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缺少类别标识时的辅助标记分类AI 解读

Constructing classification rules for accurate diagnosis of a disorder is an important goal in medical practice. In many clinical applications, there is no clinically significant anatomical or physiological deviation exists to identify the gold standard disease status to inform development of classification algorithms. Despite absence of perfect disease class identifiers, there are usually one or more disease-informative auxiliary markers along with feature variables…

一般变换模型中具有根号n收敛率的非参数估计AI 解读

We propose simple estimators for the transformation function $\Lambda$ and the distribution function F of the error for the model $$\Lambda (Y) = \alpha + \mathbf{X} \mathbf{\beta} + \varepsilon.$$ It is proved that these estimators are consistent and can achieve the unusual $n^{-1/2}$ rate of convergence on any finite interval under some regularity conditions. We show that our estimators are more attractive than another class of estimators proposed by Horowitz. Interesting…

Box–Cox 幂变换模型的敏感性分析：对比参数AI 解读

Sensitivity analysis is an important tool for the evaluation of scientific models. We consider the Box-Cox power transformation model and study the sensitivity for the estimated slope vector when the transformation parameter is perturbed. This is a key issue in the debate among Bickel & Doksum (1981), Box & Cox (1982) and Hinkley & Runger (1984) on the application of the power transformation model. Hinkley & Runger (1984) conjectured that Box & Cox's (1964) z transformation…

Box–Cox 幂变换模型的敏感性分析：对比参数AI 解读

Sensitivity analysis is an important tool for the evaluation of scientific models. We consider the Box-Cox power transformation model and study the sensitivity for the estimated slope vector when the transformation parameter is perturbed. This is a key issue in the debate among Bickel & Doksum (1981), Box & Cox (1982) and Hinkley & Runger (1984) on the application of the power transformation model. Hinkley & Runger (1984) conjectured that Box & Cox's (1964) z transformation…

切片回归：一种无需指定链接函数的回归方法AI 解读

Consider a general regression model of the form $y = g(\alpha + \mathbf{x}'\beta, \varepsilon)$, with an arbitrary and unknown link function $g$. We study a link-free method, the slicing regression, for estimating the direction of $\beta$. The method is easy to implement and does not require iterative computation. First, we estimate the inverse regression function $E(\mathbf{x}\mid y)$ using a step function. We then estimate $\Gamma = \operatorname{Cov}\lbrack E(\mathbf{x}\mid y)\rbrack$…

伴随投影寻踪回归AI 解读

Consider a projection pursuit regression model y = g(α + β x) + ε, with an arbitrary monotonic link function g. We assume the link function is unknown; thus we can only estimate the direction of β, that is, the ratios among the components of β, say, β 1/β 2. The direction of β is a useful estimand that measures, say, how many units of x 2 is equivalent to one unit of x 1 in terms of potency in affecting the outcome y. Projection pursuit regression usually solves the equation…

伴随投影寻踪回归AI 解读

Consider a projection pursuit regression model y = g(α + β x) + ε, with an arbitrary monotonic link function g. We assume the link function is unknown; thus we can only estimate the direction of β, that is, the ratios among the components of β, say, β 1/β 2. The direction of β is a useful estimand that measures, say, how many units of x 2 is equivalent to one unit of x 1 in terms of potency in affecting the outcome y. Projection pursuit regression usually solves the equation…

链接函数设定偏离下的回归分析AI 解读

We study the behavior of regression analysis when there might be some violation of the assumed link function, the functional form of the model which relates the outcome variable $y$ to the regressor variable $\mathbf{x}$ and the random error. We allow the true link function to be completely arbitrary, except that $y$ depends on $\mathbf{x}$ only through a linear combination $\beta\mathbf{x}$. The slope vector $\beta$ is identified only up to a multiplicative scalar. Under…

摘要暂缺

样本选择模型与多部模型之间的选择AI 解读

Hay and Olsen (1984) incorrectly argue that a multi-part model, the two-part model used in Duan et al. (1982,1983), is nested within the sample-selection model. Their proof relies on an unmentioned restrictive assumption that cannot be satisfied. We provide a counterexample to show that the propensity to use medical care and the level of expense can be positively associated in the two-part model, contrary to their assertion. The conditional specification in the multi-part…

涂抹估计：一种非参数逆变换方法AI 解读

The smearing estimate is proposed as a nonparametric estimate of the expected response on the untransformed scale after fitting a linear regression model on a transformed scale. The estimate is consistent under mild regularity conditions, and usually attains high efficiency relative to parametric estimates. It can be viewed as a low-premium insurance policy against departures from parametric distributional assumptions. A real-world example of predicting medical expenditures…