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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Semiparametric model ： ウィキペディア英語版 Semiparametric model In statistics a semiparametric model is a model that has parametric and nonparametric components. A model is a collection of distributions: $\backslash$ indexed by a parameter $\backslash theta$. * A parametric model is one in which the indexing parameter is a finite-dimensional vector (in $k$-dimensional Euclidean space for some integer $k$); i.e. the set of possible values for $\backslash theta$ is a subset of $\backslash mathbb^k$, or $\backslash Theta\; \backslash subset\; \backslash mathbb^k$. In this case we say that $\backslash theta$ is finite-dimensional. * In nonparametric models, the set of possible values of the parameter $\backslash theta$ is a subset of some space, not necessarily finite-dimensional. For example, we might consider the set of all distributions with mean 0. Such spaces are vector spaces with topological structure, but may not be finite-dimensional as vector spaces. Thus, $\backslash Theta\; \backslash subset\; \backslash mathbb$ for some possibly infinite-dimensional space $\backslash mathbb$. * In semiparametric models, the parameter has both a finite-dimensional component and an infinite-dimensional component (often a real-valued function defined on the real line). Thus the parameter space $\backslash Theta$ in a semiparametric model satisfies $\backslash Theta\; \backslash subset\; \backslash mathbb^k\; \backslash times\; \backslash mathbb$, where $\backslash mathbb$ is an infinite-dimensional space. It may appear at first that semiparametric models include nonparametric models, since they have an infinite-dimensional as well as a finite-dimensional component. However, a semiparametric model is considered to be "smaller" than a completely nonparametric model because we are often interested only in the finite-dimensional component of $\backslash theta$. That is, we are not interested in estimating the infinite-dimensional component. In nonparametric models, by contrast, the primary interest is in estimating the infinite-dimensional parameter. Thus the estimation task is statistically harder in nonparametric models. These models often use smoothing or kernels. ==Example== A well-known example of a semiparametric model is the Cox proportional hazards model. If we are interested in studying the time $T$ to an event such as death due to cancer or failure of a light bulb, the Cox model specifies the following distribution function for $T$: :$$ F(t) = 1 - \exp\left(-\int_0^t \lambda_0(u) e^ du\right), where $x$ is the covariate vector, and $\backslash beta$ and $\backslash lambda\_0(u)$ are unknown parameters. $\backslash theta\; =\; (\backslash beta,\; \backslash lambda\_0(u))$. Here $\backslash beta$ is finite-dimensional and is of interest; $\backslash lambda\_0(u)$ is an unknown non-negative function of time (known as the baseline hazard function) and is often a nuisance parameter. The collection of possible candidates for $\backslash lambda\_0(u)$ is infinite-dimensional. 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「Semiparametric model」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.