scholarly journals Consistency of the Mean and the Principal Components of Spatially Distributed Functional Data

2011 ◽  
pp. 169-175 ◽  
Author(s):  
Siegfried Hörmann ◽  
Piotr Kokoszka
Keyword(s):  
Principal Components ◽  
Functional Data ◽  
Spatially Distributed ◽  
The Mean

scholarly journals Consistency of the mean and the principal components of spatially distributed functional data

Bernoulli ◽  
2013 ◽  
Vol 19 (5A) ◽  
pp. 1535-1558 ◽  
Author(s):  
Siegfried Hörmann ◽  
Piotr Kokoszka
Keyword(s):  
Principal Components ◽  
Functional Data ◽  
Spatially Distributed ◽  
The Mean

scholarly journals Basis Expansions for Functional Snippets

Biometrika ◽  
2020 ◽  
Author(s):  
Zhenhua Lin ◽  
Jane-Ling Wang ◽  
Qixian Zhong
Keyword(s):  
Data Analysis ◽  
Convergence Rate ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Covariance Function ◽  
Covariance Estimation ◽  
Simulation Studies ◽  
Finite Sample ◽  
Covariance Functions ◽  
The Mean

Summary Estimation of mean and covariance functions is fundamental for functional data analysis. While this topic has been studied extensively in the literature, a key assumption is that there are enough data in the domain of interest to estimate both the mean and covariance functions. In this paper, we investigate mean and covariance estimation for functional snippets in which observations from a subject are available only in an interval of length strictly (and often much) shorter than the length of the whole interval of interest. For such a sampling plan, no data is available for direct estimation of the off-diagonal region of the covariance function. We tackle this challenge via a basis representation of the covariance function. The proposed estimator enjoys a convergence rate that is adaptive to the smoothness of the underlying covariance function, and has superior finite-sample performance in simulation studies.

Letters to the Editor

1997 ◽  
Vol 83 (6) ◽  
pp. 2167-2168 ◽  
Author(s):  
Alan Nevill
Keyword(s):  
Confidence Interval ◽  
Principal Components ◽  
Human Subjects ◽  
Predictor Variable ◽  
Reliability And Validity ◽  
Peak Oxygen Uptake ◽  
Letters To The Editor ◽  
The Mean ◽  
Log Linear ◽  
Dimensionality Theory

The following is the abstract of the article discussed in the subsequent letter: Batterham, Alan M., Keith Tolfrey, and Keith P. George. Nevill’s explanation of Kleiber’s 0.75 mass exponent: an artifact of collinearity problems in least squares models? J. Appl. Physiol. 82(2): 693–697, 1997.—Intraspecific allometric modeling (Y = a ⋅ mass b , where Y is the physiological dependent variable and ais the proportionality coefficient) of peak oxygen uptake (V˙o 2peak) has frequently revealed a mass exponent ( b) greater than that predicted from dimensionality theory, approximating Kleiber’s 3/4 exponent for basal metabolic rate. Nevill ( J. Appl. Physiol. 77: 2870–2873, 1994) proposed an explanation and a method that restores the inflated exponent to the anticipated 2/3. In human subjects, the method involves the addition of “stature” as a continuous predictor variable in a multiple log-linear regression model: ln Y = ln a + c ⋅ ln stature + b ⋅ ln mass + ln ε, where c is the general body size exponent and ε is the error term. It is likely that serious collinearity confounds may adversely affect the reliability and validity of the model. The aim of this study was to critically examine Nevill’s method in modelingV˙o 2peak in prepubertal, teenage, and adult men. A mean exponent of 0.81 (95% confidence interval, 0.65–0.97) was found when scaling by mass alone. Nevill’s method reduced the mean mass exponent to 0.67 (95% confidence interval, 0.44–0.9). However, variance inflation factors and tolerance for the log-transformed stature and mass variables exceeded published criteria for severe collinearity. Principal components analysis also diagnosed severe collinearity in two principal components, with condition indexes >30 and variance decomposition proportions exceeding 50% for two regression coefficients. The derived exponents may thus be numerically inaccurate and unstable. In conclusion, the restoration of the mean mass exponent to the anticipated 2/3 may be a fortuitous statistical artifact.

scholarly journals Landscape analysis of soil methane flux across complex terrain

2018 ◽  
Vol 15 (10) ◽  
pp. 3143-3167 ◽  
Author(s):  
Kendra E. Kaiser ◽  
Brian L. McGlynn ◽  
John E. Dore
Keyword(s):  
Environmental Conditions ◽  
Methane Flux ◽  
Time Variability ◽  
Sink Strength ◽  
Watershed Scale ◽  
Ch4 Flux ◽  
Creek Watershed ◽  
Spatially Distributed ◽  
Dry Down ◽  
The Mean

Abstract. Relationships between methane (CH4) fluxes and environmental conditions have been extensively explored in saturated soils, while research has been less prevalent in aerated soils because of the relatively small magnitudes of CH4 fluxes that occur in dry soils. Our study builds on previous carbon cycle research at Tenderfoot Creek Experimental Forest, Montana, to identify how environmental conditions reflected by topographic metrics can be leveraged to estimate watershed scale CH4 fluxes from point scale measurements. Here, we measured soil CH4 concentrations and fluxes across a range of landscape positions (7 riparian, 25 upland), utilizing topographic and seasonal (29 May–12 September) gradients to examine the relationships between environmental variables, hydrologic dynamics, and CH4 emission and uptake. Riparian areas emitted small fluxes of CH4 throughout the study (median: 0.186 µg CH4–C m−2 h−1) and uplands increased in sink strength with dry-down of the watershed (median: −22.9 µg CH4–C m−2 h−1). Locations with volumetric water content (VWC) below 38 % were methane sinks, and uptake increased with decreasing VWC. Above 43 % VWC, net CH4 efflux occurred, and at intermediate VWC net fluxes were near zero. Riparian sites had near-neutral cumulative seasonal flux, and cumulative uptake of CH4 in the uplands was significantly related to topographic indices. These relationships were used to model the net seasonal CH4 flux of the upper Stringer Creek watershed (−1.75 kg CH4–C ha−1). This spatially distributed estimate was 111 % larger than that obtained by simply extrapolating the mean CH4 flux to the entire watershed area. Our results highlight the importance of quantifying the space–time variability of net CH4 fluxes as predicted by the frequency distribution of landscape positions when assessing watershed scale greenhouse gas balances.

scholarly journals In vivo measurement of the frame-based application accuracy of the Neuromate neurosurgical robot

2015 ◽  
Vol 122 (1) ◽  
pp. 191-194 ◽  
Author(s):  
Daniel von Langsdorff ◽  
Philippe Paquis ◽  
Denys Fontaine
Keyword(s):  
Independent System ◽  
In Vivo Measurement ◽  
Stereotactic Frame ◽  
Spatially Distributed ◽  
The Mean ◽  
Neurosurgical Robot ◽  
Better Than ◽  
Deep Brain

OBJECT The application accuracy of the Neuromate neurosurgical robot has been validated in vitro but has not been evaluated in vivo for deep brain stimulation (DBS) electrode implantations. The authors conducted a study to evaluate this application accuracy in routine frame-based DBS procedures, with an independent system of measurement. METHODS The Euclidian distance was measured between the point theoretically targeted by the robot and the point actually reached, based on their respective stereotactic coordinates. The coordinates of the theoretical target were given by the robot's dedicated targeting software. The coordinates of the point actually reached were recalculated using the Stereoplan localizer system. This experiment was performed in vitro, with the frame fixed in the robot space without a patient, for 21 points spatially distributed. The in vivo accuracy was then measured in 30 basal ganglia targets in 17 consecutive patients undergoing DBS for movement disorders. RESULTS The mean in vitro application accuracy was 0.44 ± 0.23 mm. The maximal localization error was 1.0 mm. The mean (± SD) in vivo application accuracy was 0.86 ± 0.32 mm (Δx = 0.37 ± 0.34 mm, Δy = 0.32 ± 0.24 mm, Δz = 0.58 ± 0.31 mm). The maximal error was 1.55 mm. CONCLUSIONS The in vivo application accuracy of the Neuromate neurosurgical robot, measured with a system independent from the robot, in frame-based DBS procedures was better than 1 mm. This accuracy is at least similar to the accuracy of stereotactic frame arms and is compatible with the accuracy required in DBS procedures.

Simultaneous inference for the mean of repeated functional data

2018 ◽  
Vol 165 ◽  
pp. 279-295 ◽  
Author(s):  
Guanqun Cao ◽  
Li Wang
Keyword(s):  
Functional Data ◽  
Simultaneous Inference ◽  
The Mean

scholarly journals Principal components applied to modeling: Dealing with the mean vector

2004 ◽  
Vol 29 (4) ◽  
pp. 261-266 ◽  
Author(s):  
James A. Worthey ◽  
Michael H. Brill
Keyword(s):  
Principal Components ◽  
The Mean ◽  
Mean Vector

scholarly journals Joint modelling of paired sparse functional data using principal components

Biometrika ◽  
2008 ◽  
Vol 95 (3) ◽  
pp. 601-619 ◽  
Author(s):  
L. Zhou ◽  
J. Z. Huang ◽  
R. J. Carroll
Keyword(s):  
Principal Components ◽  
Functional Data ◽  
Joint Modelling ◽  
Sparse Functional Data
Sign in / Sign up

Export Citation Format

Share Document