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• W4213367098 abstract "The goal of the thesis is to construct the simultaneous confidence bands for structural relationship models introduced by Freitag (2000), Freitag and Munk (2005). Consider the two-sample case, where $X_1, ldots, X_n$ and $Y_1, ldots, Y_m$ are independent samples with distribution functions $F_1$ and $F_2$ respectively. The structural relationship model $F_1^{-1}(u) = phi_1(F_2^{-1}(phi_2(u,h)),h)$, where $phi_1$ and $phi_2$ are some twice differentiable real-valued functions, describes several important relationships between the two distribution functions $F_1$ and $F_2$. For example, if $phi_1(t,h) = t + h$ and $phi_2(u,h) = u$ we get the well-known location model.To construct the bands, we first estimate the unknown structural parameter $h$ and plug it in the P-P (probability-probability) plot function of structural relationship models. Further the simultaneous bands have been constructed using the two-sample plug-in empirical likelihood method, which has been established in the thesis.The thesis generalizes Hjort {sl et al.} (2004) work, where the one-sample plug-in empirical likelihood has been defined. A plug-in version of empirical likelihood allows us to derive the pointwise confidence bands. %for the P-P plot of general structural relationship models. To obtain the simultaneous confidence bands we have used the method introduced by Hall and Owen (1993), where the empirical likelihood method sets the shape of the bands and bootstrap sets the level of the test.Claesken's {sl et al.} (2003) results, where the confidence bands have been constructed for the usual P-P plot of two distribution functions $F_1$ and $F_2$, follow from our results with functions $phi_1(t,h) = phi_2(t,h) = t$. We show also that the P-P and Q-Q (quantile-quantile) plots for the independent samples can be treated in the same way. However, in the context of structural relationship models we found P-P plots advantageous above Q-Q plots. P-P plots have become even more interesting because they are closely related to Receiver Operating Characteristic (ROC) curves, which are important in signal theory, psychology, medicine, etc. (cf. Li {sl et al.}, 1996).We complete our work with establishing a smoothed version of plug-in empirical likelihood for structural relationship models. To do this we have used the smoothed empirical likelihood method, which has been introduced by Chen and Hall (1993) for the one-sample case. For the location model we simulated the coverage levels and constructed the simultaneous bands for some real data problems." @default.
• W4213367098 created "2022-02-24" @default.
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• W4213367098 date "2022-02-20" @default.
• W4213367098 modified "2023-10-18" @default.
• W4213367098 title "Confidence bands for structural relationship models" @default.
• W4213367098 doi "https://doi.org/10.53846/goediss-2474" @default.
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