3,215 incident breast cancers). For the best PRSs (313 SNPs), the odds ratio for overall disease per 1 standard deviation in ten prospective studies was 1.61 (95%CI: 1.57-1.65) with area under receiver-operator curve (AUC) = 0.630 (95%CI: 0.628-0.651). The lifetime risk of overall breast cancer in the top centile of the PRSs was 32.6%. Compared with women in the middle quintile, those in the highest 1% of risk had 4.37- and 2.78-fold risks, and those in the lowest 1% of risk had 0.16- and 0.27-fold risks, of developing ER-positive and ER-negative disease, respectively. Goodness-of-fit tests indicated that this PRS was well calibrated and predicts disease risk accurately in the tails of the distribution. This PRS is a powerful and reliable predictor of breast cancer risk that may improve breast cancer prevention programs.NovartisEli Lilly and CompanyAstraZenecaAbbViePfizer UKCelgeneEisaiGenentechMerck Sharp and DohmeRocheCancer Research UKGovernment of CanadaArray BioPharmaGenome CanadaNational Institutes of HealthEuropean CommissionMinistère de l'Économie, de l’Innovation et des Exportations du QuébecSeventh Framework ProgrammeCanadian Institutes of Health Researc

Optimasi Portofolio Resiko Menggunakan Model Markowitz MVO Dikaitkan dengan Keterbatasan Manusia dalam Memprediksi Masa Depan dalam Perspektif Al-Qur`an

Risk portfolio on modern finance has become increasingly technical, requiring the use of sophisticated mathematical tools in both research and practice. Since companies cannot insure themselves completely against risk, as human incompetence in predicting the future precisely that written in Al-Quran surah Luqman verse 34, they have to manage it to yield an optimal portfolio. The objective here is to minimize the variance among all portfolios, or alternatively, to maximize expected return among all portfolios that has at least a certain expected return. Furthermore, this study focuses on optimizing risk portfolio so called Markowitz MVO (Mean-Variance Optimization). Some theoretical frameworks for analysis are arithmetic mean, geometric mean, variance, covariance, linear programming, and quadratic programming. Moreover, finding a minimum variance portfolio produces a convex quadratic programming, that is minimizing the objective function ðð¥with constraintsð ð 𥠥 ðandð´ð¥ = ð. The outcome of this research is the solution of optimal risk portofolio in some investments that could be finished smoothly using MATLAB R2007b software together with its graphic analysis