Hideaki Nagahata

Institute of Statistical Mathematics · Risk Analysis Research Center

In this chapter, we illustrate some numerical studies investigating the finite sample performance of the tests for one-way and two-way models presented in the previous chapters. First, we demonstrate the performance of the Lawley–Hotelling test statistic (LH), the likelihood ratio test statistic (LR), and the Bartlett–Nanda–Pillai test statistic (B...

The optimality of the tests has not been discussed so far. For the test for the existence of fixed effects, the locally asymptotically maximin test based on local asymptotic normality (LAN) was proposed by Hallin et al. (2021) for i.i.d. data. In this chapter, we show that the one-way random effect model for i.i.d. sequences does not have the LAN p...

While ANOVA for independent errors has been well-tuned, ANOVA for time-dependent errors is in its infancy. In this chapter, we extend the one-way fixed model with independent errors and groups to a one-way fixed model with time-dependent errors and independent groups.

This chapter extends the one-way models with time-dependent errors and correlated groups dealt with in Chapter 4 to the two-way models with time-dependent errors and correlated groups. We propose a test for the existence of random effects in Section 5.1 and a test for the existence of random interactions in Section 5.2. We show that the tests have...

The independence between groups was imposed in Chapter 2 but this assumption is not fulfilled by some real data, e.g., stock prices. This chapter extends one-way fixed models with time-dependent errors and independent groups dealt with in Chapter 2 to one-way fixed and random models with time-dependent errors and correlated groups. We propose a tes...

Although finite dimensionality was assumed in Chapter 2, ANOVA for high-dimensional time-dependent errors has not been fully developed. In this chapter, we extend the one-way fixed model with time-dependent errors and independent groups to a one-way fixed model with high-dimensional time-dependent errors and independent groups. In Section 3.1, we d...

This chapter analyzes the average wind speed data observed in seven cities located in coastal and inland areas in Japan by assuming the one-way effect model with time-dependent errors and correlated groups. The purpose is to assess the existence of area effects. To this end, both the \( T_{\textrm{GALT},n}\) statistic designed for correlated groups...

Analysis of variance (ANOVA) is tailored for independent observations. Recently, there has been considerable demand for ANOVA of high-dimensional and dependent observations in many fields. For example, it is important to analyze differences among industry averages of financial data. However, ANOVA for these types of observations has been inadequate...

This study establishes a new approach for the analysis of variance (ANOVA) of time series. ANOVA has been sufficiently tailored for cases with independent observations, but there has recently been substantial demand across many fields for ANOVA in cases with dependent observations. For example, ANOVA for dependent observations is important to analy...

Discriminant and cluster analysis of high-dimensional time series data have been an urgent need in more and more academic fields. To settle the always-existing problem of bias in distance-based classifiers for high-dimensional models, we consider a new classifier with jackknife type bias adjustment for stationary time series data. The consistency o...