scholarly journals Continuous L1 Norm Estimation of Lorenz Curve

2019 ◽  
Vol 1 (1) ◽  
pp. 41-49
Author(s):  
Bijan Bidabad

In this paper, the L1 norm of continuous functions and corresponding continuous estimation of regression parameters are defined. The continuous L1 norm estimation problem of one and two parameters linear models in the continuous case is solved. We proceed to use the functional form and parameters of the probability distribution function of income to exactly determine the L1 norm approximation of the corresponding Lorenz curve of the statistical population under consideration.    

2019 ◽  
Vol 3 (1) ◽  
pp. 11-21
Author(s):  
Bijan Bidabad

In this paper, the L1 norm of continuous functions and corresponding continuous estimation of regression parameters are defined. The continuous L1 norm estimation problem of one and two parameters linear models in the continuous case are solved. We proceed to use the functional form and parameters of the probability distribution function of income to exactly determine the L1 norm approximation of the corresponding Lorenz curve of the statistical population under consideration. Iran family budget data were used to estimate income distribution for the period of 1362-1370.  


2019 ◽  
Vol 4 (2) ◽  
pp. 11-26
Author(s):  
Bijan Bidabad

In this paper, the L1 norm of continuous functions and corresponding continuous estimation of regression parameters are defined. The continuous L1 norm estimation problems of linear one and two parameters models are solved. We proceed to use the functional form and parameters of the probability distribution function of income to exactly determine the L1 norm approximation of the corresponding Lorenz curve of the statistical population under consideration. U.S. economic data used to estimate income distribution. An interesting finding of these calculations is that the distribution of income obeys counter-wise business cycles fluctuations. This finding is a new area for research in the realm of the theory and application of income distribution and business cycles interrelationship.


Econometrica ◽  
1984 ◽  
Vol 52 (5) ◽  
pp. 1313 ◽  
Author(s):  
Manash Ranjan Gupta

2019 ◽  
Vol 1 (1) ◽  
pp. 1-18
Author(s):  
Bijan Bidabad

In this paper, we propose four algorithms for L1 norm computation of regression parameters, where two of them are more efficient for simple and multiple regression models.  However, we start with restricted simple linear regression and corresponding derivation and computation of the weighted median problem. In this respect, a computing function is coded.  With discussion on the m parameters model, we continue to expand the algorithm to include unrestricted simple linear regression, and two crude and efficient algorithms are proposed. The procedures are then generalized to the m parameters model by presenting two new algorithms, where the algorithm 4 is selected as more efficient. Various properties of these algorithms are discussed.


1996 ◽  
Vol 72 (1-2) ◽  
pp. 251-274 ◽  
Author(s):  
Hang K. Ryu ◽  
Daniel J. Slottje

2020 ◽  
Vol 4 (2) ◽  
pp. 1-23
Author(s):  
Dane Bax ◽  
◽  
Temesgen Zewotir ◽  
Delia North ◽  

Due to the heterogeneous nature of residential properties, determining selling prices which will reconcile supply and demand is difficult. Establishing realistic listing prices is vitally important for sellers to prevent prolonged time on market. Sellers have several resources available to assist in this endeavour, all of which involve understanding current market dynamics through analysing recent sales and listing data. Property portals which aggregate real estate agencies’ data, hosting it on online platforms, are one such resource, along with individual real estate agencies. Leveraging this data to develop solutions that could aid sellers in listing price decision making is a potential business objective that could not only add value to sellers but create a competitive advantage by increasing traffic to an online real estate platform. Using data provided by a South African online property portal, this paper creates a web application using machine learning to estimate listing prices for different types of homes throughout South Africa. This study compared log linear and gradient boosted models, estimating residential listing prices over a four-year period. The results indicate that although log linear models are suitable to account for spatial dependency in the data through the inclusion of a fixed location effect, the assumption of linear functional form was not satisfied. The gradient boosted models do not impose explicit functional form requirements, making them flexible candidates. Similarly, these models were able to handle the spatial dependency adequately. The gradient boosted models also achieved a lower out of sample error compared to the log linear models. The findings show that over observation periodperiod, larger properties consistently experience a diminishing return at some point over the marginal distribution of physical characteristics. The web application details how sellers are easily able to obtain mean listing price estimates and gauge the growth thereof, by simply inputting their property interest criteria.


2019 ◽  
Vol 24 (3) ◽  
pp. 234-241 ◽  
Author(s):  
Antje Janosch ◽  
Carolin Kaffka ◽  
Marc Bickle

Phenotypic screens using automated microscopy allow comprehensive measurement of the effects of compounds on cells due to the number of markers that can be scored and the richness of the parameters that can be extracted. The high dimensionality of the data is both a rich source of information and a source of noise that might hide information. Many methods have been proposed to deal with this complex data in order to reduce the complexity and identify interesting phenotypes. Nevertheless, the majority of laboratories still only use one or two parameters in their analysis, likely due to the computational challenges of carrying out a more sophisticated analysis. Here, we present a novel method that allows discovering new, previously unknown phenotypes based on negative controls only. The method is compared with L1-norm regularization, a standard method to obtain a sparse matrix. The analytical pipeline is implemented in the open-source software KNIME, allowing the implementation of the method in many laboratories, even ones without advanced computing knowledge.


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