翻訳と辞書 Words near each other ・ Twister...Ride it Out ・ Twisterlend ・ Twisters ・ Twistesee ・ Twistetal ・ TWISTEX ・ Twistgrip ・ Twistie ・ Twisties ・ Twistin' at the Woodchopper's Ball ・ Twistin' Postman ・ Twistin' the Night Away ・ Twistin' the Night Away (album) ・ Twisting and Shouting ・ Twisting by the Pool ・ Twisting properties ・ Twisting the Jug ・ Twistlock ・ Twisto ・ Twiston ・ Twistor ・ Twistor correspondence ・ Twistor memory ・ Twistor space ・ Twistor string theory ・ Twistor theory ・ Twistringen ・ Twistringen station ・ Twists of curves ・ Twists of Fate Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Twisting properties ： ウィキペディア英語版 Twisting properties Starting with a sample $\backslash$ observed from a random variable ''X'' having a given distribution law with a non-set parameter, a parametric inference problem consists of computing suitable values – call them estimates – of this parameter precisely on the basis of the sample. An estimate is suitable if replacing it with the unknown parameter does not cause major damage in next computations. In algorithmic inference, suitability of an estimate reads in terms of compatibility with the observed sample. In turn, parameter compatibility is a probability measure that we derive from the probability distribution of the random variable to which the parameter refers. In this way we identify a random parameter Θ compatible with an observed sample. Given a sampling mechanism $M\_X=(g\_\backslash theta,Z)$, the rationale of this operation lies in using the ''Z'' seed distribution law to determine both the ''X'' distribution law for the given θ, and the Θ distribution law given an ''X'' sample. Hence, we may derive the latter distribution directly from the former if we are able to relate domains of the sample space to subsets of Θ support. In more abstract terms, we speak about twisting properties of samples with properties of parameters and identify the former with statistics that are suitable for this exchange, so denoting a well behavior w.r.t. the unknown parameters. The operational goal is to write the analytic expression of the cumulative distribution function $F\_\backslash Theta(\backslash theta)$, in light of the observed value ''s'' of a statistic ''S'', as a function of the ''S'' distribution law when the ''X'' parameter is exactly θ. ==Method== Given a sampling mechanism $M\_X=(g\_\backslash theta,Z)$ for the random variable ''X'', we model $\backslash boldsymbol\; X=\backslash$ to be equal to $\backslash$. Focusing on a relevant statistic $S=h\_1(X\_1,\backslash ldots,X\_m)$ for the parameterθ, the master equation reads :$s=\; h(g\_\backslash theta(z\_1),\backslash ldots,\; g\_\backslash theta(z\_m))=\; \backslash rho(\backslash theta;z\_1,\backslash ldots,z\_m)$. When ''s'' is a well-behaved statistic w.r.t the parameter, we are sure that a monotone relation exists for each $\backslash boldsymbol\; z=\backslash$ between ''s'' and θ. We are also assured that Θ, as a function of $\backslash boldsymbol\; Z$ for given ''s'', is a random variable since the master equation provides solutions that are feasible and independent of other (hidden) parameters.〔By default, capital letters (such as ''U'', ''X'') will denote random variables and small letters (''u'', ''x'') their corresponding realizations.〕 The direction of the monotony determines for any $\backslash boldsymbol\; z$ a relation between events of the type $s\backslash geq\; s\text{'}\backslash leftrightarrow\; \backslash theta\backslash geq\; \backslash theta\text{'}$ or ''vice versa'' $s\backslash geq\; s\text{'}\backslash leftrightarrow\; \backslash theta\backslash leq\; \backslash theta\text{'}$, where $s\text{'}$ is computed by the master equation with $\backslash theta\text{'}$. In the case that ''s'' assumes discrete values the first relation changes into $s\backslash geq\; s\text{'}\backslash rightarrow\; \backslash theta\backslash geq\; \backslash theta\text{'}\backslash rightarrow\; s\backslash geq\; s\text{'}+\backslash ell$ where $\backslash ell>0$ is the size of the ''s'' discretization grain, idem with the opposite monotony trend. Resuming these relations on all seeds, for ''s'' continuous we have either :$F\_(\backslash theta)=\; F\_(s)$ or :$F\_(\backslash theta)=\; 1-F\_(s)$ For ''s'' discrete we have an interval where $F\_(\backslash theta)$ lies, because of $\backslash ell>0$. The whole logical contrivance is called a twisting argument. A procedure implementing it is as follows. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Twisting properties」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.