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利用验证数据对非线性协变量测量误差模型进行经验似然推断AI 解读

In this article we study inference in parametric–nonparametric errors-in-covariables regression models using an empirical likelihood approach based on validation data. It is shown that the asymptotic behavior of the proposed estimator depends on the ratio of the sizes of the primary sample and the validation sample, respectively. Unlike cases without measurement errors, the limit distribution of the estimator is no longer tractable and cannot be used for constructing…

单指标模型的非参数检验AI 解读

In this paper we study goodness-of-fit testing of single-index models. The large sample behavior of certain score-type test statistics is investigated. As a by-product, we obtain asymptotically distribution-free maximin tests for a large class of local alternatives. Furthermore, characteristic function based goodness-of-fit tests are proposed which are omnibus and able to detect peak alternatives. Simulation results indicate that the approximation through the limit…

时间序列的非参数模型检验AI 解读

This paper studies a class of tests useful for testing the goodness-of-fit of an autoregressive model. These tests are based on a class of empirical processes marked by certain residuals. The paper first gives their large sample behavior under null hypotheses. Then a martingale transformation of the underlying process is given that makes tests based on it asymptotically distribution free. Consistency of these tests is also discussed briefly.

回归模型检验：创新过程方法AI 解读

In the context of regression analysis it is known that the residual cusum process may serve as a basis for the construction of various omnibus, smooth and directional goodness-of-fit tests. Since a deeper analysis requires the decomposition of the cusums into their principal components and this is difficult to obtain, we propose to replace this process by its innovation martingale. It turns out that the resulting tests are (asymptotically) distribution free under composite…

回归模型的非参数检验AI 解读

In this paper we study a marked empirical process based on residuals. Results on its large-sample behavior may be used to provide nonparametric full-model checks for regression. Their decomposition into principal components gives new insight into the question: which kind of departure from a hypothetical model may be well detected by residual-based goodness-of-fit methods? The work also contains a small simulation study on straight-line regression.

Kaplan–Meier 积分方差的刀切估计AI 解读

Let $\hat{F}_n$ be the Kaplan-Meier estimator of a distribution function F computed from randomly censored data. It is known that, under certain integrability assumptions on a function $\varphi$, the Kaplan-Meier integral $\int \varphi d \hat{F}_n$, when properly standardized, is asymptotically normal. In this paper it is shown that, with probability 1, the jackknife estimate of variance consistently estimates the (limit) variance.

Let $\hat{F}_n$ be the Kaplan-Meier estimator of a distribution function $F$ computed from randomly censored data. We show that under optimal integrability assumptions on a function $\varphi$, the Kaplan-Meier integral $\int \varphi d\hat{F}_n$, when properly standardized, is asymptotically normal.

具有普适一致性的条件 U 统计量AI 解读

We introduce a general class of conditional $U$-statistics and present sufficient conditions for their universal consistency in $r$th mean. It is shown that under mild assumptions on the smoothing parameters, window and $k_n$-nearest neighbor estimators are universally consistent. An application to a new nonparametric discrimination problem is also included.

Kaplan–Meier积分的刀切法估计AI 解读

We derive an explicit formula for the jackknife estimate of a Kaplan-Meier integral. From this the asymptotic analysis of the jackknifed Kaplan-Meier process becomes straightforward. In a small simulation study it is demonstrated that jackknifing may lead to a considerable reduction of the bias.

截断数据乘积极限估计量的几乎必然表示AI 解读

In the left-truncation model, one observes data $(X_i,Y_i)$ only when $Y_i\leq X_i$. Let F denote the marginal d.f. of $X_i$ , the variable of interest. The nonparametric MLE $\hat{F}_n$ of F aims at reconstructing F from truncated data. In this paper an almost sure representation of $\hat{F}_n$ is derived with improved error bounds on the one hand and under weaker distributional assumptions on the other hand.

条件经验过程AI 解读

We prove a Donsker-type invariance principle for a nearest-neighbor-type conditional empirical process. As an application we show asymptotic normality of conditional quantiles and derive large-sample distribution-free tests and confidence bands for a conditional distribution function.

最近邻回归函数估计的渐近正态性AI 解读

Let $(X, Y)$ be a random vector in the plane. We show that a smoothed N.N. estimate of the regression function $m(x) = \mathbb{E}(Y\mid X = x)$ is asymptotically normal under conditions much weaker than needed for the Nadaraya-Watson estimate. It also turns out that N.N. estimates are more efficient than kernel-type estimates if (in the mean) there are few observations in neighborhoods of $x$.