Harmonizing biomass tables by generalized least squares

1985 ◽  
Vol 15 (2) ◽  
pp. 331-340 ◽  
Author(s):  
T. Cunia ◽  
R. D. Briggs
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Weighted Least Squares ◽  
Regression Function ◽  
Generalized Least Squares ◽  
Ordinary Least Squares ◽  
Sample Tree ◽  
Tree Data ◽  
Regression Techniques ◽  
Ordinary Least Squares Method

To construct biomass tables for various tree components that are consistent with each other, one may use linear regression techniques with dummy variables. When the biomass of these components is measured on the same sample trees, one should also use the generalized rather than ordinary least squares method. A procedure is shown which allows the estimation of the covariance matrix of the sample biomass values and circumvents the problem of storing and inverting large covariance matrices. Applied to 20 sets of sample tree data, the generalized least squares regressions generated estimates which, on the average were slightly higher (about 1%) than the sample data. The confidence and prediction bands about the regression function were wider, sometimes considerably wider than those estimated by the ordinary weighted least squares.

Forcing additivity of biomass tables: use of the generalized least squares method

1985 ◽  
Vol 15 (1) ◽  
pp. 23-28 ◽  
Author(s):  
T. Cunia ◽  
R. D. Briggs
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Weighted Least Squares ◽  
Generalized Least Squares ◽  
Ordinary Least Squares ◽  
Prediction Intervals ◽  
Sample Tree ◽  
Generalized Least Squares Method ◽  
Tree Data ◽  
Biomass Components

The generalized least squares procedure is applied to sample tree data for which additive biomass tables are required. This procedure is proposed as an alternative to the ordinary weighted least squares in order to account for the fact that several biomass components are measured on the same sample trees. The biomass tables generated by the generalized and the ordinary least squares are very similar, the confidence intervals are sometimes wider, sometimes narrower, but the prediction intervals are always narrower for the generalized least squares method.

scholarly journals GM(1,1;λ) with Constrained Linear Least Squares

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 278
Author(s):  
Ming-Feng Yeh ◽  
Ming-Hung Chang
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Model Fitting ◽  
Ordinary Least Squares ◽  
Linear Least Squares ◽  
Unknown Parameters ◽  
Constrained Problems ◽  
Linear Least Squares Problems ◽  
Ordinary Least Squares Method ◽  
Better Than

The only parameters of the original GM(1,1) that are generally estimated by the ordinary least squares method are the development coefficient a and the grey input b. However, the weight of the background value, denoted as λ, cannot be obtained simultaneously by such a method. This study, therefore, proposes two simple transformation formulations such that the unknown parameters, and can be simultaneously estimated by the least squares method. Therefore, such a grey model is termed the GM(1,1;λ). On the other hand, because the permission zone of the development coefficient is bounded, the parameter estimation of the GM(1,1) could be regarded as a bound-constrained least squares problem. Since constrained linear least squares problems generally can be solved by an iterative approach, this study applies the Matlab function lsqlin to solve such constrained problems. Numerical results show that the proposed GM(1,1;λ) performs better than the GM(1,1) in terms of its model fitting accuracy and its forecasting precision.

scholarly journals Optimal data processing in the ballistic laser gravimeter under the effect of correlated interference

2021 ◽  
pp. 10-16
Author(s):  
Anatolii Omelchenko ◽  
Oleksandr Vinnichenko ◽  
Pavel Neyezhmakov ◽  
Oleksii Fedorov ◽  
Volodymyr Bolyuh
Keyword(s):  
Mathematical Model ◽  
Data Processing ◽  
Least Squares ◽  
Measurement Method ◽  
Weighted Least Squares ◽  
Generalized Least Squares ◽  
Ordinary Least Squares ◽  
Gravitational Acceleration ◽  
Time Data ◽  
Hahn Polynomials

Abstract In order to develop optimal data processing algorithms in ballistic laser gravimeters under the effect of correlated interference, the method of generalized least squares is applied. In this case, to describe the interference, a mathematical model of the autoregression process is used, for which the inverse correlation matrix has a band type and is expressed through the values of the autoregression coefficients. To convert the “path-time” data from the output of the coincidence circuit of ballistic laser gravimeters to a process uniform in time, their local quadratic interpolation is used. Algorithms for data processing in a ballistic gravimeter, developed on the basis of a method of weighted least squares using orthogonal Hahn polynomials, are considered. To implement a symmetric measurement method, the symmetric Hahn polynomials, characterized by one parameter, are used. The method of mathematical modelling is used to study the gain in the accuracy of measuring the gravitational acceleration by the synthesized algorithms in comparison with the algorithm based on the method of least squares. It is shown that auto seismic interference in ballistic laser gravimeters with a symmetric measurement method can be significantly reduced by using a mathematical model of the second-order autoregressive process in the method of generalized least squares. A comparative analysis of the characteristics of the algorithms developed using the method of generalized least squares, the method of weighted least squares and the method of ordinary least squares is carried out.

scholarly journals Linear modeling and regression for exponential engineering functions by a generalized ordinary least squares method

2014 ◽  
Vol 3 (2) ◽  
pp. 174
Author(s):  
Yaser Abdelhadi
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Simulated Data ◽  
Ordinary Least Squares ◽  
Parametric Estimation ◽  
Linear Least Squares ◽  
Linear Modeling ◽  
Linear Transformations ◽  
Data Points ◽  
Ordinary Least Squares Method

Linear transformations are performed for selected exponential engineering functions. The Optimum values of parameters of the linear model equation that fits the set of experimental or simulated data points are determined by the linear least squares method. The classical and matrix forms of ordinary least squares are illustrated. Keywords: Exponential Functions; Linear Modeling; Ordinary Least Squares; Parametric Estimation; Regression Steps.

Metrological evaluation of a bourdon manometer from the ordinary least squares method

2018 ◽  
Vol 11 (94) ◽  
pp. 4681-4689
Author(s):  
Cristian Pedraza-Yepes ◽  
Jose Daniel Hernandez-Vasquez ◽  
Fernando Pastor Forero ◽  
Leonardo Perez Manotas ◽  
Jorge Gonzalez-Coneo
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Ordinary Least Squares ◽  
Metrological Evaluation ◽  
Ordinary Least Squares Method

Characteristics of visitor expenditure in Macao and their impact on its economic growth

2018 ◽  
Vol 24 (2) ◽  
pp. 218-233 ◽  
Author(s):  
Wang Jingwen ◽  
Liang Mingzhu
Keyword(s):  
Economic Growth ◽  
Gross Domestic Product ◽  
Least Squares ◽  
Least Squares Method ◽  
Ordinary Least Squares ◽  
Consumer Group ◽  
Tourism Experience ◽  
Ordinary Least Squares Method ◽  
Statistical Indicators ◽  
Consumption Habits

This article assesses the economic impact of visitor expenditure in Macao and the impacts of major expense types to the visitor expenditure. As consumption habits are changing gradually, which can be reflected in the consumption habits of the tourists, we concentrate on the characteristics of visitor expenditure to analyze the factors that drive up the consumption. This article analyzes the relative statistical indicators from 2010 to 2016 in Macao using the ordinary least squares method. According to empirical analysis of this study, 1 Macanese Patacas (MOP) of visitor expenditure can create 7.896 MOP in additional gross domestic product (GDP) in Macao. Moreover, “transportation” and “shopping” present obvious equal status on the pulling function to the visitor expenditure, which indicates that a better transportation system can increase more consumption opportunities. The items of “shopping” and “cosmetics and perfume” have a distinctively high pulling function to the visitor expenditure. This indicates that the power of female consumer group should be emphasized. Compared with other commodities, we observed the obvious pulling function of “local food products,” which shows that the culture-based tourism experience will be helpful to promote the visitor expenditure. In discussing the results, relevant suggestions for developing the diversified tourism in Macao are presented in the article.

Calibration of stormwater quality regression models: a random process?

2010 ◽  
Vol 62 (4) ◽  
pp. 875-882 ◽  
Author(s):  
A. Dembélé ◽  
J.-L. Bertrand-Krajewski ◽  
B. Barillon
Keyword(s):  
Experimental Data ◽  
Least Squares ◽  
Regression Models ◽  
Linear Models ◽  
Least Squares Method ◽  
Weighted Least Squares ◽  
Ordinary Least Squares ◽  
Data Sets ◽  
Data Set ◽  
Urban Catchments

Regression models are among the most frequently used models to estimate pollutants event mean concentrations (EMC) in wet weather discharges in urban catchments. Two main questions dealing with the calibration of EMC regression models are investigated: i) the sensitivity of models to the size and the content of data sets used for their calibration, ii) the change of modelling results when models are re-calibrated when data sets grow and change with time when new experimental data are collected. Based on an experimental data set of 64 rain events monitored in a densely urbanised catchment, four TSS EMC regression models (two log-linear and two linear models) with two or three explanatory variables have been derived and analysed. Model calibration with the iterative re-weighted least squares method is less sensitive and leads to more robust results than the ordinary least squares method. Three calibration options have been investigated: two options accounting for the chronological order of the observations, one option using random samples of events from the whole available data set. Results obtained with the best performing non linear model clearly indicate that the model is highly sensitive to the size and the content of the data set used for its calibration.

Total Least-Squares Methods for Active View Registration of Three-Dimensional Line Laser Scanning Data

2004 ◽  
Vol 127 (1) ◽  
pp. 50-56 ◽  
Author(s):  
F. Xi ◽  
D. Nancoo ◽  
G. Knopf
Keyword(s):  
Least Squares ◽  
Laser Scanning ◽  
Least Squares Method ◽  
Three Dimensional ◽  
Measurement Data ◽  
Ordinary Least Squares ◽  
Total Least Squares ◽  
Position Measurement ◽  
Point Position ◽  
Ordinary Least Squares Method

In this paper a method is proposed to register three-dimensional line laser scanning data acquired in two different viewpoints. The proposed method is based on three-point position measurement by scanning three reference balls to determine the transformation between two views. Since there are errors in laser scanning data and sphere fitting, the two sets of three-point position measurement data at two different views are both subject to errors. For this reason, total least-squares methods are applied to determine the transformation, because they take into consideration the errors both at inputs and outputs. Simulations and experiment are carried to compare three methods, namely, ordinary least-squares method, unconstrained total least-squares method, and constrained total least-squares method. It is found that the last method gives the most accurate results.

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