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纵向数据的非参数回归分析AI 解读

Nonparametric methods are developed for estimating the dose effect when a response consists of correlated observations over time measured in a dose–response experiment. The methods can also be applied to data collected from a completely randomized design experiment. Methods are developed for the detection and description of the effects of dose, time, and their interaction. The methods allow for individual variation in the timing and number of observations. A generalization…

半参数模型中的拟似然估计AI 解读

Suppose the expected value of a response variable Y may be written h(Xβ +γ(T)) where X and T are covariates, each of which may be vector-valued, β is an unknown parameter vector, γ is an unknown smooth function, and h is a known function. In this article, we outline a method for estimating the parameter β, γ of this type of semiparametric model using a quasi-likelihood function. Algorithms for computing the estimates are given and the asymptotic distribution theory for the…

回归模型整体与局部拟合诊断AI 解读

We concern ourselves with diagnostics for checking the overall and local goodness of fit of a model s(x) used in the regression of Y on x ∈ U = [0, 1] d . The model for s(x) is a functional form that depends on a finite number of unknown parameters. Two statistics, Λ and Λ w , are proposed that measure the level of agreement between the model fit to the data and the nonparametric kernel estimator on m preselected points in U. Conditions are given under which Λ and λ w , are…

核估计的局部带宽选择AI 解读

A kernel estimate of a curve that uses an adaptive procedure for local selection of the bandwidth is considered here. A two-step procedure is proposed for estimating the local bandwidth that minimizes the mean squared error (MSE) of a kernel estimator for nonparametric regression. First, a consistent estimate of the exact MSE is constructed. Then the bandwidth that minimizes the estimate of the MSE is calculated. Sufficient conditions under which this bandwidth is…

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