Prediction of spectral reflectance factor distribution of automotive paint finishes

It is necessary to determine the accurate reflectance of painted surfaces for the review of paint finishes by computer graphics (CG) before actual painting of the exterior color of automobiles, and for quality control during production and inspection processes. We have optimized a method for measuring reflectance by using a statistical technique. We have found that the reflectance of a painted surface is best measured at an incident angle of 60° and at five aspecular angles of 10°, 18°, 28°, 40°, and 90°. Our method makes it possible to accurately reproduce reflection characteristics of paint finishes containing special flake pigments, such as pearl mica. Also it was proved that our method can apply not only to solid and metallic coatings but to all painted surfaces. © 2005 Wiley Periodicals, Inc. Col Res Appl, 30, 275–282, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20125     

Tests for Comparing Time‐Invariant and Time‐Varying Spectra Based on the Pearson Statistic

Two tests are proposed in this paper for comparing spectra of two univariate time series. One is a Pearson‐like statistic based only on periodograms of the compared time series and applicable for testing the equality of two time‐invariant spectra of two independent or dependent time series, with an asymptotic chi‐squared distribution under the null hypothesis. The other is based on the maximum of the Pearson‐like statistics. Not only does this test, again, depend only on periodograms but also approximately equals the maximum of a chi‐squared distribution of the same degrees of freedom under the null. It can be used to test the equality of spectra of two locally stationary time series regardless of whether they are dependent or independent. Multiple simulation examples show that both statistics achieve good performance. The proposed approach is illustrated by an application to longitudinal vibration data from a container ship.     

Asymptotics for the Conditional‐Sum‐of‐Squares Estimator in Multivariate Fractional Time‐Series Models

This article proves consistency and asymptotic normality for the conditional‐sum‐of‐squares estimator, which is equivalent to the conditional maximum likelihood estimator, in multivariate fractional time‐series models. The model is parametric and quite general and, in particular, encompasses the multivariate non‐cointegrated fractional autoregressive integrated moving average (ARIMA) model. The novelty of the consistency result, in particular, is that it applies to a multivariate model and to an arbitrarily large set of admissible parameter values, for which the objective function does not converge uniformly in probability, thus making the proof much more challenging than usual. The neighbourhood around the critical point where uniform convergence fails is handled using a truncation argument.