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In many experiments, time series data can be collected from multiple units and multiple time series segments can be collected from the same unit. This article introduces a mixed effects Cramér spectral representation which can be used to model the effects of design covariates on the second-order power spectrum while accounting for potential correlations among the time series segments collected from the same unit. The transfer function is composed of a deterministic component to account for the population-average effects and a random component to account for the unit-specific deviations. The resulting log-spectrum has a functional mixed effects representation where both the fixed effects and random effects are functions in the frequency domain. It is shown that, when the replicate-specific spectra are smooth, the log-periodograms converge to a functional mixed effects model. A data-driven iterative estimation procedure is offered for the periodic smoothing spline estimation of the fixed effects, penalized estimation of the functional covariance of the random effects, and unit-specific random effects prediction via the best linear unbiased predictor. [ABSTRACT FROM PUBLISHER]

In this article we develop a nonparametric estimation procedure for the varying coefficient model when the within-subject covariance is unknown. Extending the idea of iterative reweighted least squares to the functional setting, we iterate between estimating the coefficients conditional on the covariance and estimating the functional covariance conditional on the coefficients. Smoothing splines for correlated errors are used to estimate the functional coefficients with smoothing parameters selected via the generalized maximum likelihood. The covariance is nonparametrically estimated using a penalized estimator with smoothing parameters chosen via a Kullback–Leibler criterion. Empirical properties of the proposed method are demonstrated in simulations and the method is applied to the data collected from an ovarian tumor study in mice to analyze the effects of different chemotherapy treatments on the volumes of two classes of tumors. [ABSTRACT FROM AUTHOR]

In this article we propose a smoothing spline ANOVA model (SS-ANOVA) to estimate and to make inference on the time-varying log-spectrum of a locally stationary process. The time-varying spectrum is assumed to be smooth in both time and frequency. This assumption essentially turns a time-frequency spectral estimation problem into a 2-dimensional surface estimation problem. A smooth localized complex exponential (SLEX) basis is used to calculate the initial periodograms, and a SS-ANOVA is fitted to the log-periodograms. This approach allows the time and frequency domains to be modeled in a unified approach and jointly estimated. Inference procedures, such as confidence intervals, and hypothesis tests proposed for the SS-ANOVA can be adopted for the time-varying spectrum. Because of the smoothness assumption of the underlying spectrum, once we have the estimates on a time-frequency grid, we can calculate the estimate at any given time and frequency. This leads to a high computational efficiency, because for large datasets we need only estimate the initial raw periodograms at a much coarser grid. We study a penalized least squares estimator and a penalized Whittle likelihood estimator. The penalized Whittle likelihood estimator has smaller mean squared errors, whereas inference based on the penalized least squares method can adopt existing results. We present simulation results and apply our method to electroencephalogram data recorded during an epileptic seizure. [ABSTRACT FROM AUTHOR]

The article discusses the need to refine and improve a proposed method for the study of traditional Chinese herbal medications (TCHMs) and extend it to other statistical and applied problems. The role of the mean chromatographic fingerprint technique in the simplification of the covariance structure is mentioned. The importance of combining the preprocessing and estimation procedures in biomedical applications is also noted.