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.

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.

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.

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.

scholarly journals Parameter Estimation for Long-Memory Stochastic Volatility at Discrete Observation

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Xiaohui Wang ◽  
Weiguo Zhang
Keyword(s):  
Least Squares ◽  
Stochastic Volatility ◽  
Long Memory ◽  
Least Squares Method ◽  
Ordinary Least Squares ◽  
Discrete Observations ◽  
Least Squares Estimators ◽  
And Diffusion ◽  
Ordinary Least Squares Method ◽  
Explicit Estimators

Ordinary least squares estimators of variogram parameters in long-memory stochastic volatility are studied in this paper. We use the discrete observations for practical purposes under the assumption that the Hurst parameterH∈(1/2,1)is known. Based on the ordinary least squares method, we obtain both the explicit estimators for drift and diffusion by minimizing the distance function between the variogram and the data periodogram. Furthermore, the resulting estimators are shown to be consistent and to have the asymptotic normality. Numerical examples are also presented to illustrate the performance of our method.

Ridge Regression in the Presence of Multicollinearity

1984 ◽  
Vol 54 (2) ◽  
pp. 559-566 ◽  
Author(s):  
Rashmi Garg
Keyword(s):  
Social Sciences ◽  
Least Squares ◽  
Simple Form ◽  
Ridge Regression ◽  
Least Squares Method ◽  
Ordinary Least Squares ◽  
Regression Coefficients ◽  
Predictor Variables ◽  
Regression Problems ◽  
Ordinary Least Squares Method

The ordinary least squares solution is generally applied to multiple regression problems in social sciences. When the intercorrelations among predictor variables are close to one, the estimates of regression coefficients obtained from ordinary least squares are very unstable. This situation is often referred to as near multicollinearity. When there is a problem of near mulricollinearity, the ridge regression provides an alternative to the ordinary least squares method. The ridge estimates are biased but more stable from sample to sample. The purpose of this article is to describe the method of ridge regression in a simple form and to provide examples of its application.

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