The Optimal Confidence Region for a Random Parameter

Under a two-level hierarchical model, suppose that the distribution of the random parameter is known or can be estimated well. Data are generated via a fixed, but unobservable realization of this parameter. In this paper, we derive the smallest confidence region of the random parameter under a joint Bayesian/frequentist paradigm. On average this optimal region can be much smaller than the corresponding Bayesian highest posterior density region. The new estimation procedure is appealing when one deals with data generated under a highly parallel structure, for example, data from a trial with a large number of clinical centers involved or genome-wide gene-expession data for estimating individual gene- or center-specific parameters simultaneously. The new proposal is illustrated with a typical microarray data set and its performance is examined via a small simulation study

Evaluating Prediction Rules for t-Year Survivors With Censored Regression Models

Suppose that we are interested in establishing simple, but reliable rules for predicting future t-year survivors via censored regression models. In this article, we present inference procedures for evaluating such binary classification rules based on various prediction precision measures quantified by the overall misclassification rate, sensitivity and specificity, and positive and negative predictive values. Specifically, under various working models we derive consistent estimators for the above measures via substitution and cross validation estimation procedures. Furthermore, we provide large sample approximations to the distributions of these nonsmooth estimators without assuming that the working model is correctly specified. Confidence intervals, for example, for the difference of the precision measures between two competing rules can then be constructed. All the proposals are illustrated with two real examples and their finite sample properties are evaluated via a simulation study

Checking the Cox model with cumulative sums of martingale-based residuals

This paper presents a new class of graphical and numerical methods for checking the adequacy of the Cox regression model. The procedures are derived from cumulative sums of martingale-based residuals over follow-up time and/or covariate values. The distributions of these stochastic processes under the assumed model can be approximated by zero-mean Gaussian processes. Each observed process can then be compared, both visually and analytically, with a number of simulated realizations from the approximate null distribution. These comparisons enable the data analyst to assess objectively how unusual the observed residual patterns are. Special attention is given to checking the functional form of a covariate, the form of the link function, and the validity of the proportional hazards assumption. An omnibus test, consistent against any model misspecification, is also studied. The proposed techniques are illustrated with two real data sets

Quantized adiabatic charge pumping and resonant transmission

Adiabatically pumped charge, carried by non-interacting electrons through a quantum dot in a turnstile geometry, is studied as function of the strength of the two modulating potentials (related to the conductances of the two point-contacts to the leads) and of the phase shift between them. It is shown that the magnitude and sign of the pumped charge are determined by the relative position and orientation of the closed contour traversed by the system in the parameter plane, and the transmission peaks (or resonances) in that plane. Integer values (in units of the electronic charge $e$) of the pumped charge (per modulation period) are achieved when a transmission peak falls inside the pumping contour. The integer value is given by the winding number of the pumping contour: double winding in the same direction gives a charge of 2, while winding around two opposite branches of the transmission peaks or winding in opposite directions can give a charge close to zero.Comment: 7 pages, 12 figure

Semiparametric regression for the mean and rate functions of recurrent events

The counting process with the Cox‐type intensity function has been commonly used to analyse recurrent event data. This model essentially assumes that the underlying counting process is a time‐transformed Poisson process and that the covariates have multiplicative effects on the mean and rate function of the counting process. Recently, Pepe and Cai, and Lawless and co‐workers have proposed semiparametric procedures for making inferences about the mean and rate function of the counting process without the Poisson‐type assumption. In this paper, we provide a rigorous justification of such robust procedures through modern empirical process theory. Furthermore, we present an approach to constructing simultaneous confidence bands for the mean function and describe a class of graphical and numerical techniques for checking the adequacy of the fitted mean–rate model. The advantages of the robust procedures are demonstrated through simulation studies. An illustration with multiple‐infection data taken from a clinical study on chronic granulomatous disease is also provided

Effect of Pin Diameters on the Wear Characteristics of Friction Pairs

The tribological tests are carried out to assess the effect of pin diameters on wear characteristics via changing contact stresses and sliding speeds to provide support for choosing friction pair sizes. The friction couple is set as CuZn pins for medium carbon steel (No. 1045 steel) rings. The differential wear rate and its calculation formula are defined to express the line wear rate or the wear resistance of unit cross-section area. The effect of the pin end surface diameter on differential wear rate and its scale/increased multiplier are investigated. When the product (P×V=0.095) is kept constant, the abrasion loss for the specimens of a small diameter (d1=0.6 mm) is lesser than that of the specimens of a large diameter (d2=4.0 mm). As compared to the sliding speed, the change in contact stresses exerts a greater influence on the wear behavior, especially for small-diameter specimens. The differential wear rate of small-diameter specimens is always higher than that of the specimens of a large diameter. The scale multiplier of the differential wear rate is always larger than that of the contact pressure stress, especially for small-diameter specimens.С целью обоснования выбора размеров пар трения проводятся трибологические испытания по оценке влияния диаметров штифта на характеристики износа путем изменения нагрузок и скорости скольжения. Пара трения представляется в виде штифтов из CuZn к кольцам из среднеуглеродистой стали (сталь 1045). Дифференциальная скорость изнашивания и формула для ее расчета определяются для выражения линейной скорости изнашивания или сопротивления износу единицы площади поперечного сечения. Исследуются влияние различного диаметра торцевой поверхности штифтов, дифференциальная скорость изнашивания и ее увеличенный множитель. Результаты показывают, что при поддержании постоянства произведения P×V=0,095 потери при истирании образцов малого диаметра (d1=0,6 мм) меньше, чем образцов большого диаметра (d2 =4,0 мм). По сравнению со скоростью скольжения изменение нагрузки более существенно влияет на характеристики износа, особенно для образцов малого диаметра. Дифференциальная скорость изнашивания образцов малого диаметра всегда больше, чем образцов большого диаметра. Увеличенный множитель дифференциальной скорости изнашивания всегда превышает увеличенный множитель повышения напряжения контактного давления, особенно для образцов малого диаметра.З метою обґрунтування вибору розмірів пар тертя проводяться трибологичні випробування з оцінки впливу діаметрів штифта на характеристики зносу шляхом зміни навантажень і швидкості ковзання. Пара тертя представляється у вигляді штифтів з СuZn до кілець з середньовуглецевої сталі (сталь 1045). Диференціальна швидкість зношування і формула для її розрахунку визначаються для вираження лінійної швидкості зношування або опору зносу одиниці площі поперечного перерізу. Досліджуються вплив різного діаметру торцевої поверхні штифтів, диференціальна швидкість зношування і її збільшений множник. Результати показують, що при підтримці сталості Р x V = 0,095 втрати при стиранні зразків малого діаметра (d1 = 0,6 мм) менше, ніж зразків великого діаметра (d2 = 4,0 мм). У порівнянні зі швидкістю ковзання зміна навантаження більш істотно впливає на характеристики зносу, особливо для зразків малого діаметра. Диференціальна швидкість зношування зразків малого діаметра завжди більше, ніж зразків великого діаметру. Збільшений множник диференціальної швидкості зношування завжди перевищує збільшений множник підвищення напружень контактного тиску, особливо для зразків малого діаметра

Interface effects on the shot noise in normal metal- d-wave superconductor Junctions

The current fluctuation in normal metal / d-wave superconductor junctions are studied for various orientation of the crystal by taking account of the spatial variation of the pair potentials. Not only the zero-energy Andreev bound states (ZES) but also the non-zero energy Andreev bound states influence on the properties of differential shot noise. At the tunneling limit, the noise power to current ratio at zero voltage becomes 0, once the ZES are formed at the interface. Under the presence of a subdominant s-wave component at the interface which breaks time-reversal symmetry, the ratio becomes 4eComment: 13 pages, 3 figure

The transition form factors for semi-leptonic weak decays of J/ψJ/\psi in QCD sum rules

Within the Standard Model, we investigate the semi-leptonic weak decays of $J/\psi$. The various form factors of $J/\psi$ transiting to a single charmed meson ($D^{(*)}_{(d,s)}$) are studied in the framework of the QCD sum rules. These form factors fully determine the rates of the weak semi-leptonic decays of $J/\psi$ and provide valuable information about the non-perturbative QCD effects. Our results indicate that the decay rate of the semi-leptonic weak decay mode $J/\psi \to D^{(*)-}_{s}+e^{+}+\nu_{e}$ is at order of $10^{-10}$.Comment: 28 pages, 6 figures, revised version to be published in Eur.Phys.J.