Robertas Gabrys

Reviewed 6 chapters for for Data Analytics, 1e by Alison Kelly, Sanjiv Jaggia, Kevin Lertwachara, Leida Chen 6 on the general content, organization, and approach of the text:

Chapter 6: Regression Analysis
Chapter 7: Advanced Regression Analysis
Chapter 8: Introduction to Data Mining
Chapter 9: Supervised Data Mining: k-Nearest Neighbors and Naïve Bayes
Chapter 10: Supervised Data Mining: Decision Trees
Chapter 11: Unsupervised Data Mining

A functional time series consists of curves, typically one curve per day. The most

important parameter of such a series is the mean curve. We propose two methods

of detecting a change in the mean function of a functional time series. The change

is detected on line, as new functional observations arrive. The general methodology

is motivated by and applied to the detection of a change in the average intraday

volatility pattern. The methodology is asymptotically justified by applying a new

notion of weak dependence for functional time series. It is calibrated and validated

by simulations based on real intraday volatility curves.

The paper proposes two inferential tests for error correlation in the functional linear model, which complement the available graphical

goodness-of-fit checks. To construct them, finite dimensional residuals are computed in two different ways, and then their autocorrelations

are suitably defined. From these autocorrelation matrices, two quadratic forms are constructed whose limiting distribution are chi-squared

with known numbers of degrees of freedom (different for the two forms). The asymptotic approximations are suitable for moderate sample

sizes. The test statistics can be relatively easily computed using the R package fda, or similar MATLAB software. Application of the tests

is illustrated on magnetometer and financial data. The asymptotic theory emphasizes the differences between the standard vector linear

regression and the functional linear regression. To understand the behavior of the residuals obtained from the functional linear model,

the interplay of three types of approximation errors must be considered, whose sources are: projection on a finite dimensional subspace,

estimation of the optimal subspace, and estimation of the regression kernel.