Trying to understand some concepts of Measure Theory for Statistical Inference

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I have the next set of measures $P_theta,thetain Theta$ for a parameter space $Theta$. I found the next statement in a book:



$$boxedtextWe assume that the measures P_theta;textare all dominated by some sigmatext-finite textmeasure Q,;textso that the density function f_X(cdot;theta);textunder P_theta;textof X;textwith respect to Q;textexists. Formally, f_X(cdot;theta);textis the Radon-Nikodym derivate of P_theta;textwith respect to Q.$$



I have never been in a Measure Theory class, so for me most of the concepts are new. I have try to study myself but I end up with the same questions.



Is there a way to understand the statement without going to the details? I just want to move on to study statistical inference.



Will I have some problems understanding some concepts of statistics if I don't understand the concepts related to the statement presentend?




probability-theory measure-theory statistical-inference




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  • 1




    This is a fairly deep result (existence of Radon-Nikodym derivative). Just read the statement as you have a bunch of probability densities and move on (assuming you learned about densities in your elementary probability class, how you compute stuff with them and their properties ).
    – Calculon
    Jul 16 at 16:56










  • Yes, I have a solid background in probability distributions, both univariate and multivariate. But, will I have some problems understanding some concepts of statistics if I don't understand the concepts related to the statement presentend?
    – Roberto Cabal
    Jul 16 at 17:02










  • I doubt it. I would suggest you move forward and if you encounter anything you don't understand, just ask here.
    – Calculon
    Jul 16 at 17:04










  • Thanks a lot! I'll move forward.
    – Roberto Cabal
    Jul 16 at 17:06










  • You are welcome. Good luck.
    – Calculon
    Jul 16 at 17:12














up vote
1
down vote

favorite












I have the next set of measures $P_theta,thetain Theta$ for a parameter space $Theta$. I found the next statement in a book:



$$boxedtextWe assume that the measures P_theta;textare all dominated by some sigmatext-finite textmeasure Q,;textso that the density function f_X(cdot;theta);textunder P_theta;textof X;textwith respect to Q;textexists. Formally, f_X(cdot;theta);textis the Radon-Nikodym derivate of P_theta;textwith respect to Q.$$



I have never been in a Measure Theory class, so for me most of the concepts are new. I have try to study myself but I end up with the same questions.



Is there a way to understand the statement without going to the details? I just want to move on to study statistical inference.



Will I have some problems understanding some concepts of statistics if I don't understand the concepts related to the statement presentend?




probability-theory measure-theory statistical-inference




share|cite|improve this question

















  • 1




    This is a fairly deep result (existence of Radon-Nikodym derivative). Just read the statement as you have a bunch of probability densities and move on (assuming you learned about densities in your elementary probability class, how you compute stuff with them and their properties ).
    – Calculon
    Jul 16 at 16:56










  • Yes, I have a solid background in probability distributions, both univariate and multivariate. But, will I have some problems understanding some concepts of statistics if I don't understand the concepts related to the statement presentend?
    – Roberto Cabal
    Jul 16 at 17:02










  • I doubt it. I would suggest you move forward and if you encounter anything you don't understand, just ask here.
    – Calculon
    Jul 16 at 17:04










  • Thanks a lot! I'll move forward.
    – Roberto Cabal
    Jul 16 at 17:06










  • You are welcome. Good luck.
    – Calculon
    Jul 16 at 17:12












up vote
1
down vote

favorite









up vote
1
down vote

favorite











I have the next set of measures $P_theta,thetain Theta$ for a parameter space $Theta$. I found the next statement in a book:



$$boxedtextWe assume that the measures P_theta;textare all dominated by some sigmatext-finite textmeasure Q,;textso that the density function f_X(cdot;theta);textunder P_theta;textof X;textwith respect to Q;textexists. Formally, f_X(cdot;theta);textis the Radon-Nikodym derivate of P_theta;textwith respect to Q.$$



I have never been in a Measure Theory class, so for me most of the concepts are new. I have try to study myself but I end up with the same questions.



Is there a way to understand the statement without going to the details? I just want to move on to study statistical inference.



Will I have some problems understanding some concepts of statistics if I don't understand the concepts related to the statement presentend?




probability-theory measure-theory statistical-inference




share|cite|improve this question













I have the next set of measures $P_theta,thetain Theta$ for a parameter space $Theta$. I found the next statement in a book:



$$boxedtextWe assume that the measures P_theta;textare all dominated by some sigmatext-finite textmeasure Q,;textso that the density function f_X(cdot;theta);textunder P_theta;textof X;textwith respect to Q;textexists. Formally, f_X(cdot;theta);textis the Radon-Nikodym derivate of P_theta;textwith respect to Q.$$



I have never been in a Measure Theory class, so for me most of the concepts are new. I have try to study myself but I end up with the same questions.



Is there a way to understand the statement without going to the details? I just want to move on to study statistical inference.



Will I have some problems understanding some concepts of statistics if I don't understand the concepts related to the statement presentend?





probability-theory measure-theory statistical-inference





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited Jul 16 at 17:02
























asked Jul 16 at 16:46









Roberto Cabal

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1137







  • 1




    This is a fairly deep result (existence of Radon-Nikodym derivative). Just read the statement as you have a bunch of probability densities and move on (assuming you learned about densities in your elementary probability class, how you compute stuff with them and their properties ).
    – Calculon
    Jul 16 at 16:56










  • Yes, I have a solid background in probability distributions, both univariate and multivariate. But, will I have some problems understanding some concepts of statistics if I don't understand the concepts related to the statement presentend?
    – Roberto Cabal
    Jul 16 at 17:02










  • I doubt it. I would suggest you move forward and if you encounter anything you don't understand, just ask here.
    – Calculon
    Jul 16 at 17:04










  • Thanks a lot! I'll move forward.
    – Roberto Cabal
    Jul 16 at 17:06










  • You are welcome. Good luck.
    – Calculon
    Jul 16 at 17:12












  • 1




    This is a fairly deep result (existence of Radon-Nikodym derivative). Just read the statement as you have a bunch of probability densities and move on (assuming you learned about densities in your elementary probability class, how you compute stuff with them and their properties ).
    – Calculon
    Jul 16 at 16:56










  • Yes, I have a solid background in probability distributions, both univariate and multivariate. But, will I have some problems understanding some concepts of statistics if I don't understand the concepts related to the statement presentend?
    – Roberto Cabal
    Jul 16 at 17:02










  • I doubt it. I would suggest you move forward and if you encounter anything you don't understand, just ask here.
    – Calculon
    Jul 16 at 17:04










  • Thanks a lot! I'll move forward.
    – Roberto Cabal
    Jul 16 at 17:06










  • You are welcome. Good luck.
    – Calculon
    Jul 16 at 17:12







1




1




This is a fairly deep result (existence of Radon-Nikodym derivative). Just read the statement as you have a bunch of probability densities and move on (assuming you learned about densities in your elementary probability class, how you compute stuff with them and their properties ).
– Calculon
Jul 16 at 16:56




This is a fairly deep result (existence of Radon-Nikodym derivative). Just read the statement as you have a bunch of probability densities and move on (assuming you learned about densities in your elementary probability class, how you compute stuff with them and their properties ).
– Calculon
Jul 16 at 16:56












Yes, I have a solid background in probability distributions, both univariate and multivariate. But, will I have some problems understanding some concepts of statistics if I don't understand the concepts related to the statement presentend?
– Roberto Cabal
Jul 16 at 17:02




Yes, I have a solid background in probability distributions, both univariate and multivariate. But, will I have some problems understanding some concepts of statistics if I don't understand the concepts related to the statement presentend?
– Roberto Cabal
Jul 16 at 17:02












I doubt it. I would suggest you move forward and if you encounter anything you don't understand, just ask here.
– Calculon
Jul 16 at 17:04




I doubt it. I would suggest you move forward and if you encounter anything you don't understand, just ask here.
– Calculon
Jul 16 at 17:04












Thanks a lot! I'll move forward.
– Roberto Cabal
Jul 16 at 17:06




Thanks a lot! I'll move forward.
– Roberto Cabal
Jul 16 at 17:06












You are welcome. Good luck.
– Calculon
Jul 16 at 17:12




You are welcome. Good luck.
– Calculon
Jul 16 at 17:12















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