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总体归属不确定时多个总体的密度估计AI 解读

We devise methods to estimate probability density functions of several populations using observations with uncertain population membership, meaning from which population an observation comes is unknown. The probability of an observation being sampled from any given population can be calculated. We develop general estimation procedures and bandwidth selection methods for our setting. We establish large-sample properties and study finite-sample performance using simulation…

经典测量误差模型中的局部与总体拟合优度检验AI 解读

Summary We consider functional measurement error models, i.e. models where covariates are measured with error and yet no distributional assumptions are made about the mismeasured variable. We propose and study a score-type local test and an orthogonal series-based, omnibus goodness-of-fit test in this context, where no likelihood function is available or calculated—i.e. all the tests are proposed in the semiparametric model framework. We demonstrate that our tests have…

密度估计的间接交叉验证AI 解读

A new method of bandwidth selection for kernel density estimators is proposed. The method, termed indirect cross-validation (ICV), makes use of so-called selection kernels. Least-squares cross-validation (LSCV) is used to select the bandwidth of a selection-kernel estimator and this bandwidth is appropriately rescaled for use in a Gaussian kernel estimator. The proposed selection kernels are linear combinations of two Gaussian kernels and need not be unimodal or positive. A…

贝叶斯动机的函数拟合检验及其渐近频率学性质AI 解读

We propose and analyze nonparametric tests of the null hypothesis that a function belongs to a specified parametric family. The tests are based on BIC approximations, πBIC, to the posterior probability of the null model, and may be carried out in either Bayesian or frequentist fashion. We obtain results on the asymptotic distribution of πBIC under both the null hypothesis and local alternatives. One version of πBIC, call it π*BIC, uses a class of models that are orthogonal…

摘要暂缺

参数函数的拟合检验AI 解读

General methods for testing the fit of a parametric function are proposed. The idea underlying each method is to “accept” the prescribed parametric model if and only if it is chosen by a model selection criterion. Several different selection criteria are considered, including one based on a modified version of the Akaike information criterion and others based on various score statistics. The tests have a connection with nonparametric smoothing because they use orthogonal…

单侧交叉验证AI 解读

A new method of selecting the smoothing parameters of nonparametric regression estimators is introduced. The method, termed one-sided cross-validation (OSCV), has the objectivity of cross-validation and statistical properties comparable to those of a plug-in rule. The new method may be viewed as an application of the prequential model selection method of Dawid. As such, our results identify a situation in which the prequential method is a more efficient model selector than…

用时间序列交叉验证自动平滑依赖数据AI 解读

SUMMARY The problem of selecting the bandwidth of a kernel regression estimator when the observed data are serially correlated is considered. The bandwidth is selected by using a version of cross-validation that seeks a good one-step-ahead predictor of the data. This method, referred to as time series cross-validation (TSCV), simultaneously estimates an optimal bandwidth and, given a time series model for the errors, the autocorrelation function of the data. In addition,…

Cusum、von Neumann 与平滑型拟合优度检验的共同结构AI 解读

Recent papers by Munson & Jernigan (1989) and Buckley (1991) propose nonparametric tests for the hypothesis of no predictor effect in regression. The Munson-Jernigan test is similar to the von Neumann (1941) test, while that of Buckley is based on a functional of cusums. These tests are shown to be special cases of a wider class of tests based on nonparametric function estimation ideas. Fourier analysis is used to qualitatively compare the Munson & Jernigan and Buckley tests…

累积和、冯·诺伊曼与基于平滑的拟合优度检验的共同框架AI 解读

Recent papers by Munson & Jernigan (1989) and Buckley (1991) propose nonparametric tests for the hypothesis of no predictor effect in regression. The Munson-Jernigan test is similar to the von Neumann (1941) test, while that of Buckley is based on a functional of cusums. These tests are shown to be special cases of a wider class of tests based on nonparametric function estimation ideas. Fourier analysis is used to qualitatively compare the Munson & Jernigan and Buckley tests…

大边界区域下的核回归及其在多项式模型适合性检验中的应用AI 解读

It is well known that kernel regression estimators are subject to so-called boundary or edge effects, a phenomenon in which the bias of an estimator increases near the endpoints of the estimation interval. When the regression curve is linear or nearly linear, the requisite amount of smoothing is so great that the boundary region is effectively the entire estimation interval. Special boundary kernels are proposed here to deal with such cases. It is shown that the proposed…

通过阶数选择准则检验回归拟合优度AI 解读

A new test is derived for the hypothesis that a regression function has a prescribed parametric form. Unlike many recent proposals, this test does not depend on arbitrarily chosen smoothing parameters. In fact, the test statistic is itself a smoothing parameter which is selected to minimize an estimated risk function. The exact distribution of the test statistic is obtained when the error terms in the regression model are Gaussian, while the large sample distribution is…

收入效应矩阵正定性的 Bootstrap 检验AI 解读

Positive definiteness of income effect matrices provides a sufficient condition for the law of demand to hold. Given cross section household expenditure data, empirical evidence for the law of demand can be obtained by estimating such matrices. Härdle, Hildenbrand, and Jerison used the bootstrap method to simulate the distribution of the smallest eigenvalue of random matrices and to test their positive definiteness. Here, theoretical aspects of this bootstrap test of…

具有时间序列误差的核回归估计AI 解读

SUMMARY Suppose that data y 1, ..., yn are observed according to the model yi=f((i−12)/n)+ϵi,i=1,…,n, where f is a smooth function and {ϵ1,…,ϵn} is a sample from a zero-mean, covariance stationary time series. The problem of objectively choosing the bandwidth of a kernel estimate for f is addressed. It is shown both theoretically and by simulation that cross-validation produces extremely rough kernel estimates when the data are sufficiently positively correlated. This makes…

非参数回归中均值函数差异的 Bootstrap 检验AI 解读

A bootstrap test is proposed for detecting a difference between two mean functions in the setting of nonparametric regression. Error distributions in the regression model are permitted to be arbitrary and unequal. The test enjoys power properties akin to those in a parametric setting, in the sense that it can distinguish between regression functions distant only n −1/2 apart, where n is the sample size. It has exceptional level accuracy, with level error of only n −2, and…

相依数据核密度估计的数据驱动带宽选择AI 解读

The bandwidth selection problem in kernel density estimation is investigated in situations where the observed data are dependent. The classical leave-out technique is extended, and thereby a class of cross-validated bandwidths is defined. These bandwidths are shown to be asymptotically optimal under a strong mixing condition. The leave-one out, or ordinary, form of cross-validation remains asymptotically optimal under the dependence model considered. However, a simulation…

一种 ARMA 型概率密度估计量AI 解读

Properties of a probability density estimator having the rational form of an ARMA spectrum are investigated. Under various conditions on the underlying density's Fourier coefficients, the ARMA estimator is shown to have asymptotically smaller mean integrated squared error (MISE) than the best tapered Fourier series estimator. The most interesting cases are those in which the Fourier coefficients $\phi_j$ are asymptotic to $Kj^{-p}$ as $j \rightarrow \infty$, where $\rho > 1/2$…

摘要暂缺

自回归依赖模型下核密度估计量的效率AI 解读

The problem of estimating the probability density function of a strictly stationary process is considered. To study the effect of a dependence structure on the efficiency of a kernel density estimator, the mean integrated squared error (MISE) of the Fourier integral estimator (FIE) is derived on the assumption that the observed data are generated by a first-order autoregressive process. Numerical results for the normal and Cauchy densities show that even moderate departures…