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We consider a binary multivariate regression model where the conditional expectation of a binary variable given a higher-dimensional input variable belongs to a parametric family. Based on this, we introduce a model-based bootstrap (MBB) for higher-dimensional input variables. This test can be used to check whether a sequence of independent and identically distributed observations belongs to such a parametric family. The approach is based on the empirical residual process introduced by Stute (Ann Statist 25:613–641, 1997). In contrast to Stute and Zhu’s approach (2002) Stute & Zhu (Scandinavian J Statist 29:535–545, 2002), a transformation is not required. Thus, any problems associated with non-parametric regression estimation are avoided. As a result, the MBB method is much easier for users to implement. To illustrate the power of the MBB based tests, a small simulation study is performed. Compared to the approach of Stute & Zhu (Scandinavian J Statist 29:535–545, 2002), the simulations indicate a slightly improved power of the MBB based method. Finally, both methods are applied to a real data set.
Evaluation of Particle Size Distributions by Means of Particle Counters / Fißan, H. J. ; Helsper, C.
(1979)
It has been observed that carcinogenic polycyclic aromatic hydrocarbons (PAH) are present in the atmosphere. Combustion processes are considered the most important sources for PAH. Among these, the burning of coal produces the highest emission, but in cities with high traffic density and low meteorological exchange activities, vehicle emissions determine the immission situation, especially in narrow streets. For estimating the potential health effects caused by PAH, it is sufficient to characterize the emission of PAH with respect to their physical state, concentrations, and, as far as the particulate phase is concerned, size distribution. The size distribution is important for transport phenomena, inhalation, and deposition in the respiratory tract. These parameters mainly depend on the combustion system, on system operating conditions, on the exhaust system, and on exhaust cooling conditions. At exhaust-gas temperatures in the range of ambient air temperatures, almost the whole emission of PAH is made up of particulate matter.