Asymptotic expansions in mean and covariance structure analysis

Asymptotic Distributions of Estimators of Eigenvalues and Eigenfunctions in Functional Data

Functional data analysis is a relatively new and rapidly growing area of statistics. This is partly due to technological advancements which have made it possible to generate new types of data that are in the form of curves. Because the data are functions, they lie in function spaces, which are of infinite dimension. To analyse functional data, one way, which is widely used, is to employ princip...

Asymptotic expansions of the distributions of estimators in canonical correlation analysis under nonnormality

Asymptotic expansions of the distributions of typical estimators in canonical correlation analysis under nonnormality are obtained. The expansions include the Edgeworth expansions up to order O(1/n) for the parameter estimators standardized by the population standard errors, and the corresponding expansion by Hall’s method with variable transformation. The expansions for the Studentized estimat...

Second Order Moment Asymptotic Expansions for a Randomly Stopped and Standardized Sum

This paper establishes the first four moment expansions to the order o(a^−1) of S_{t_{a}}^{prime }/sqrt{t_{a}}, where S_{n}^{prime }=sum_{i=1}^{n}Y_{i} is a simple random walk with E(Yi) = 0, and ta is a stopping time given by t_{a}=inf left{ ngeq 1:n+S_{n}+zeta _{n}>aright}‎ where S_{n}=sum_{i=1}^{n}X_{i} is another simple random walk with E(Xi) = 0, and {zeta _{n},ngeq 1} is a sequence of ran...

Asymptotic expansions in the singular value decomposition for cross covariance and correlation under nonnormality

Higher Order Asymptotic Cumulants of Studentized Estimators in Covariance Structures

This note gives corrections of the numerical values of the higher-order asymptotic variances (standard errors) and kurtoses of the Studentized estimators (and consequently the root mean square errors of the two-term Edgeworth expansions) shown in the tables of Ogasawara (2008a, 2008b). The corrections are due to a minor bug in the computer program. The corrected values given in the following Ta...