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加性模型平滑回拟合的带宽选择AI 解读

The smooth backfitting introduced by Mammen, Linton and Nielsen [Ann. Statist. 27 (1999) 1443–1490] is a promising technique to fit additive regression models and is known to achieve the oracle efficiency bound. In this paper, we propose and discuss three fully automated bandwidth selection methods for smooth backfitting in additive models. The first one is a penalized least squares approach which is based on higher-order stochastic expansions for the residual sums of…

单调非减风险率的检验AI 解读

A test of the null hypothesis that a hazard rate is monotone nondecreasing, versus the alternative that it is not, is proposed. Both the test statistic and the means of calibrating it are new. Unlike previous approaches, neither is based on the assumption that the null distribution is exponential. Instead, empirical information is used to effectively identify and eliminate from further consideration parts of the line where the hazard rate is clearly increasing; and to…

核型函数估计量关于带宽的一致性AI 解读

We introduce a general method to prove uniform in bandwidth consistency of kernel-type function estimators. Examples include the kernel density estimator, the Nadaraya–Watson regression estimator and the conditional empirical process. Our results may be useful to establish uniform consistency of data-driven bandwidth kernel-type function estimators.

自回归时间序列单位根检验的自助法AI 解读

The theory developed for bootstrapping unit root tests in an autoregressive (AR) context has been concerned mainly with the large-sample behavior of the methods proposed under the assumption that the null hypothesis is true. No results exist for the relative performance and the power behavior of the bootstrap methods under the alternative. This article studies the properties of different AR bootstrap schemes of the unit root hypothesis, including a new proposal based on…

二元反应生物测定中有效剂量的非参数估计札记AI 解读

For the common binary response model, we propose a direct method for the nonparametric estimation of the effective dose level. The estimator is obtained by the composition of a nonparametric estimate of the quantile response curve and a classical density estimate. The new method yields a simple and reliable monotone estimate of the effective dose-level curve α → EDα and is appealing to users of conventional smoothing methods as kernel estimators, local polynomials, series…

GMM、GEL、序列相关与渐近偏差AI 解读

For stationary time series models with serial correlation, we consider generalized method of moments (GMM) estimators that use heteroskedasticity and autocorrelation consistent (HAC) positive definite weight matrices and generalized empirical likelihood (GEL) estimators based on smoothed moment conditions. Following the analysis of Newey and Smith (2004) for independent observations, we derive second order asymptotic biases of these estimators. The inspection of bias…

序列依赖非参数熵度量的渐近分布理论AI 解读

Entropy is a classical statistical concept with appealing properties. Establishing asymptotic distribution theory for smoothed nonparametric entropy measures of dependence has so far proved challenging. In this paper, we develop an asymptotic theory for a class of kernel-based smoothed nonparametric entropy measures of serial dependence in a time-series context. We use this theory to derive the limiting distribution of Granger and Lin's (1994) normalized entropy measure of…

利用核平滑方法估计半参数 ARCH(∞) 模型AI 解读

We investigate a class of semiparametric ARCH(∞) models that includes as a special case the partially nonparametric (PNP) model introduced by Engle and Ng (1993) and which allows for both flexible dynamics and flexible function form with regard to the “news impact” function. We show that the functional part of the model satisfies a type II linear integral equation and give simple conditions under which there is a unique solution. We propose an estimation method that is based…

利用基因表达数据进行肿瘤的贝叶斯分类AI 解读

Summary Precise classification of tumours is critical for the diagnosis and treatment of cancer. Diagnostic pathology has traditionally relied on macroscopic and microscopic histology and tumour morphology as the basis for the classification of tumours. Current classification frameworks, however, cannot discriminate between tumours with similar histopathologic features, which vary in clinical course and in response to treatment. In recent years, there has been a move towards…

相依删失下边际比例风险回归的似然方法AI 解读

In many public health problems, an important goal is to identify the effect of some treatment/intervention on the risk of failure for the whole population. A marginal proportional hazards regression model is often used to analyze such an effect. When dependent censoring is explained by many auxiliary covariates, we utilize two working models to condense high-dimensional covariates to achieve dimension reduction. Then the estimator of the treatment effect is obtained by…

带辅助数据的测量误差模型AI 解读

We study the problem of parameter inference in (possibly non-linear and non-smooth) econometric models when the data are measured with error. We allow for arbitrary correlation between the true variables and the measurement errors. To solve the identification problem, we require the existence of an auxiliary data-set that contains information about the conditional distribution of the true variables given the mismeasured variables. Our main assumption requires that the…

平均导数与平均差分的核估计AI 解读

In this article we consider the problem of estimating average derivatives and differences using kernel estimators. Our analysis focuses on developing new methods that are appropriate in the context of bounded and discrete regressors and do not require higher-order kernels for consistency or asymptotic normality. We derive a new nonparametric estimator that we call the average difference estimator. We show that this estimator is consistent and root-N asymptotically normally…

非对称核密度估计与平滑直方图的一致性及收入数据应用AI 解读

We consider asymmetric kernel density estimators and smoothed histograms when the unknown probability density function f is defined on [0,+∞). Uniform weak consistency on each compact set in [0,+∞) is proved for these estimators when f is continuous on its support. Weak convergence in L1 is also established. We further prove that the asymmetric kernel density estimator and the smoothed histogram converge in probability to infinity at x = 0 when the density is unbounded at x…

惩罚样条的精确似然比检验AI 解读

Penalised-spline-based additive models allow a simple mixed model representation where the variance components control departures from linear models. The smoothing parameter is the ratio of the random-coefficient and error variances and tests for linear regression reduce to tests for zero random-coefficient variances. We propose exactlikelihood and restricted likelihood ratio tests for testing polynomial regression versus a general alternative modelled by penalised splines.…

惩罚样条回归的理论AI 解读

Penalised spline regression is a popular new approach to smoothing, but its theoretical properties are not yet well understood. In this paper, mean squared error expressions and consistency results are derived by using a white-noise model representation for the estimator. The effect of the penalty on the bias and variance of the estimator is discussed, both for general splines and for the case of polynomial splines. The penalised spline regression estimator is shown to…

聚类数据的局部多项式回归分析AI 解读

This paper proposes a classical weighted least squares type of local polynomial smoothing for the analysis of clustered data, with the key idea of using generalised inverses of correlation matrices. The estimator has a simple closed-form expression. Simplicity is achieved also for nonparametric generalised linear models with arbitrary link function via a transformation. Our approach can be characterised by ‘local observations with local variances’, which yields intuitively…

卡方型混合分布的近似与渐近分布及其应用AI 解读

In this article we study how to approximate a random variable T of general chi-squared–type mixtures by a random variable of the form via matching the first three cumulants. The approximation error bounds for the density functions of the chi-squared approximation and the normal approximation are established. Applications of the results to some nonparametric goodness-of-fit tests, including those tests based on orthogonal series, smoothing splines, and local polynomial…

具有时变回归系数的Cox模型AI 解读

In the analysis of censored failure time observations, the standard Cox proportional hazards model assumes that the regression coefficients are time invariant. Often, these parameters vary over time, and the temporal covariate effects on the failure time are of great interest. In this article, following previous work of Cai and Sun, we propose a simple estimation procedure for the Cox model with time-varying coefficients based on a kernel-weighted partial likelihood…

量子层析入门AI 解读

Summary We describe quantum tomography as an inverse statistical problem in which the quantum state of a light beam is the unknown parameter and the data are given by results of measurements performed on identical quantum systems. The state can be represented as an infinite dimensional density matrix or equivalently as a density on the plane called the Wigner function. We present consistency results for pattern function projection estimators and for sieve maximum likelihood…

平滑回拟合的实践应用AI 解读

Summary Compared with the classical backfitting of Buja, Hastie and Tibshirani, the smooth backfitting estimator (SBE) of Mammen, Linton and Nielsen not only provides complete asymptotic theory under weaker conditions but is also more efficient, robust and easier to calculate. However, the original paper describing the SBE method is complex and the practical as well as the theoretical advantages of the method have still neither been recognized nor accepted by the statistical…

高维协变量下非参数回归的差分型方差估计AI 解读

Summary We consider the problem of estimating the noise variance in homoscedastic nonparametric regression models. For low dimensional covariates t ∈ ℝd, d=1, 2, difference-based estimators have been investigated in a series of papers. For a given length of such an estimator, difference schemes which minimize the asymptotic mean-squared error can be computed for d=1 and d=2. However, from numerical studies it is known that for finite sample sizes the performance of these…

总体分位数的迭代平滑自助法置信区间AI 解读

This paper investigates the effects of smoothed bootstrap iterations on coverage probabilities of smoothed bootstrap and bootstrap-t confidence intervals for population quantiles, and establishes the optimal kernel bandwidths at various stages of the smoothing procedures. The conventional smoothed bootstrap and bootstrap-t methods have been known to yield one-sided coverage errors of orders O(n−1/2) and o(n−2/3), respectively, for intervals based on the sample quantile of a…

非参数分类中的带宽选择AI 解读

It is shown that, for kernel-based classification with univariate distributions and two populations, optimal bandwidth choice has a dichotomous character. If the two densities cross at just one point, where their curvatures have the same signs, then minimum Bayes risk is achieved using bandwidths which are an order of magnitude larger than those which minimize pointwise estimation error. On the other hand, if the curvature signs are different, or if there are multiple…

自动半正定 HAC 协方差矩阵与 GMM 估计AI 解读

This paper proposes a new class of heteroskedastic and autocorrelation consistent (HAC) covariance matrix estimators. The standard HAC estimation method reweights estimators of the autocovariances. Here we initially smooth the data observations themselves using kernel function–based weights. The resultant HAC covariance matrix estimator is the normalized outer product of the smoothed random vectors and is therefore automatically positive semidefinite. A corresponding…