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时间序列的经验似然拟合优度检验AI 解读

Summary Standard goodness-of-fit tests for a parametric regression model against a series of nonparametric alternatives are based on residuals arising from a fitted model. When a parametric regression model is compared with a nonparametric model, goodness-of-fit testing can be naturally approached by evaluating the likelihood of the parametric model within a nonparametric framework. We employ the empirical likelihood for an α-mixing process to formulate a test statistic that…

长记忆参数半参数 Whittle 估计的 Edgeworth 展开AI 解读

The semiparametric local Whittle or Gaussian estimate of the long memory parameter is known to have especially nice limiting distributional properties, being asymptotically normal with a limiting variance that is completely known. However in moderate samples the normal approximation may not be very good, so we consider a refined, Edgeworth, approximation, for both a tapered estimate and the original untapered one. For the tapered estimate, our higher-order correction…

加速随机化随机优化AI 解读

We propose a general class of randomized gradient estimates to be employed in a recursive search for the minimum of an unknown multivariate regression function. Here only two observations per iteration step are used. Special cases include random direction stochastic approximation (Kushner and Clark), simultaneous perturbation stochastic approximation (Spall) and a special kernel based stochastic approximation method (Polyak and Tsybakov). If the unknown regression is…

齐次函数的非参数估计AI 解读

Consider the regression , where and the exact functional form of f is unknown, although we do know that f is homogeneous of known degree r. Using a local linear approach, we examine two ways of nonparametrically estimating f: (i) a “direct” approach and (ii) a “projection based” approach. We show that depending upon the nature of the conditional variance , one approach may be asymptotically better than the other. Results of a small simulation experiment are presented to…

变换模型的成对差分秩估计AI 解读

coefficient vector in a transformation model. These estimators, like other existing rank estimators, require no subjective bandwidth choice. Monte Carlo simulations, numerical asymptotic efficiency comparisons, and two empirical applications suggest that the proposed estimators perform well in comparison with existing semiparametric estimators.

完全贝叶斯样条平滑与内蕴自回归先验AI 解读

There is a well‐known Bayesian interpretation for function estimation by spline smoothing using a limit of proper normal priors. The limiting prior and the conditional and intrinsic autoregressive priors popular for spatial modelling have a common form, which we call partially informative normal. We derive necessary and sufficient conditions for the propriety of the posterior for this class of partially informative normal priors with noninformative priors on the variance…

回归曲线的非参数比较：经验过程方法AI 解读

We propose a new test for the comparison of two regression curves that is based on a difference of two marked empirical processes based on residuals. The large sample behavior of the corresponding statistic is studied to provide a full nonparametric comparison of regression curves. In contrast to most procedures suggested in the literature, the new procedure is applicable in the case of different design points and heteroscedasticity. Moreover, it is demonstrated that the…

时间虚拟变量对质量特征均值独立时的特征价格指数估计AI 解读

. In addition to these, several interesting practical lessons are noted in doing the two-stage PLR model estimation. First, the cross validation (CV) used in the PLR model literature can fail if the mean-independence is ignored. Second, high order kernels can make the CV criterion function ill behaved. Third, product kernels work as well as spherically symmetric kernels. Fourth, nonparametric specification tests may work poorly due to a sample splitting problem with outliers…

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核苷酸序列沿线系统发育变异的推断AI 解读

We develop a Bayesian multiple changepoint model to infer spatial phylogenetic variation (SPV) along aligned molecular sequence data. SPV occurs in sequences from organisms that have undergone biological recombination or when evolutionary rates and selective pressures vary along the sequences. This Bayesian approach permits estimation of uncertainty regarding recombination, the crossing-over locations, and all other model parameters. The model assumes that the sites along…

多元自适应样条模型中线性方向的识别AI 解读

Identifying linear directions in multivariate regression has been a statistical challenge and has attracted particular attention since projection pursuit was developed. To this end, we propose and investigate the use of linear discriminant analysis and projection Hessian directions in conjunction with multivariate adaptive regression splines. Simulation studies in a variety of settings demonstrate the usefulness of our approach in revealing both the functional forms and the…

基于多元自由结点回归样条的广义非线性建模AI 解读

A Bayesian method is presented for the nonparametric modeling of univariate and multivariate non-Gaussian response data. Data-adaptive multivariate regression splines are used where the number and location of the knot points are treated as random. The posterior model space is explored using a reversible-jump Markov chain Monte Carlo sampler. Computational difficulties are partly alleviated by introducing a random residual effect in the model that leaves many of the posterior…

采用平方损失的提升方法AI 解读

This article investigates a computationally simple variant of boosting, L2Boost, which is constructed from a functional gradient descent algorithm with the L2-loss function. Like other boosting algorithms, L2Boost uses many times in an iterative fashion a prechosen fitting method, called the learner. Based on the explicit expression of refitting of residuals of L2Boost, the case with (symmetric) linear learners is studied in detail in both regression and classification. In…

时间序列误差下非参数回归推断的差分方法AI 解读

Summary We show that difference-based methods can be used to construct simple and explicit estimators of error covariance and autoregressive parameters in nonparametric regression with time series errors. When the error process is Gaussian our estimators are efficient, but they are available well beyond the Gaussian case. As an illustration of their usefulness we show that difference-based estimators can be used to produce a simplified version of time series…

长记忆参数的高阶核半参数 M 估计AI 解读

Econometric interest in the possibility of long memory has developed as a flexible alternative to, or compromise between, the usual short memory or unit root prescriptions, for example in the context of modelling cointegrating or other relationships and in describing the dependence structure of nonlinear functions of financial returns. Semiparametric methods of estimating the memory parameter can avoid bias incurred by misspecification of the short memory component. We…

具有 GARCH 误差的非平稳 ARMA 模型中的自适应估计AI 解读

This paper considers adaptive estimation in nonstationary autoregressive moving average models with the noise sequence satisfyinga generalized autoregressive conditional heteroscedastic process. The locally asymptotic quadratic form of the log-likelihood ratio for the model is obtained. It is shown that the limit experiment is neither LAN nor LAMN, but is instead LABF. For the model with symmetric density of the rescaled error, a new efficiency criterion is established for a…

加性与乘性风险率函数的核估计AI 解读

We propose new procedures for estimating the component functions in both additive and multiplicative nonparametric marker-dependent hazard models. We work with a full counting process framework that allows for left truncation and right censoring and time-varying covariates. Our procedures are based on kernel hazard estimation as developed by Nielsen and Linton and on the idea of marginal integration. We provide a central limit theorem for the marginal integration estimator.…

考虑个体内相关性的边际非参数核回归AI 解读

There has been substantial recent interest in non‐ and semiparametric methods for longitudinal or clustered data with dependence within clusters. It has been shown rather inexplicably that, when standard kernel smoothing methods are used in a natural way, higher efficiency is obtained by assuming independence than by using the true correlation structure. It is shown here that this result is a natural consequence of how standard kernel methods incorporate the within‐subject…

扩散估计量的重新审视及其在金融模型检验中的应用AI 解读

Time-homogeneous diffusion models have been widely used for describing the stochastic dynamics of the underlying economic variables. Recently, Stanton proposed drift and diffusion estimators based on a higher-order approximation scheme and kernel regression method. He claimed that “higher order approximations must outperform lower order approximations” and concluded nonlinearity in the instantaneous return function of short-term interest rates. To examine the impact of…

统计逆问题的双重平滑 EM 算法AI 解读

Recent results on discretization effects in unfolding intensity function of an indirectly observed nonhomogeneous Poisson process show that a critical feasibility condition for the strong L2 consistency of the histogram sieve maximum likelihood estimates requires that the approximation error of the function of interest with step functions tend to 0 faster than the squared singular values of the discretized folding operator. This condition may not be fulfilled in some…

薄板回归样条AI 解读

Summary I discuss the production of low rank smoothers for d ≥ 1 dimensional data, which can be fitted by regression or penalized regression methods. The smoothers are constructed by a simple transformation and truncation of the basis that arises from the solution of the thin plate spline smoothing problem and are optimal in the sense that the truncation is designed to result in the minimum possible perturbation of the thin plate spline smoothing problem given the dimension…

自适应变系数线性模型AI 解读

Summary Varying-coefficient linear models arise from multivariate nonparametric regression, non-linear time series modelling and forecasting, functional data analysis, longitudinal data analysis and others. It has been a common practice to assume that the varying coefficients are functions of a given variable, which is often called an index. To enlarge the modelling capacity substantially, this paper explores a class of varying-coefficient linear models in which the index is…

约翰·W.图基在时间序列与谱分析方面的工作AI 解读

The contributions of John W. Tukey to time series analysis, particularly spectrum analysis, are reviewed and discussed. The contributions include: methods, their properties, terminology, popularization, philosophy, applications and education. Much of Tukey's early work on spectrum analysis remained unpublished for many years, but the 1959 book by Blackman and Tukey made his approach accessible to a wide audience. In 1965 the Cooley-Tukey paper on the Fast Fourier Transform…

随机场方法的线性检验与似然推断准确性考察AI 解读

We analyze the random field regression model approach recently suggested by Hamilton (2001, Econometrica, 69, 537--73). We show through extensive simulation studies that although the random field approach is indeed very closely related to the non-parametric spline smoother it seems to offer several advantages over the latter. First, tests for neglected nonlinearity based on Hamilton's random field approach seem to be more powerful than existing test statistics developed…