论文检索

切片逆回归核估计的渐近性质AI 解读

To explore nonlinear structures hidden in high-dimensional data and to estimate the effective dimension reduction directions in multivariate nonparametric regression, Li and Duan proposed the sliced inverse regression (SIR) method which is simple to use. In this paper, the asymptotic properties of the kernel estimate of sliced inverse regression are investigated. It turns out that regardless of the kernel function, the asymptotic distribution remains the same for a wide…

基于受扰直方图数据的间接密度估计带宽选择AI 解读

Motivated by a number of practical applications, we consider a class of indirect nonparametric density estimation problems in which the observed data consist of a histogram of binned empirically corrected counts. Due to variability in the process of correction, the histogram cannot be modeled in terms of simple scaled Poisson statistics. This departure necessitates the development of a new methodology for bandwidth selection. A variant of the method of unbiased risk…

基于受扰直方图数据的间接密度估计带宽选择AI 解读

Motivated by a number of practical applications, we consider a class of indirect nonparametric density estimation problems in which the observed data consist of a histogram of binned empirically corrected counts. Due to variability in the process of correction, the histogram cannot be modeled in terms of simple scaled Poisson statistics. This departure necessitates the development of a new methodology for bandwidth selection. A variant of the method of unbiased risk…

Hilbert 空间值 mixingale 的大数定律及其应用AI 解读

To obtain consistency results for nonparametric estimators based on stochastic processes relevant in econometrics, we introduce the notions of Hilbert space-valued L p mixingales and near-epoch dependent arrays, and we prove weak and strong laws of large numbers by using a new exponential inequality for Hilbert ( H ) space-valued martingale difference arrays. We follow Andrews (1988, Econometric Theory 4, 458–467), Hansen (1991, Econometric Theory 7, 213–221; 1992,…

摘要暂缺

多元正态矩形概率及其导数的模拟：理论与计算结果AI 解读

An extensive literature in econometrics and in numerical analysis has considered the problem of evaluating the multiple integral P(B; μ, Ω) = ∝ab n(v − μ, Ω)dv ≡ Ev1(V ϵ B), where V is a m-dimensional normal vector with mean μ, covariance matrix Ω, and density n(v − μ, Ω), and 1(V ϵ B) is an indicator for the event B = (V¦a < V < b). A leading case of such an integral is the negative orthant probability, where B = (V ¦V < 0). The problem is computationally difficult except…

SNP 密度估计量的收敛速度AI 解读

The SNP density estimator is a truncation (or sieve) estimator based upon a Hermite series expansion. Other nonparametric estimators based on orthogonal series expansions have been proposed.

双变量删失模型的有效估计与非参数极大似然修复AI 解读

The NPMLE in the bivariate censoring model is not consistent for continuous data. The problem is caused by the singly censored observations. In this paper we prove that if we observe the censoring times or if the censoring times are discrete, then a NPMLE based on a slightly reduced data set, in particular, we interval censor the singly censored observations, is asymptotically efficient for this reduced data and moreover if we let the width of the interval converge to zero…

利用多元正态混合进行贝叶斯曲线拟合AI 解读

Problems of regression smoothing and curve fitting are addressed via predictive inference in a flexible class of mixture models. Multidimensional density estimation using Dirichlet mixture models provides the theoretical basis for semi-parametric regression methods in which fitted regression functions may be deduced as means of conditional predictive distributions. These Bayesian regression functions have features similar to generalised kernel regression estimates, but the…

非线性动力系统的条件密度与敏感度度量估计AI 解读

Using locally polynomial regression, we develop nonparametric estimators for the conditional density function and its square root, and their partial derivatives. Two measures of sensitivity to initial conditions in nonlinear stochastic dynamic systems are proposed, one of which relates Fisher information with initial-value sensitivity in dynamical systems. We propose estimators for these, and show asymptotic normality for one of them. We further propose a simple method for…

多元时间序列广义预测误差方差的估计AI 解读

For a multivariate stationary time series, we propose a nonparametric estimator for its generalized prediction error variance using a multivariate analog of the Szegö-Kolmogorov formula, replacing the integral by a sum and replacing the unknown spectral density matrix by a consistent estimator. Asymptotic normality of this estimator is established, and its small-sample behavior is assessed through simulation and application to two real data sets. These examples show that the…

利用仅含方位角的跟踪数据进行路径样条估计AI 解读

In many applications, bearings are measured to a moving object with the goal of estimating the object's course of movement. If movement is appropriately modeled as a smooth deterministic curve in the plane, then a cubic spline is a reasonable representation of the curve. Maximum likelihood estimators are presented for parameters of regression splines, assuming that observation errors follow a Von Mises distribution. Location estimates are obtainable even when data are…

局部多项式的有限样本方差：分析与解决方法AI 解读

Fitting local polynomials in nonparametric regression has a number of advantages. The attractive theoretical features are in a partial contradiction to variance properties for random design and to practical experience over a broad range of situations. No upper bound can be given for the conditional variance. The unconditional variance is infinite when using optimal weights with compact support. Properties are better for Gaussian weights. We analyze local polynomials for…

非参数曲线估计的局部平滑AI 解读

We develop new local versions of familiar smoothing methods, such as cross-validation and smoothed cross-validation, in the contexts of density estimation and regression. These new methods are locally adaptive in the sense that they capture smooth local fluctuations in the curve by using smoothly varying bandwidths that change as the character of the curve changes. Moreover, the new methods are accurate, easy to apply, and computationally expedient.

密度估计带宽选择简述AI 解读

There has been major progress in recent years in data-based bandwidth selection for kernel density estimation. Some “second generation” methods, including plug-in and smoothed bootstrap techniques, have been developed that are far superior to well-known “first generation” methods, such as rules of thumb, least squares cross-validation, and biased cross-validation. We recommend a “solve-the-equation” plug-in bandwidth selector as being most reliable in terms of overall…

适用于强非线性关系多元密度的局部自适应重要性抽样AI 解读

We consider adaptive importance sampling techniques that use kernel density estimates at each iteration as importance sampling functions. These can provide more nearly constant importance weights and more precise estimates of quantities of interest than the sampling importance resampling algorithm when the initial importance sampling function is diffuse relative to the target. We propose a new method that adapts to the varying local structure of the target. When the target…

多元时间序列广义预测误差方差的估计AI 解读

For a multivariate stationary time series, we propose a nonparametric estimator for its generalized prediction error variance using a multivariate analog of the Szegö-Kolmogorov formula, replacing the integral by a sum and replacing the unknown spectral density matrix by a consistent estimator. Asymptotic normality of this estimator is established, and its small-sample behavior is assessed through simulation and application to two real data sets. These examples show that the…

仅方位跟踪数据的轨迹样条估计AI 解读

In many applications, bearings are measured to a moving object with the goal of estimating the object's course of movement. If movement is appropriately modeled as a smooth deterministic curve in the plane, then a cubic spline is a reasonable representation of the curve. Maximum likelihood estimators are presented for parameters of regression splines, assuming that observation errors follow a Von Mises distribution. Location estimates are obtainable even when data are…

非参数曲线估计的局部平滑AI 解读

We develop new local versions of familiar smoothing methods, such as cross-validation and smoothed cross-validation, in the contexts of density estimation and regression. These new methods are locally adaptive in the sense that they capture smooth local fluctuations in the curve by using smoothly varying bandwidths that change as the character of the curve changes. Moreover, the new methods are accurate, easy to apply, and computationally expedient.

连续单参数指数族经验贝叶斯检验的最优收敛率AI 解读

The empirical Bayes linear loss two-action problem in the continuous one-parameter exponential family is studied. Previous results on this problem construct empirical Bayes tests via kernel density estimates. They also obtain upper bounds for the unconditional regret at some prior distribution. In this paper, we discuss the general question of how difficult the above empirical Bayes problem is, and why empirical Bayes rules based on kernel density estimates are useful.…

灵活风险率估计量的渐近性质AI 解读

Suppose one has a stochastic time-dependent covariate $Z(t)$, and is interested in estimating the hazard relationship $\lambda(t|\overline{Z}(t)) = \omega(Z(t))$, where $\overline{Z}(t)$ denotes the history of $Z(t)$ up to and including time t. In this paper, we consider a model of the form $\exp(s_n(Z(t)))$, where $s_n(Z(t))$ is a spline of finite but arbitrary order, and investigate the behavior of the maximum likelihood estimator of the hazard as the number of knots in…

广义核分位数密度估计量的一致相合性AI 解读

Various smoothing methods for quantile density estimation are unified into a generalized kernel smoothing. Based on a stochastic upper bound of the derivatives sequence for a sequence of smoothed Brownian bridges, uniform in-probability consistency of generalized kernel quantile density estimators on any closed subinterval of the open unit interval is derived.

依赖数据密度估计中的带宽选择AI 解读

We address the empirical bandwidth choice problem in cases where the range of dependence may be virtually arbitrarily long. Assuming that the observed data derive from an unknown function of a Gaussian process, it is argued that, unlike more traditional contexts of statistical inference, in density estimation there is no clear role for the classical distinction between short- and long-range dependence. Indeed, the "boundaries" that separate different modes of behaviour for…

密度函数的序贯置信带AI 解读

This paper proposes a fully sequential procedure for constructing a fixed-width confidence band for an unknown density on a finite interval and shows the procedure has the desired coverage probability asymptotically as the width of the band approaches zero. The procedure is based on a result of Bickel and Rosenblatt. Its implementation in the sequential setting cannot be obtained using Anscombe's theorem, because the normalized maximal deviations between the kernel estimate…