Why Us? >>

  • - Open Access
  • - Peer-reviewed
  • - Rapid publication
  • - Lifetime hosting
  • - Free indexing service
  • - Free promotion service
  • - More citations
  • - Search engine friendly

Free SCIRP Newsletters>>

Add your e-mail address to receive free newsletters from SCIRP.

 

Contact Us >>

WhatsApp  +86 18163351462(WhatsApp)
   
Paper Publishing WeChat
Book Publishing WeChat
(or Email:book@scirp.org)

Article citations

More>>

Paris, Q. (2015) The Dual of the Least-Squares Method. Open Journal of Statistics, 5, 658-664.
http://dx.doi.org/10.4236/ojs.2015.57067

has been cited by the following article:

  • TITLE: The Dual of the Maximum Likelihood

    AUTHORS: Quirino Paris

    KEYWORDS: Maximum Likelihood, Primal, Dual, Signal, Noise, Value of Sample Information

    JOURNAL NAME: Open Journal of Statistics, Vol.6 No.1, February 26, 2016

    ABSTRACT: The Maximum Likelihood method estimates the parameter values of a statistical model that maximizes the corresponding likelihood function, given the sample information. This is the primal approach that, in this paper, is presented as a mathematical programming specification whose solution requires the formulation of a Lagrange problem. A result of this setup is that the Lagrange multipliers associated with the linear statistical model (where sample observations are regarded as a set of constraints) are equal to the vector of residuals scaled by the variance of those residuals. The novel contribution of this paper consists in deriving the dual model of the Maximum Likelihood method under normality assumptions. This model minimizes a function of the variance of the error terms subject to orthogonality conditions between the model residuals and the space of explanatory variables. An intuitive interpretation of the dual problem appeals to basic elements of information theory and an economic interpretation of Lagrange multipliers to establish that the dual maximizes the net value of the sample information. This paper presents the dual ML model for a single regression and provides a numerical example of how to obtain maximum likelihood estimates of the parameters of a linear statistical model using the dual specification.