Tassus Posted July 18, 2015 Share Posted July 18, 2015 Please see the attached file. Many thanks, T. question_max_functional.pdf Link to comment Share on other sites More sharing options...
imatfaal Posted July 19, 2015 Share Posted July 19, 2015 ! Moderator Note Please put the question here on the forum. Lots of members will not read/download a file from the Net. Link to comment Share on other sites More sharing options...
Tassus Posted July 20, 2015 Author Share Posted July 20, 2015 Ok thank you, I hope now is fine. Please, tell me if the following statement is true or false and if it is possible give me some reference. Many Thanks. T. Link to comment Share on other sites More sharing options...
Tassus Posted December 14, 2015 Author Share Posted December 14, 2015 Please see the updated version: Under what conditions can we state the following? [latex]\max_{\theta>0} F \left( \theta \right)= \int_{\rho_{min}}^{\rho_{max}} g \left( \rho \right)\pi\left(\rho,\widehat{\theta \left( \rho \right)} \right)d\rho[/latex] where, [latex]F\left ( \theta \right )=\int_{\rho_{min}}^{\rho_{max}}g\left(\rho \right )\pi\left(\rho,\theta \right)d\rho[/latex] and [latex]\widehat{\theta\left( \rho \right)}[/latex] is the argument that maximize [latex]\pi(\rho,\theta)[/latex] with respect to [latex]\theta[/latex] Let [latex]\rho_{min}=0[/latex] and [latex]\rho_{max}=1[/latex]. Assume also that [latex]g(\theta)[/latex] and [latex]\pi(\rho,\theta)[/latex] are proper unimodal densities of [latex]\rho[/latex] and the parameter [latex]\theta>0[/latex] Alternatively, we can state the problem in the following way: Determine the conditions that satisfy [latex]\max_{\theta>0} F \left( \theta \right)= \int_{0}^{1} g \left( \rho \right)\max_{\theta>0}(\pi\left(\rho,\theta \right))d\rho[/latex] Link to comment Share on other sites More sharing options...
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