A Least Squares Wind Estimation Technique for Autonomous Parafoils

In the last few years, traffic congestions are often occurred in Yogyakarta. This situation is caused byÂ the increasing number of vehicles in Yogyakarta.This study evaluates the effect of the gross regional domesticproduct (PDRB), the people of Daerah Istimewa Yogyakarta (JP), and region income (PD) to the number ofÂ vehicles in Daerah Istimewa Yogyakarta (JKB). The model consists of one behavioral equation: the numberÂ of vehicles equation. The estimation technique uses Ordinary Least Squares (OLS). MacKinnon, White, andÂ Davidson test (MWD test) is used to choose between the two models: linear regression model or log-linearregression model.The sample covers observations for 23 years (1990 - 2012). The data are obtained from (1)Â Bank Indonesia (2) Badan Pusat Statistik DIY and various other sources. It is found that individually lnJP andlnPD are statistically significant (positive) except ln PDRB on the basis of (separate) t test. It is also found that onÂ the basis of the F test collectively all the regressors have a significant effect on the regressand lnJKB.Keywords: the number of vehicles, traffic congestion, linear regression model, log-linear regression model.

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Total Least-Squares Collocation: An Optimal Estimation Technique for the EIV-Model with Prior Information

Mathematics ◽

10.3390/math8060971 ◽

2020 ◽

Vol 8 (6) ◽

pp. 971

Author(s):

Burkhard Schaffrin

Keyword(s):

Least Squares ◽

Random Effects ◽

Prior Information ◽

Optimal Estimation ◽

Total Least Squares ◽

Data Matrix ◽

Estimation Technique ◽

Least Squares Collocation ◽

Wide Range ◽

Least Squares Adjustment

In regression analysis, oftentimes a linear (or linearized) Gauss-Markov Model (GMM) is used to describe the relationship between certain unknown parameters and measurements taken to learn about them. As soon as there are more than enough data collected to determine a unique solution for the parameters, an estimation technique needs to be applied such as ‘Least-Squares adjustment’, for instance, which turns out to be optimal under a wide range of criteria. In this context, the matrix connecting the parameters with the observations is considered fully known, and the parameter vector is considered fully unknown. This, however, is not always the reality. Therefore, two modifications of the GMM have been considered, in particular. First, ‘stochastic prior information’ (p. i.) was added on the parameters, thereby creating the – still linear – Random Effects Model (REM) where the optimal determination of the parameters (random effects) is based on ‘Least Squares collocation’, showing higher precision as long as the p. i. was adequate (Wallace test). Secondly, the coefficient matrix was allowed to contain observed elements, thus leading to the – now nonlinear – Errors-In-Variables (EIV) Model. If not using iterative linearization, the optimal estimates for the parameters would be obtained by ‘Total Least Squares adjustment’ and with generally lower, but perhaps more realistic precision. Here the two concepts are combined, thus leading to the (nonlinear) ’EIV-Model with p. i.’, where an optimal estimation (resp. prediction) technique is developed under the name of ‘Total Least-Squares collocation’. At this stage, however, the covariance matrix of the data matrix – in vector form – is still being assumed to show a Kronecker product structure.

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Insights from analysing tourist expenditure using quantile regression

Tourism Economics ◽

10.1177/1354816616668108 ◽

2016 ◽

Vol 23 (5) ◽

pp. 1138-1145 ◽

Cited By ~ 5

Author(s):

António Almeida ◽

Brian Garrod

Keyword(s):

Quantile Regression ◽

Least Squares ◽

Empirical Studies ◽

Ordinary Least Squares ◽

Estimation Technique ◽

Least Squares Regression ◽

Data Set ◽

Detailed Understanding ◽

Tourism Destinations ◽

Single Data

Mature tourism destinations are increasingly needing to diversify their products and markets. To be successful, such strategies require a very detailed understanding of potential tourists’ levels and patterns of spending. Empirical studies of tourist expenditure have tended to employ ordinary least squares regression for this purpose. There are, however, a number of important limitations to this technique, chief among which is its inability to distinguish between tourists who have higher- and lower-than-average levels of spending. As such, some researchers recommend the use of an alternative estimation technique, known as quantile regression, which does allow such distinctions to be made. This study uses a single data set, collected among rural tourists in Madeira, to analyse the determinants of tourist expenditure using both techniques. This enables direct comparison to be made and illustrates the additional insights to be gained using quantile regression.

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