Browsing by Author "Scharf, Louis, advisor"

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Open Access
Multi-channel factor analysis: properties, extensions, and applications
(Colorado State University. Libraries, 2024) Stanton, Gray, author; Wang, Haonan, advisor; Scharf, Louis, advisor; Kokoszka, Piotr, committee member; Wang, Tianying, committee member; Luo, Jie, committee member
Multi-channel Factor Analysis (MFA) extends factor analysis to the multi-channel or multi-view setting, where latent common factors influence all channels while distinct factors are specific to individual channels. The within- and across-channel covariance is determined by a low-rank matrix, a block-diagonal matrix with low-rank blocks, and a diagonal matrix, which provides a parsimonious model for both covariances. MFA and related multi-channel methods for data fusion are discussed in Chapter 1. Under conditions on the channel sizes and factor numbers, the results of Chapter 2 show that the generic global identifiability of the aforementioned covariance matrices can be guaranteed a priori, and the estimators obtained by maximizing a Gaussian likelihood are shown to be consistent and asymptotically normal even under misspecification. To handle temporal correlation in the latent factors, Chapter 3 introduces Multi-channel Factor Spectral Analysis (MFSA). Results for the identifiability and parameterization properties of the MFSA spectral density model are derived, and a Majorization-Minimization procedure to optimize the Whittle pseudo-likelihood is designed to estimate the MFSA parameters. A simulation study is conducted to explore how temporal correlations in the latent factors affect estimation, and it is demonstrated that MFSA significantly outperforms MFA when the factor series are highly autocorrelated. In Chapter 4, a locally stationary joint multivariate Gaussian process with MFA-type cross-sectional covariance is developed to model multi-vehicle trajectories in a highway environment. A dynamic model-based clustering procedure is designed to partition cohorts of nearby vehicles into pods based on the stability of the intra-pod relative vehicle configuration. The performance of this procedure is illustrated by its application to the Next GENeration SIMulation dataset of vehicle trajectories on U.S. Highway 101.
Open Access
Outlier discordancy tests based on saddlepoint approximations
(Colorado State University. Libraries, 2019) Sleeper, Andrew D., author; Scharf, Louis, advisor; Boes, Duane, committee member; Breidt, Jay, committee member; Jayasumana, Anura, committee member
When testing for the discordancy of a single observed value, a test based on large values of the maximum absolute studentized residual (MASR) or maximum squared studentized residual (MSSR) is known to be optimal, by maximizing the probability of correctly identifying an outlying value, while controlling the risk of a false identification to α. The exact distribution of MASR and MSSR is not known. In its place, the first Bonferroni bound on the distribution of these statistics is commonly used as an outlier test; see Grubbs (1950). We present new approximations to the distribution of MASR or MSSR, based on saddlepoint approximations of the density of statistics calculated from truncated normal random variables. These approximations are developed in three settings: a one-sample case, univariate regression, and multivariate regression. In comparisons with three versions of Bonferroni bounds and a Monte Carlo simulation, the saddlepoint approximations are shown to perform well in a wide range of situations, especially at larger sample size. The saddlepoint approximations also calculate faster than the improved versions of Bonferroni bounds.