By Jin-Ting Zhang
Despite examine curiosity in practical information research within the final 3 a long time, few books can be found at the topic. Filling this hole, Analysis of Variance for sensible Data provides up to date speculation checking out tools for sensible facts research. The booklet covers the reconstruction of practical observations, sensible ANOVA, sensible linear types with practical responses, ill-conditioned practical linear types, diagnostics of useful observations, heteroscedastic ANOVA for sensible facts, and checking out equality of covariance capabilities. even though the methodologies offered are designed for curve info, they are often prolonged to floor data.
Useful for statistical researchers and practitioners studying practical info, this self-contained publication provides either a theoretical and utilized remedy of useful info research supported by way of easy-to-use MATLAB® code. the writer presents a few basic tools for sensible speculation trying out. He discusses pointwise, L2-norm-based, F-type, and bootstrap assessments.
Assuming in basic terms simple wisdom of facts, calculus, and matrix algebra, the ebook explains the major rules at a comparatively low technical point utilizing actual info examples. each one bankruptcy additionally contains bibliographical notes and workouts. actual useful facts units from the textual content and MATLAB codes for interpreting the information examples can be found for obtain from the author’s website.
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Additional resources for Analysis of Variance for Functional Data
In Chapters 2 and 3 of this book, we also provide some tools to overcome diﬃculties encountered in the ﬁrst two situations while other chapters of the book provide methodologies to overcome diﬃculties encountered in the third situation. 4 17 Overview of the Book In this book, we aim to conduct a thorough survey on the topics of hypothesis testing in the context of analysis of variance for functional data and give a systematic treatment of the methodologies. For this purpose, the remaining chapters are arranged as follows.
In FDA, the Mahalanobis distance often cannot be well-deﬁned as the sample covariance matrices of discretized functional data are often degenerated. Instead we have to use the L2 -norm distance (and its modiﬁcations). In fact, the Gaussian process and the L2 -norm distance in FDA play the roles of normal distribution and Mahalanobis distance in classical MDA. Thus, we shall discuss the properties of the L2 -norm of a Gaussian process in Chapter 4. We also discuss the properties of Wishart processes (a natural extension of Wishart matrices), chi-squared mixtures, and F-type mixtures there.
This observation seems reasonable as the Eastern and Western weather stations are located at about the same latitudes while the Northern weather stations are located at higher latitudes. Statistically, we can ask the following question. Is there a location eﬀect among the mean temperature curves of the Eastern, Western, and Northern weather stations? This is a three-sample or one-way ANOVA problem for functional data. This problem will be treated in Chapters 5 and 9, respectively, when the three samples of the temperature curves are assumed to have the same and diﬀerent covariance functions.
Analysis of Variance for Functional Data by Jin-Ting Zhang