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超额质量与 Dip 峰态检验的校准AI 解读

Summary Nonparametric tests of modality are a distribution-free way of assessing evidence about inhomogeneity in a population, provided that the potential sub populations are sufficiently well separated. They include the excess mass and dip tests, which are equivalent in univariate settings and are alternatives to the bandwidth test. Only very conservative forms of the excess mass and dip tests are available at presently, however, and for that reason they are generally not…

二元分位数平滑样条AI 解读

Summary It has long been recognized that the mean provides an inadequate summary whereas the set of quantiles can supply a more complete description of a sample. We introduce bivariate quantile smoothing splines, which belong to the space of bilinear tensor product splines, as nonparametric estimators for the conditional quantile functions in a two-dimensional design space. The estimators can be computed by using standard linear programming techniques and can further be used…

通过再生实现自适应马尔可夫链蒙特卡洛AI 解读

Markov chain Monte Carlo (MCMC) is used for evaluating expectations of functions of interest under a target distribution π. This is done by calculating averages over the sample path of a Markov chain having π as its stationary distribution. For computational efficiency, the Markov chain should be rapidly mixing. This sometimes can be achieved only by careful design of the transition kernel of the chain, on the basis of a detailed preliminary exploratory analysis of π. An…

嵌套与交叉曲线样本分析的平滑样条模型AI 解读

We introduce a class of models for an additive decomposition of groups of curves stratified by crossed and nested factors, generalizing smoothing splines to such samples by associating them with a corresponding mixed-effects model. The models are also useful for imputation of missing data and exploratory analysis of variance. We prove that the best linear unbiased predictors (BLUPs) from the extended mixed-effects model correspond to solutions of a generalized penalized…

通过再生实现自适应马尔可夫链蒙特卡洛AI 解读

Markov chain Monte Carlo (MCMC) is used for evaluating expectations of functions of interest under a target distribution π. This is done by calculating averages over the sample path of a Markov chain having π as its stationary distribution. For computational efficiency, the Markov chain should be rapidly mixing. This sometimes can be achieved only by careful design of the transition kernel of the chain, on the basis of a detailed preliminary exploratory analysis of π. An…

从家庭总量推断个人需求：膳食构成的时间与年龄变化AI 解读

This paper uses non-parametric regression with smoothness induced by imposition of a roughness penalty to estimate time-dependent relationships between age and intakes of energy, total fat and saturated fatty acids employing data on household food acquisitions from a continuous survey covering the period 1975-94. A discrete analogue of the bivariate thin plate spline smoother is used to smooth the estimates across age and time. With age and calendar time-specific estimated…

从家庭总量恢复个人需求：膳食构成的时间与年龄变化AI 解读

This paper uses non-parametric regression with smoothness induced by imposition of a roughness penalty to estimate time-dependent relationships between age and intakes of energy, total fat and saturated fatty acids employing data on household food acquisitions from a continuous survey covering the period 1975-94. A discrete analogue of the bivariate thin plate spline smoother is used to smooth the estimates across age and time. With age and calendar time-specific estimated…

非参数自回归中的回归式推断AI 解读

We derive a strong approximation of a local polynomial estimator LPE in nonparametric autoregression by an (LPE) in a corresponding nonparametric regression model. This generally suggests the application of regression-typical tools for statistical inference in nonparametric autoregressive models. It provides an important simplification for the boot-strap method to be used: It is enough to mimic the structure of a nonparametric regression model rather than to imitate the more…

通过自适应窗口局部多项式拟合估计含不连续点的函数AI 解读

We propose a method of adaptive estimation of a regression function which is near optimal in the classical sense of the mean integrated error. At the same time, the estimator is shown to be very sensitive to discontinuities or change-points of the underlying function $f$ or its derivatives. For instance, in the case of a jump of a regression function, beyond the intervals of length (in order) $n^{-1} \log n$ around change-points the quality of estimation is essentially the…

样本选择模型的有效半参数评分估计AI 解读

A semiparametric likelihood method is proposed for the estimation of sample selection models. The method is a two-step semiparametric scoring estimation procedure based on an index restriction and kernel estimation. Under some regularity conditions, the estimator is square-root n -consistent and asymptotically normal. The estimator is also asymptotically efficient in the sense that its asymptotic covariance matrix attains the semiparametric efficiency bound under the index…

基于凸核的 M 估计量渐近理论AI 解读

We study the convergence in distribution of M -estimators over a convex kernel. Under convexity, the limit distribution of M -estimators can be obtained under minimal assumptions. We consider the case when the limit is arbitrary, not necessarily normal. If some Taylor expansions hold, the limit distribution is stable. As an application, we examine the limit distribution of M -estimators for the multivariate linear regression model. We obtain the distributional convergence of…

自相关误差下的加性非参数回归AI 解读

Summary A Bayesian approach is presented for nonparametric estimation of an additive regression model with autocorrelated errors. Each of the potentially non-linear components is modelled as a regression spline using many knots, while the errors are modelled by a high order stationary autoregressive process parameterized in terms of its autocorrelations. The distribution of significant knots and partial autocorrelations is accounted for using subset selection. Our approach…

利用改进的 Akaike 信息准则选择非参数回归的平滑参数AI 解读

Summary Many different methods have been proposed to construct nonparametric estimates of a smooth regression function, including local polynomial, (convolution) kernel and smoothing spline estimators. Each of these estimators uses a smoothing parameter to control the amount of smoothing performed on a given data set. In this paper an improved version of a criterion based on the Akaike information criterion (AIC), termed AICC, is derived and examined as a way to choose the…

流动性指标的年龄曲线：西德收入的应用AI 解读

This paper develops a technique for estimating age-profiles of earnings mobility using conditional kernel density estimation and establishes their statistical properties. Both pointwise and simultaneous confidence intervals are derived. The paper then examines the age-profile of short-run earnings mobility in Germany between 1983 and 1993 using the Socio-Economic Panel data. It turns out that earnings mobility is significantly higher for young people than for elder ones.…

杂记：非参数曲线估计中的设计变换与等数量分箱AI 解读

Methods based on design transformation and equal-number binning are shown to overcome problems of design sparseness, while retaining excellent theoretical properties. In company with local linear smoothing they produce optimal estimators, although with optirnality defined a little differently from in the nontransformed case. When used in conjunction with wavelet techniques they overcome problems of stochastic design, but, unlike related techniques based on convolution and…

局部线性平滑的偏差降低AI 解读

The standard approach to local linear regression involves fitting a straight line segment to a curve in a symmetrical way, in that the segment is fitted directly above a small region whose midpoint is the abscissa, x, at which we wish to estimate the curve. In this paper we show that, if the segment is fitted in a skew manner, with its centre a little to the left or right of x, then bias can be reduced by an order of magnitude, without affecting the order of magnitude of…

缺失数据下广义线性模型的局部线性回归AI 解读

Fan, Heckman and Wand proposed locally weighted kernel polynomial regression methods for generalized linear models and quasilikelihood functions. When the covariate variables are missing at random, we propose a weighted estimator based on the inverse selection probability weights. Distribution theory is derived when the selection probabilities are estimated nonparametrically. We show that the asymptotic variance of the resulting nonparametric estimator of the mean function…

加性模型中低维分量的直接估计AI 解读

Additive regression models have turned out to be a useful statistical tool in analyses of high-dimensional data sets. Recently, an estimator of additive components has been introduced by Linton and Nielsen which is based on marginal integration. The explicit definition of this estimator makes possible a fast computation and allows an asymptotic distribution theory. In this paper an asymptotic treatment of this estimate is offered for several models. A modification of this…

核与小波曲线估计中的块阈值规则AI 解读

Motivated by recently developed threshold rules for wavelet estimators, we suggest threshold methods for general kernel density estimators, including those of classical Rosenblatt–Parzen type. Thresholding makes kernel methods competitive in terms of their adaptivity to a wide variety of aberrations in complex signals. It is argued that term-by-term thresholding does not always produce optimal performance, since individual coefficients cannot be estimated sufficiently…

通过小波收缩实现极小极大估计AI 解读

We attempt to recover an unknown function from noisy, sampled data. Using orthonormal bases of compactly supported wavelets, we develop a nonlinear method which works in the wavelet domain by simple nonlinear shrinkage of the empirical wavelet coefficients. The shrinkage can be tuned to be nearly minimax over any member of a wide range of Triebel- and Besov-type smoothness constraints and asymptotically mini-max over Besov bodies with $p \leq q$. Linear estimates cannot…

纵向数据的半参数随机混合模型AI 解读

We consider inference for a semiparametric stochastic mixed model for longitudinal data. This model uses parametric fixed effects to represent the covariate effects and an arbitrary smooth function to model the time effect and accounts for the within-subject correlation using random effects and a stationary or nonstationary stochastic process. We derive maximum penalized likelihood estimators of the regression coefficients and the nonparametric function. The resulting…

分箱数据密度估计的高阶收敛率AI 解读

A method is proposed for achieving fast—O(n –8/9) and faster—asymptotic mean integrated squared error (AMISE) convergence rates in density estimation using data condensed to standard histogram bin counts and edges. The method involves the two elements of B splines and the correct mass proportions property, in which the probability mass for the histogram bins equals exactly the fraction of the data found in those bins. It is shown that the asymptotic bias of such an estimate…

单调 B 样条平滑AI 解读

Estimation of growth curves or item response curves often involves monotone data smoothing. Methods that have been studied in the literature tend to be either less flexible or more difficult to compute when constraints such as monotonicity are incorporated. Built on the ideas of Koenker, Ng, and Portnoy and Ramsay, we propose monotone B-spline smoothing based on L 1 optimization. This method inherits the desirable properties of spline approximations and the computational…

用于刚体运动估计与几何质量检验的线性模型AI 解读

A geometrical method to assess the quality of a part is to sample points on the surface of the part and to bring an ideal computer representation of the part as close as possible to the sampled locations. The points are sampled with a coordinate measuring machine (CMM) that gives the coordinates, with respect to the machine's own three-dimensional system of axis, of the sampled locations. Computer-assisted design (CAD) gives the ideal representation of the part. The matching…