Densities, spectral densities and modality

This paper considers the problem of specifying a simple approximating density function for a given data set (x_1,...,x_n). Simplicity is measured by the number of modes but several different definitions of approximation are introduced. The taut string method is used to control the numbers of modes and to produce candidate approximating densities. Refinements are introduced that improve the local adaptivity of the procedures and the method is extended to spectral densities.Comment: Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Statistics (http://www.imstat.org/aos/) at http://dx.doi.org/10.1214/00905360400000036

Confidence sets and non-parametric regression

--Nonparametric regression , shape regularization , confidence bounds

Nonparametric Regression on a Graph

The 'Signal plus Noise' model for nonparametric regression can be extended to the case of observations taken at the vertices of a graph. This model includes many familiar regression problems. This article discusses the use of the edges of a graph to measure roughness in penalized regression. Distance between estimate and observation is measured at every vertex in the L2 norm, and roughness is penalized on every edge in the L1 norm. Thus the ideas of total variation penalization can be extended to a graph. The resulting minimization problem presents special computational challenges, so we describe a new and fast algorithm and demonstrate its use with examples. The examples include image analysis, a simulation applicable to discrete spatial variation, and classification. In our examples, penalized regression improves upon kernel smoothing in terms of identifying local extreme values on planar graphs. In all examples we use fully automatic procedures for setting the smoothing parameters. Supplemental materials are available online. © 2011 American Statistical Association

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

Impacts of the Tropical Pacific/Indian Oceans on the Seasonal Cycle of the West African Monsoon

The current consensus is that drought has developed in the Sahel during the second half of the twentieth century as a result of remote effects of oceanic anomalies amplified by local land–atmosphere interactions. This paper focuses on the impacts of oceanic anomalies upon West African climate and specifically aims to identify those from SST anomalies in the Pacific/Indian Oceans during spring and summer seasons, when they were significant. Idealized sensitivity experiments are performed with four atmospheric general circulation models (AGCMs). The prescribed SST patterns used in the AGCMs are based on the leading mode of covariability between SST anomalies over the Pacific/Indian Oceans and summer rainfall over West Africa. The results show that such oceanic anomalies in the Pacific/Indian Ocean lead to a northward shift of an anomalous dry belt from the Gulf of Guinea to the Sahel as the season advances. In the Sahel, the magnitude of rainfall anomalies is comparable to that obtained by other authors using SST anomalies confined to the proximity of the Atlantic Ocean. The mechanism connecting the Pacific/Indian SST anomalies with West African rainfall has a strong seasonal cycle. In spring (May and June), anomalous subsidence develops over both the Maritime Continent and the equatorial Atlantic in response to the enhanced equatorial heating. Precipitation increases over continental West Africa in association with stronger zonal convergence of moisture. In addition, precipitation decreases over the Gulf of Guinea. During the monsoon peak (July and August), the SST anomalies move westward over the equatorial Pacific and the two regions where subsidence occurred earlier in the seasons merge over West Africa. The monsoon weakens and rainfall decreases over the Sahel, especially in August.Peer reviewe

Search for heavy resonances decaying to two Higgs bosons in final states containing four b quarks

A search is presented for narrow heavy resonances X decaying into pairs of Higgs bosons (H) in proton-proton collisions collected by the CMS experiment at the LHC at root s = 8 TeV. The data correspond to an integrated luminosity of 19.7 fb(-1). The search considers HH resonances with masses between 1 and 3 TeV, having final states of two b quark pairs. Each Higgs boson is produced with large momentum, and the hadronization products of the pair of b quarks can usually be reconstructed as single large jets. The background from multijet and t (t) over bar events is significantly reduced by applying requirements related to the flavor of the jet, its mass, and its substructure. The signal would be identified as a peak on top of the dijet invariant mass spectrum of the remaining background events. No evidence is observed for such a signal. Upper limits obtained at 95 confidence level for the product of the production cross section and branching fraction sigma(gg -> X) B(X -> HH -> b (b) over barb (b) over bar) range from 10 to 1.5 fb for the mass of X from 1.15 to 2.0 TeV, significantly extending previous searches. For a warped extra dimension theory with amass scale Lambda(R) = 1 TeV, the data exclude radion scalar masses between 1.15 and 1.55 TeV

Search for supersymmetry in events with one lepton and multiple jets in proton-proton collisions at root s=13 TeV

Peer reviewe