A Rank-Invariant Method of Linear and Polynomial Regression Analysis

Theil, Henri

doi:10.1007/978-94-011-2546-8_20

Cited by 1,511 publications

(1,387 citation statements)

References 3 publications

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“…For this purpose, another nonparametric method referred to as the Theil-Sen (TS) approach is very popular among researchers to quantify the slope of the trend (magnitude). TS was originally described by Theil [69] and Sen [70]. This approach provides a more robust slope estimate than the least squares method because it is insensitive to outliers or extreme values and competes well against simple least squares even for normally distributed data in a time series [71,72].…”

Section: Resultsmentioning

confidence: 99%

Precipitation Trends over Slovakia in the Period 1981–2013

Zeleňáková

Vido

Portela

et al. 2017

Water

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Abstract:The objective of this paper was to analyze the temporal and spatial trends in annual and seasonal precipitation in Slovakia utilizing 487 gauging station data collected statewide in the period from 1981 to 2013. The nonparametric Mann-Kendall (MK) statistical test, which has been widely used to assess the significance of trends in hydrological time series, was applied to detect the significant trends. The Theil-Sen (TS) approach was applied to quantify the trend magnitude, and the Sequential Mann-Kendall (SQMK) test was used to detect abrupt temporal trend shifts. In general, precipitation data in the study area have not changed during the last 33 years, and there are no big gaps. However, predominantly increasing trends in precipitation time series were found at most of the gauging stations in Slovakia. The results corroborate previous climatic studies in the area of central Europe. In Slovakia, there is evidence of different rain distribution from the monthly point of view. Decreasing trends were detected in December in the northern part of Slovakia, while the central and southern parts revealed increasing trends. Most of the stations showed increasing summer precipitation trends, especially in July. It is expected that the findings of this comprehensive study of precipitation trends over Slovakia will produce more insights for the understanding of the regional hydrological behavior in Slovakia over the last several decades.

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Section: Resultsmentioning

confidence: 99%

Precipitation Trends over Slovakia in the Period 1981–2013

Zeleňáková

Vido

Portela

et al. 2017

Water

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“…The regression models are specific to each site, and are not intended as predictive tools, but rather as a means to provide insight into the nature of the relationship between the response and explanatory variables. Kendall's tau correlation coefficients (s) [Kendall, 1975] and Kendall-Theil lines [Theil, 1950] were generated to describe the relationships between k and daily variability in dissolved oxygen concentration. All statistical analyses were conducted using R (http://r-project.…”

Section: Methodsmentioning

confidence: 99%

Quantifying watershed‐scale groundwater loading and in‐stream fate of nitrate using high‐frequency water quality data

Miller

Tesoriero

Capel

et al. 2016

Water Resources Research

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We describe a new approach that couples hydrograph separation with high-frequency nitrate data to quantify time-variable groundwater and runoff loading of nitrate to streams, and the net in-stream fate of nitrate at the watershed scale. The approach was applied at three sites spanning gradients in watershed size and land use in the Chesapeake Bay watershed. Results indicate that 58-73% of the annual nitrate load to the streams was groundwater-discharged nitrate. Average annual first-order nitrate loss rate constants (k) were similar to those reported in both modeling and in-stream process-based studies, and were greater at the small streams (0.06 and 0.22 day 21 ) than at the large river (0.05 day 21 ), but 11% of the annual loads were retained/lost in the small streams, compared with 23% in the large river. Larger streambed area to water volume ratios in small streams results in greater loss rates, but shorter residence times in small streams result in a smaller fraction of nitrate loads being removed than in larger streams. A seasonal evaluation of k values suggests that nitrate was retained/lost at varying rates during the growing season. Consistent with previous studies, streamflow and nitrate concentrations were inversely related to k. This new approach for interpreting high-frequency nitrate data and the associated findings furthers our ability to understand, predict, and mitigate nitrate impacts on streams and receiving waters by providing insights into temporal nitrate dynamics that would be difficult to obtain using traditional field-based studies.

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“…The values are obtained from linearization of the curve segments with respect to intervals of ± 0.15 N around the force values of ± 0.8 N and of + 0.55 Nmm around moment values of ± 4 Nmm (Fig. 6) by using distribution-free estimation methods (Dawson-Saunders and Trapp, 1990;Theil, 1950). The load ranges were chosen such as to cover enough data points around the selected load levels and to cover a more-or-less linear region in the upper and lower branch in the curve.…”

Section: Methodsmentioning

confidence: 99%

In vitro laxity-testers for knee joints of mice

Blankevoort

Osch

Janssen

et al. 1996

Journal of Biomechanics

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The knee joints of mice can be used as a model for studying the effects of interventions on knee laxity. The goal of this study was to quantify knee joint laxity in vitro. Three devices were developed: a positioning-and cemcnting device, an anterior-posterior (AP) laxity tester and a varus-valgus (VV) laxity tester. The positioningand cementing device was used to position the joint in a reproducible way and to attach clamping pins to the proximal femur and distal tibia using PMMA. The clamping pins were used to fix the joint to the AP-and VV-testers. In both testers the load was applied by means of a spindle-actuated spring while load and displacements were measured simultaneously. The load-displacement data were used to calculate displacement and compliance parameters, The performance of the testers was evaluated by testing 5 normal knee joints of 5 mice.

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A Rank-Invariant Method of Linear and Polynomial Regression Analysis

Cited by 1,511 publications

References 3 publications

Precipitation Trends over Slovakia in the Period 1981–2013

Precipitation Trends over Slovakia in the Period 1981–2013

Quantifying watershed‐scale groundwater loading and in‐stream fate of nitrate using high‐frequency water quality data

In vitro laxity-testers for knee joints of mice

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