Summary Methodology is proposed to uncover structural breaks in functional data that is ‘fully functional’ in the sense that it does not rely on dimension reduction techniques. A thorough asymptotic theory is developed for a fully functional break detection procedure as well as for a break date estimator, assuming a fixed break size and a shrinking break size. The latter result is utilized to derive confidence intervals for the unknown break date. The main results highlight that the fully functional procedures perform best under conditions when analogous estimators based on functional principal component analysis are at their worst, namely when the feature of interest is orthogonal to the leading principal components of the data. The theoretical findings are confirmed by means of a Monte Carlo simulation study in finite samples. An application to annual temperature curves illustrates the practical relevance of the procedures proposed.

This paper deals with analyzing structural breaks in the covariance operator of sequentially observed functional data. For this purpose, procedures are developed to segment an observed stretch of curves into periods for which second-order stationarity may be reasonably assumed. The proposed methods are based on measuring the fluctuations of sample eigenvalues, either individually or jointly, and traces of the sample covariance operator computed from segments of the data. To implement the tests, new limit results are introduced that deal with the large-sample behavior of vector-valued processes built from partial sample eigenvalue estimates. These results in turn enable the calibration of the tests to a prescribed asymptotic level. Applications to Australian annual minimum temperature curves and sea surface temperature anomaly records confirm that the proposed methods work well in finite samples. The first application suggests that the variation in annual minimum temperature underwent a structural break in the 1950s, after which typical fluctuations from the generally increasing trend started to be significantly smaller. KEYWORDS annual temperature profiles, change-point analysis, functional data, functional principal components, functional time series, structural breaks MSC CLASSIFICATION 62G99, 62H99, Secondary: 62M10, 91B84 Environmetrics. 2020;31:e2617.wileyonlinelibrary.com/journal/env

The objectives were to develop and evaluate: 1) growth rate models, 2) body lipid, moisture, and energy models for white sturgeon fed at various feeding rates (FR; % body weight [BW] per day) and then evaluate responses at proportions of optimum feeding rate (OFR) across increasing BW (g). For objective 1, 19 datasets from the literature containing initial BW, FR and specific growth rate (SGR; % BW increase per day) were used. For objective 2, 12 datasets from the literature (11 from objective 1) containing SGR, FR, final BW, body lipid (%), protein (%), ash (%), moisture (%), and energy (kJ/g) were used. The average rearing temperatures was 19.2 ± 1.5 °C (mean ± SD). The average nutrient compositions and gross energy of the diets were 45.7 ± 4.3% protein, 14.8 ± 3.2% lipid, and 20.4 ± 1.3 kJ/g, respectively. The logistic model was used for objectives 1 and 2 to develop a statistical relationship between SGR and FR, then an iterative technique was used to estimate OFR for each dataset. For objective 2, the statistical relationship between body lipid, energy, and moisture and FR was established. Using the OFR estimate, SGR, body lipid, energy and moisture were computed at various FR as a proportion of OFR. Finally, a nonparametric fitting procedure was used to establish relationships between SGR, body lipid, energy and moisture (responses) compared with BW (predictor) at various proportions of OFR. This allows visualization of the effect of under- or over-feeding on the various responses. When examining the differences between OFR at 100% and various proportions of OFR, SGR differences decrease and moisture differences increase as BW increases. Lipid and energy differences decrease as BW increases. To our knowledge, these are the first description of changes in nutrient compositions when white sturgeon are fed at various FR. Because physiological and behavioral properties that are unique to sturgeon, results from this study are specific to sturgeon under the conditions of this study and cannot be compared directly with salmonids even if some of the results are similar. This research provides insight to designing future nutritional studies in sturgeon.

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