271,068 research outputs found

    Nonparametric Covariate Adjustment for Receiver Operating Characteristic Curves

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    The accuracy of a diagnostic test is typically characterised using the receiver operating characteristic (ROC) curve. Summarising indexes such as the area under the ROC curve (AUC) are used to compare different tests as well as to measure the difference between two populations. Often additional information is available on some of the covariates which are known to influence the accuracy of such measures. We propose nonparametric methods for covariate adjustment of the AUC. Models with normal errors and non-normal errors are discussed and analysed separately. Nonparametric regression is used for estimating mean and variance functions in both scenarios. In the general noise case we propose a covariate-adjusted Mann-Whitney estimator for AUC estimation which effectively uses available data to construct working samples at any covariate value of interest and is computationally efficient for implementation. This provides a generalisation of the Mann-Whitney approach for comparing two populations by taking covariate effects into account. We derive asymptotic properties for the AUC estimators in both settings, including asymptotic normality, optimal strong uniform convergence rates and MSE consistency. The usefulness of the proposed methods is demonstrated through simulated and real data examples

    Empirical analysis of the solar contribution to global mean air surface temperature change

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    The solar contribution to global mean air surface temperature change is analyzed by using an empirical bi-scale climate model characterized by both fast and slow characteristic time responses to solar forcing: τ1=0.4±0.1\tau_1 =0.4 \pm 0.1 yr, and τ2=8±2\tau_2= 8 \pm 2 yr or τ2=12±3\tau_2=12 \pm 3 yr. Since 1980 the solar contribution to climate change is uncertain because of the severe uncertainty of the total solar irradiance satellite composites. The sun may have caused from a slight cooling, if PMOD TSI composite is used, to a significant warming (up to 65% of the total observed warming) if ACRIM, or other TSI composites are used. The model is calibrated only on the empirical 11-year solar cycle signature on the instrumental global surface temperature since 1980. The model reconstructs the major temperature patterns covering 400 years of solar induced temperature changes, as shown in recent paleoclimate global temperature records.Comment: 9 pages, 6 figure

    On the sensitivity of desirability functions for multiresponse optimization

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    Desirability functions have been one of the most important multiresponse optimization technique since the early eighties. Main reasons for this popularity might be counted as the convenience of the implementation of the method and it's availability in many experimental design software packages. Technique itself involves somehow subjective parameters such as the importance coefficients between response characteristics that are used to calculate overall desirability, weights used in determining the shape of each individual response and the size of the specification band of the response. However, the impact of these sensitive parameters on the solution set is mostly uninvestigated. This paper proposes a procedure to analyze the sensitivity of the important characteristic parameters of desirability functions and their impact on pareto-optimal solution set. The proposed procedure uses the experimental design tools on the solution space and estimates a prediction equation on the overall desirability to identify the sensitive parameters. For illustration, a classical desirability example is selected from the literature and results are given along with the discussion.Publisher's Versio

    Realistic Sensitivity Curves For Pulsar Timing Arrays

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    We construct realistic sensitivity curves for pulsar timing array searches for gravitational waves, incorporating both red and white noise contributions to individual pulsar noise spectra, and the effect of fitting to a pulsar timing model. We demonstrate the method on both simulated pulsars and a realistic array consisting of a subset of NANOGrav pulsars used in recent analyses. A comparison between the results presented here and measured upper limit curves from actual analyses shows agreement to tens of percent. The resulting sensitivity curves can be used to assess the detectability of predicted gravitational-wave signals in the nanohertz frequency band in a coherent, flexible, and computationally efficient manner
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