Forcing additivity of biomass tables: some empirical results

1984 ◽  
Vol 14 (3) ◽  
pp. 376-384 ◽  
Author(s):  
T. Cunia ◽  
R. D. Briggs
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Least Squares Regression ◽  
Empirical Results ◽  
Regression Procedure ◽  
Sample Data ◽  
Regression Functions ◽  
Tree Component ◽  
Better Than

Three methods for insuring the additivity of biomass tables are described and their application to a sample of trees illustrated. The advantages and drawbacks of each method are identified and the results obtained compared with each other. All three methods yield biomass tables that are not significantly different from each other (at least for the sample data used), but their estimated precision and conditions of applicability are different. At least one of the methods can be applied to the cases where the weights to use in the least squares regression procedure may differ from one to the next tree component, when sample data of some component are missing from some sample trees and when nonlinear seem better than linear regression functions.

scholarly journals Tolerance Intervals in a Heteroscedastic Linear Regression Context with Applications to Aerospace Equipment Surveillance

2009 ◽  
Vol 2009 ◽  
pp. 1-8 ◽  
Author(s):  
Janet Myhre ◽  
Daniel R. Jeske ◽  
Michael Rennie ◽  
Yingtao Bi
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Performance Metrics ◽  
Weighted Least Squares ◽  
Ordinary Least Squares ◽  
Automated System ◽  
Least Squares Regression ◽  
Data Set ◽  
Tolerance Intervals ◽  
Power Of The Test

A heteroscedastic linear regression model is developed from plausible assumptions that describe the time evolution of performance metrics for equipment. The inherited motivation for the related weighted least squares analysis of the model is an essential and attractive selling point to engineers with interest in equipment surveillance methodologies. A simple test for the significance of the heteroscedasticity suggested by a data set is derived and a simulation study is used to evaluate the power of the test and compare it with several other applicable tests that were designed under different contexts. Tolerance intervals within the context of the model are derived, thus generalizing well-known tolerance intervals for ordinary least squares regression. Use of the model and its associated analyses is illustrated with an aerospace application where hundreds of electronic components are continuously monitored by an automated system that flags components that are suspected of unusual degradation patterns.

Comparison of three different statistical approaches (non-linear least-squares regression, survival analysis and Bayesian inference) in their usefulness for estimating hydrothermal time models of seed germination

2020 ◽  
Vol 30 (1) ◽  
pp. 64-72 ◽  
Author(s):  
Elena Moltchanova ◽  
Shirin Sharifiamina ◽  
Derrick J. Moot ◽  
Ali Shayanfar ◽  
Mark Bloomberg
Keyword(s):  
Seed Germination ◽  
Linear Regression ◽  
Least Squares ◽  
Time Course ◽  
Efficient Estimation ◽  
Model Parameters ◽  
Least Squares Regression ◽  
Hydrothermal Time ◽  
Linear Least Squares ◽  
Non Linear

AbstractHydrothermal time (HTT) models describe the time course of seed germination for a population of seeds under specific temperature and water potential conditions. The parameters of the HTT model are usually estimated using either a linear regression, non-linear least squares estimation or a generalized linear regression model. There are problems with these approaches, including loss of information, and censoring and lack of independence in the germination data. Model estimation may require optimization, and this can have a heavy computational burden. Here, we compare non-linear regression with survival and Bayesian methods, to estimate HTT models for germination of two clover species. All three methods estimated similar HTT model parameters with similar root mean squared errors. However, the Bayesian approach allowed (1) efficient estimation of model parameters without the need for computation-intensive methods and (2) easy comparison of HTT parameters for the two clover species. HTT models that accounted for a species effect were superior to those that did not. Inspection of credibility intervals and estimated posterior distributions for the Bayesian HTT model shows that it is credible that most HTT model parameters were different for the two clover species, and these differences were consistent with known biological differences between species in their germination behaviour.

scholarly journals METODA ZANURZANIA REGRESJI W PRZYPADKU WYSTĘPOWANIA OBSERWACJI NIETYPOWYCH

2019 ◽  
Vol 20 (2) ◽  
pp. 83-92
Author(s):  
Małgorzata Kobylińska
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Least Squares Method ◽  
Regression Function ◽  
Maximum Depth ◽  
Two Dimensional ◽  
Structural Elements ◽  
Linear Regression Function ◽  
Regression Functions

This paper presents the application of the regression maximum depth for the estimation of linear regression function structural elements. For two-dimensional sets including untypical observations, regression functions were developed using the classical least squares method and a method based on the concept of observation depth measure in a sample. The effect of untypical observations on the estimated models has been noted.

scholarly journals Fitting limit lines (envelope curves) to spreads of geoenvironmental data

2021 ◽  
pp. 030913332110599
Author(s):  
Paul A Carling ◽  
Philip Jonathan ◽  
Teng Su
Keyword(s):  
Least Squares ◽  
Lower Limit ◽  
Statistical Models ◽  
Marked Reduction ◽  
Ad Hoc ◽  
Data Sets ◽  
Least Squares Regression ◽  
Sample Data ◽  
Considerable Spread

Geoscientists frequently are interested in defining the overall trend in x- y data clouds using techniques such as least-squares regression. Yet often the sample data exhibits considerable spread of y-values for given x-values, which is itself of interest. In some cases, the data may exhibit a distinct visual upper (or lower) ‘limit’ to a broad spread of y-values for a given x-value, defined by a marked reduction in concentration of y-values. As a function of x-value, the locus of this ‘limit’ defines a ‘limit line’, with no (or few) points lying above (or below) it. Despite numerous examples of such situations in geoscience, there has been little consideration within the general geoenvironmental literature of methods used to define limit lines (sometimes termed ‘envelope curves’ when they enclose all data of interest). In this work, methods to fit limit lines are reviewed. Many commonly applied methods are ad-hoc and statistically not well founded, often because the data sample available is small and noisy. Other methods are considered which correspond to specific statistical models offering more objective and reproducible estimation. The strengths and weaknesses of methods are considered by application to real geoscience data sets. Wider adoption of statistical models would enhance confidence in the utility of fitted limits and promote statistical developments in limit fitting methodologies which are likely to be transformative in the interpretation of limits. Supplements, a spreadsheet and references to software are provided for ready application by geoscientists.

scholarly journals Análisis de métodos de validación cruzada para la obtención robusta de parámetros biofísicos

2015 ◽  
pp. 55 ◽  
Author(s):  
Ll. Pérez-Planells ◽  
J. Delegido ◽  
J. P. Rivera-Caicedo ◽  
J. Verrelst
Keyword(s):  
Linear Regression ◽  
Gaussian Process ◽  
Least Squares ◽  
Partial Least Squares ◽  
Ridge Regression ◽  
Partial Least Squares Regression ◽  
Gaussian Process Regression ◽  
Least Squares Regression ◽  
Kernel Ridge Regression

<p class="Bodytext">Los métodos de regresión no paramétricos son una gran herramienta estadística para obtener parámetros biofísicos a partir de medidas realizadas mediante teledetección. Pero los resultados obtenidos se pueden ver afectados por los datos utilizados en la fase de entrenamiento del modelo. Para asegurarse de que los modelos son robustos, se hace uso de varias técnicas de validación cruzada. Estas técnicas permiten evaluar el modelo con subconjuntos de la base de datos de campo. Aquí, se evalúan dos tipos de validación cruzada en el desarrollo de modelos de regresión no paramétricos: hold-out y k-fold. Los métodos de regresión lineal seleccionados fueron: Linear Regression (LR) y Partial Least Squares Regression (PLSR). Y los métodos no lineales: Kernel Ridge Regression (KRR) y Gaussian Process Regression (GPR). Los resultados de la validación cruzada mostraron que LR ofrece los resultados más inestables, mientras KRR y GPR llevan a resultados más robustos. Este trabajo recomienda utilizar algoritmos de regresión no lineales (como KRR o GPR) combinando con la validación cruzada k-fold con un valor de k igual a 10 para hacer la estimación de una manera robusta.</p>

A Hybrid Modeling Technique for Partially-Known Systems Using Linear Regression and Neural Network

2009 ◽  
Author(s):  
Andrew J. Joslin ◽  
Chengying Xu
Keyword(s):  
Neural Network ◽  
Linear Regression ◽  
Least Squares ◽  
Process Model ◽  
Modeling Method ◽  
Hybrid Modeling ◽  
Model Description ◽  
Least Squares Regression ◽  
The Neural Network ◽  
Macro Scale

In this paper a hybrid modeling and system identification method, combining linear least squares regression and artificial neural network techniques, is presented to model a type of dynamic systems which have an incomplete analytical model description. This approach in modeling nonlinear, partially-understood systems is particularly useful to the study of manufacturing processes, where the linear regression portion of the hybrid model is established using a known mathematical model for the process and the neural network is constructed using the residuals from the least squares regression, therefore ensuring a more precise process model for the specific machining setup, tooling selection, workpiece properties, etc. In this paper the method is mathematically proven to give regression coefficients close to those which would be found if only a regression had been performed. The modeling method is then simulated for a macro-scale hard turning process, and the result proves the effectiveness of the proposed hybrid modeling method.

Least Squares Regression with Integrated or Dynamic Regressors under Weak Error Assumptions

1987 ◽  
Vol 3 (1) ◽  
pp. 98-116 ◽  
Author(s):  
Donald W. K. Andrews
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Least Squares ◽  
Asymptotic Distribution ◽  
Linear Regression Model ◽  
Multiple Regression Model ◽  
Least Squares Regression ◽  
Least Squares Estimators ◽  
Integrated Or ◽  
Weak Error

This paper establishes consistency of least squares estimators in (i) a multiple regression model with integrated regressors and explosive, non-mixing errors, and (ii) a dynamic linear regression model with regressors and errors that may have infinite variances. In the former context, the asymptotic distribution of the least squares estimator also is obtained, in certain cases.

Sign in / Sign up

Export Citation Format

Share Document