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Neyman–Pearson Lemma: Lemma, Statistical Hypothesis Testing, Likelihood-ratio Test, Jerzy Neyman, Egon Pearson - Couverture souple

 
9786130493028: Neyman–Pearson Lemma: Lemma, Statistical Hypothesis Testing, Likelihood-ratio Test, Jerzy Neyman, Egon Pearson
Couverture souple
ISBN 10 : 6130493029 ISBN 13 : 9786130493028
Editeur : Betascript Publishing, 2010

Synopsis

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In statistics, the Neyman-Pearson lemma states that when performing a hypothesis test between two point hypotheses H0: θ = θ0 and H1: θ = θ1, then the likelihood-ratio test which rejects H0 in favour of H1 when Lambda(x)=frac{ L( theta _{0} mid x)}{ L (theta _{1} mid x)} leq eta text{ where } P(Lambda(X)leq eta|H_0)=alpha is the most powerful test of size α for a threshold η. If the test is most powerful for all theta_1 in Theta_1, it is said to be uniformly most powerful (UMP) for alternatives in the set Theta_1 , . It is named for Jerzy Neyman and Egon Pearson. In practice, the likelihood ratio is often used directly to construct tests — see Likelihood-ratio test. However it can also be used to suggest particular test-statistics that might be of interest or to suggest simplified tests — for this one considers algebraic manipulation of the ratio to see if there are key statistics in it is related to the size of the ratio (i.e. whether a large statistic corresponds to a small ratio or to a large one).

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In statistics, the Neyman-Pearson lemma states that when performing a hypothesis test between two point hypotheses H0: θ = θ0 and H1: θ = θ1, then the likelihood-ratio test which rejects H0 in favour of H1 when Lambda(x)=frac{ L( theta _{0} mid x)}{ L (theta _{1} mid x)} leq eta text{ where } P(Lambda(X)leq eta|H_0)=alpha is the most powerful test of size α for a threshold η. If the test is most powerful for all theta_1 in Theta_1, it is said to be uniformly most powerful (UMP) for alternatives in the set Theta_1 , . It is named for Jerzy Neyman and Egon Pearson. In practice, the likelihood ratio is often used directly to construct tests — see Likelihood-ratio test. However it can also be used to suggest particular test-statistics that might be of interest or to suggest simplified tests — for this one considers algebraic manipulation of the ratio to see if there are key statistics in it is related to the size of the ratio (i.e. whether a large statistic corresponds to a small ratio or to a large one).

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Betascript Publishing
Date d'édition
2010
Langue
anglais
ISBN 10 
6130493029
ISBN 13 
9786130493028
Reliure
Broché
Nombre de pages
100
Éditeur
Surhone Lambert M., Timpledon Miriam T., Marseken Susan F.
Coordonnées du fabricant
non disponible
Personne responsable
non disponible