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利用专门构造的指数族进行密度估计AI 解读

We wish to estimate the probability density $g(y)$ that produced an observed random sample of vectors $y_1, y_2, \dots, y_n$. Estimates of $g(y)$ are traditionally constructed in two quite different ways: by maximum likelihood fitting within some parametric family such as the normal or by nonparametric methods such as kernel density estimation. These two methods can be combined by putting an exponential family "through" a kernel estimator. These are the specially designed…

局部自适应密度估计研究AI 解读

Theoretical and practical aspects of the sample-point adaptive positive kernel density estimator are examined. A closed-form expression for the mean integrated squared error is obtained through the device of preprocessing the data by binning. With this expression, the exact behavior of the optimally adaptive smoothing parameter function is studied for the first time. The approach differs from most earlier techniques in that bias of the adaptive estimator remains O(h 2) and…

利用非参数回归技术检验多项式回归模型AI 解读

In regression analysis, it is important to test the validity of the assumed model prior to making inferences regarding the population of interest. In this investigation, we utilize nonparametric regression techniques to test the validity of a kth order polynomial regression model. The departures from the polynomial model are assumed to belong to a smooth class of functions; a parametric form is not assumed. A test based on nonparametric regression fits to the residuals from…

双变量随机删失数据的密度估计AI 解读

In this article we construct a kernel estimate of the probability density function from bivariate data that have been randomly censored. We study the large-sample properties of the proposed estimator using a strong approximation result. We establish consistency and asymptotic normality and give a convenient representation of the kernel density estimator. Simulation studies show that the proposed procedure gives a good estimate of the true density function even when the…

预测振荡模式：随机场时空分解方法的综合AI 解读

Spatial-temporal decompositions of climatologic fields have been obtained using a range of techniques, including principal component analysis (PCA) and principal oscillation patterns (POPS). PCA decompositions are forced to be correlated to the original field, but they may not capture interesting aspects of temporal variation. On the other hand, POPS decompositions focus on temporal variation but are not forced to correlate to the field. Here we introduce a hybrid of these…

时变风险比：建模、假设检验及狼疮性肾炎应用AI 解读

We investigate the association between duration of untreated disease and survival in lupus nephritis, a rare rheumatologic disease. In this case, as in many other studies of survival, a priori considerations suggest that the effect of the predictor on hazard may change with increasing follow-up time. To accommodate such situations, we use regression splines to model the hazard ratio as a flexible function of time. We propose model-based tests of the hypotheses of hazards…

预测振荡模式：随机场时空分解方法的综合AI 解读

Spatial-temporal decompositions of climatologic fields have been obtained using a range of techniques, including principal component analysis (PCA) and principal oscillation patterns (POPS). PCA decompositions are forced to be correlated to the original field, but they may not capture interesting aspects of temporal variation. On the other hand, POPS decompositions focus on temporal variation but are not forced to correlate to the field. Here we introduce a hybrid of these…

摘要暂缺

随机生产前沿模型的半参数估计AI 解读

This paper extends the linear stochastic frontier model proposed by D. J. Aigner, C. A. K. Lovell, and P. Schmidt (1977) to a semiparametric frontier model in which the functional form of the production frontier is unspecified and the distributions of the composite error terms are of known form. Pseudo-likelihood estimators of the parameters characterizing the two error terms of the model are constructed based on kernel estimation of the conditional mean function. The Monte…

两个协方差平稳时间序列的独立性检验AI 解读

A one-sided asymptotically normal test for independence between two stationary time series is proposed by first prewhitening the two time series and then basing the test on the residual cross-correlation function. The test statistic is a properly standardised version of the sum of weighted squares of residual cross-correlations, with weights depending on a kernel function. Haugh's (1976) test can be viewed as a special case of our approach in the sense that it corresponds to…

用伪数据方法消除核密度估计的边界效应AI 解读

SUMMARY We suggest a method for boundary correcting kernel density estimators, based on generating pseudodata beyond the extremities of the density's support. The estimator produced in this way enjoys optimal orders of bias and variance right up to the ends of the support, and it may be used with kernels of arbitrary order. Our method is considerably more adaptive than the common data reflection approach, which is not really appropriate for kernels of order 2 or more since…

非参数风险率估计中平滑参数的 Bootstrap 选择AI 解读

An asymptotic representation of the mean weighted integrated squared error for the kernel-based estimator of the hazard rate in the presence of right-censored samples is obtained for different bootstrap resampling methods. As a consequence, a new bandwidth selector based on the bootstrap is introduced. Very satisfactory simulations results are obtained in comparison to the cross-validation selector for different models, using WARPed (i.e., binned) versions of the estimators.

劳动市场制度与工资分布，1973—1992：半参数方法AI 解读

This paper provides evidence that the decline in the real value of the minimum wage and in the rate of unionization account for a significant share of the increase in wage inequality in the United States between 1979 and 1988. The role of the minimum wage is particularly important for women, while deunionization has the largest impact on men. The authors develop a semiparametric procedure that applies kernel density methods to appropriately weighted samples. The procedure…

图像分析与非参数回归中中位数平滑器的渐近表现AI 解读

For d-dimensional images and regression functions the true object is estimated by median smoothing. The mean square error of the median smoother is calculated using the framework of M-estimation, and an expression for the asymptotic rate of convergence of the mean square error is given. It is shown that the median smoother performs asymptotically as well as the local mean. The optimal window size and the bandwidth of the median smoother are given in terms of the sample size…

局部参数化的非参数密度估计AI 解读

This paper develops a nonparametric density estimator with parametric overtones. Suppose $f(x, \theta)$ is some family of densities, indexed by a vector of parameters $\theta$. We define a local kernel-smoothed likelihood function which, for each x, can be used to estimate the best local parametric approximant to the true density. This leads to a new density estimator of the form $f(x, \hat{\theta}(x))$, thus inserting the best local parameter estimate for each new value of…

局部似然密度估计AI 解读

Local likelihood was introduced by Tibshirani and Hastie as a method of smoothing by local polynomials in non-Gaussian regression models. In this paper an extension of these methods to density estimation is discussed, and comparison with other methods of density estimation presented. The local likelihood method has particularly strong advantages over kernel methods when estimating tails of densities and in multivariate settings. Suppose constraints are incorporated in a…

非参数校准分析AI 解读

In this paper we discuss a new approach to solve calibration problems in a nonparametric setting. This approach is appealing because it yields estimates of the required quantities directly. The method combines kernel and robust estimation techniques. It relies on strong approximations of the estimating process and the extreme value theorem of Bickel and Rosenblatt. Using these results, we first obtain robust pointwise estimates of the parameters of interest. Second, we set…

非线性小波回归中平滑、阈值与截断参数的选择AI 解读

SUMMARY Concise asymptotic theory is developed for non-linear wavelet estimators of regression means, in the context of general error distributions, general designs, general normalizations in the case of stochastic design, and non-structural assumptions about the mean. The influence of the tail weight of the error distribution is addressed in the setting of choosing threshold and truncation parameters. Mainly, the tail weight is described in an extremely simple way, by a…

一致模型设定检验：遗漏变量与半参数函数形式AI 解读

By using nonparametric kernel estimation method and a central limit theorem for degenerate U-statistics of order higher than two, the authors develop several consistent model specification tests in the context of a nonparametric regression model. These include tests for omitted variables, tests for a partially linear model, and tests for a semiparametric single index model. The asymptotic normality of the test statistics are established under the respective null hypotheses…

未知形式序列相关的一致检验AI 解读

This paper proposes three classes of consistent tests for serial correlation of the residuals from a linear dynamic regression model. The tests are obtained by comparing a kernel-based spectral density estimator and the null spectral density using three divergence measures. The null normal distributions are invariant whether the regressors include lagged dependent variables. Both asymptotic local and global power properties are investigated. G. Box and D. Pierce's (1970)…

相关误差下若干单位根检验的改进及其局部渐近性质AI 解读

Many unit root tests have distorted sizes when the root of the error process is close to the unit circle. This paper analyses the properties of the Phillips-Perron tests and some of their variants in the problematic parameter space. We use local asymptotic analyses to explain why the Phillips-Perron tests suffer from severe size distortions regardless of the choice of the spectral density estimator but that the modified statistics show dramatic improvements in size when used…

二元时间序列互谱的自动估计AI 解读

The penalised Whittle likelihood has recently been shown to have good properties in nonparametric estimation of spectral density functions. This paper extends the approach to the estimation of the cross-spectrum of a bivariate time series. One major difference from the univariate case is that the cross-spectrum estimate is not constrained to be positive, but must result in a positive definite spectral density matrix. An efficient computational method based on iterative…

非参数密度估计的经验似然置信区间AI 解读

We suggest using empirical likelihood in conjunction with the kernel method to construct confidence intervals for the value of a probability density f at a point x. This suggestion arises from a simulation study which shows that confidence intervals produced by the kernel-based percentle-t bootstrap do not have the coverage claimed by the theory. This coverage discrepancy is due to a conflict between the prescribed undersmoothing and the explicit variance estimate needed by…

基于数据依赖分区的直方图回归估计AI 解读

We establish general sufficient conditions for the $L_2$-consistency of multivariate histogram regression estimates based on data-dependent partitions. These same conditions insure the consistency of partitioning regression estimates based on local polynomial fits, and, with an additional regularity assumption, the consistency of histogram estimates for conditional medians. Our conditions require shrinking cells, subexponential growth of a combinatorial complexity measure…