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多元凸变换密度的非参数估计AI 解读

We study estimation of multivariate densities p of the form p(x) = h(g(x)) for x ∈ ℝ^{d} and for a fixed monotone function h and an unknown convex function g. The canonical example is h(y) = e^{−y} for y ∈ ℝ; in this case, the resulting class of densities $P ( {e}^{− y} ) = \{ p = exp ( − g ) : g \kern0.2em \mathrm{is convex} \}$ is well known as the class of log-concave densities. Other functions h allow for classes of densities with heavier tails than the log-concave…

部分线性单指标模型的估计与检验AI 解读

In partially linear single-index models, we obtain the semiparametrically efficient profile least-squares estimators of regression coefficients. We also employ the smoothly clipped absolute deviation penalty (SCAD) approach to simultaneously select variables and estimate regression coefficients. We show that the resulting SCAD estimators are consistent and possess the oracle property. Subsequently, we demonstrate that a proposed tuning parameter selector, BIC, identifies the…

族错误率控制的序贯拒绝原理AI 解读

Closed testing and partitioning are recognized as fundamental principles of familywise error control. In this paper, we argue that sequential rejection can be considered equally fundamental as a general principle of multiple testing. We present a general sequentially rejective multiple testing procedure and show that many well-known familywise error controlling methods can be constructed as special cases of this procedure, among which are the procedures of Holm, Shaffer and…

曲线时间序列有限维数的识别AI 解读

The curve time series framework provides a convenient vehicle to accommodate some nonstationary features into a stationary setup. We propose a new method to identify the dimensionality of curve time series based on the dynamical dependence across different curves. The practical implementation of our method boils down to an eigenanalysis of a finite-dimensional matrix. Furthermore, the determination of the dimensionality is equivalent to the identification of the nonzero…

Markowitz 问题及线性约束二次规划的高维效应：风险低估AI 解读

We first study the properties of solutions of quadratic programs with linear equality constraints whose parameters are estimated from data in the high-dimensional setting where p, the number of variables in the problem, is of the same order of magnitude as n, the number of observations used to estimate the parameters. The Markowitz problem in Finance is a subcase of our study. Assuming normality and independence of the observations we relate the efficient frontier computed…

纵向数据的经验动态建模AI 解读

We demonstrate that the processes underlying on-line auction price bids and many other longitudinal data can be represented by an empirical first order stochastic ordinary differential equation with time-varying coefficients and a smooth drift process. This equation may be empirically obtained from longitudinal observations for a sample of subjects and does not presuppose specific knowledge of the underlying processes. For the nonparametric estimation of the components of…

高维情形下主成分得分的收敛与预测AI 解读

A number of settings arise in which it is of interest to predict Principal Component (PC) scores for new observations using data from an initial sample. In this paper, we demonstrate that naive approaches to PC score prediction can be substantially biased towards 0 in the analysis of large matrices. This phenomenon is largely related to known inconsistency results for sample eigenvalues and eigenvectors as both dimensions of the matrix increase. For the spiked eigenvalue…

使用位置—尺度混合先验的自适应非参数贝叶斯推断AI 解读

We study location-scale mixture priors for nonparametric statistical problems, including multivariate regression, density estimation and classification. We show that a rate-adaptive procedure can be obtained if the prior is properly constructed. In particular, we show that adaptation is achieved if a kernel mixture prior on a regression function is constructed using a Gaussian kernel, an inverse gamma bandwidth, and Gaussian mixing weights.

主成分的最优秩检验AI 解读

This paper provides parametric and rank-based optimal tests for eigenvectors and eigenvalues of covariance or scatter matrices in elliptical families. The parametric tests extend the Gaussian likelihood ratio tests of Anderson (1963) and their pseudo-Gaussian robustifications by Davis (1977) and Tyler (1981, 1983). The rank-based tests address a much broader class of problems, where covariance matrices need not exist and principal components are associated with more general…

空间自回归模型的有效 GMM 估计量AI 解读

In this paper, we consider GMM estimation of the regression and MRSAR models with SAR disturbances. We derive the best GMM estimator within the class of GMM estimators based on linear and quadratic moment conditions. The best GMM estimator has the merit of computational simplicity and asymptotic efficiency. It is asymptotically as efficient as the ML estimator under normality and asymptotically more efficient than the Gaussian QML estimator otherwise. Monte Carlo studies…

阈值双幂变差与跳跃对波动率预测的影响AI 解读

This study reconsiders the role of jumps for volatility forecasting by showing that jumps have a positive and mostly significant impact on future volatility. This result becomes apparent once volatility is separated into its continuous and discontinuous components using estimators which are not only consistent, but also scarcely plagued by small sample bias. With the aim of achieving this, we introduce the concept of threshold bipower variation, which is based on the joint…

最小方差投资组合的支配性估计量AI 解读

In this paper, we derive two shrinkage estimators for minimum-variance portfolios that dominate the traditional estimator with respect to the out-of-sample variance of the portfolio return. The presented results hold for any number of assets d>=4 and number of observations n>=d+2. The small-sample properties of the shrinkage estimators as well as their large-sample properties for fixed d but n-->[infinity] and n,d-->[infinity] but n/d-->q<=[infinity] are investigated.…

半参数 M 估计量渐近分布的刻画AI 解读

This paper develops a concrete formula for the asymptotic distribution of two-step, possibly non-smooth semiparametric M-estimators under general misspecification. Our regularity conditions are relatively straightforward to verify and also weaker than those available in the literature. The first-stage nonparametric estimation may depend on finite dimensional parameters. We characterize: (1) conditions under which the first-stage estimation of nonparametric components do not…

惩罚化高维经验似然AI 解读

We propose penalized empirical likelihood for parameter estimation and variable selection for problems with diverging numbers of parameters. Our results are demonstrated for estimating the mean vector in multivariate analysis and regression coefficients in linear models. By using an appropriate penalty function, we showthat penalized empirical likelihood has the oracle property. That is, with probability tending to 1, penalized empirical likelihood identifies the true model…

局部错设模型下的一般设定检验AI 解读

A well known result is that many of the tests used in econometrics, such as the Rao score (RS) test, may not be robust to misspecified alternatives, that is, when the alternative model does not correspond to the underlying data generating process. Under this scenario, these tests spuriously reject the null hypothesis too often. We generalize this result to generalized method of moments–based (GMM-based) tests. We also extend the method proposed in Bera and Yoon (1993,…

线性工具变量回归中的新投影型分样本得分检验AI 解读

In this paper we introduce a new method of projection-type inference and describe it in the context of two stage least squares–based split-sample inference on subsets of structural coefficients in a linear instrumental variables regression model. The use of the new method not only guards against the uncontrolled overrejection of the true value of the parameters of interest but also reduces the conservativeness of the usual method of projection proposed by Dufour and his…

函数系数变换模型的局部秩估计AI 解读

This paper considers a nonparametric functional coefficient model with an unknown link function. The model gives flexibility to the standard interaction-variable model by allowing an arbitrary functional form of heterogeneous marginal effects. A local rank estimation procedure is proposed for the functional coefficients along with its asymptotic property.

部分线性模型的结构变化检验AI 解读

We consider two tests of structural change for partially linear time-series models. The first tests for structural change in the parametric component, based on the cumulative sums of gradients from a single semiparametric regression. The second tests for structural change in the parametric and nonparametric components simultaneously, based on the cumulative sums of weighted residuals from the same semiparametric regression. We derive the limiting distributions of both tests…

条件异方差下的协整秩检验AI 解读

We analyze the properties of the conventional Gaussian-based cointegrating rank tests of Johansen (1996, Likelihood-Based Inference in Cointegrated Vector Autoregressive Models) in the case where the vector of series under test is driven by globally stationary, conditionally heteroskedastic (martingale difference) innovations. We first demonstrate that the limiting null distributions of the rank statistics coincide with those derived by previous authors who assume either…

半参数单指标模型估计与检验的偏差校正AI 解读

Semiparametric methods are widely employed in applied work where the ability to conduct inferences is important. To establish asymptotic normality for making inferences, bias control mechanisms are often used in implementing semiparametric estimators. The first contribution of this paper is to propose a mechanism that enables us to establish asymptotic normality with regular kernels. In so doing, we argue that the resulting estimator performs very well in finite samples.…

兼容定性与定量数据的平滑变系数估计与推断AI 解读

We propose a semiparametric varying-coefficient estimator that admits both qualitative and quantitative covariates along with a test for correct specification of parametric varying-coefficient models. The proposed estimator is exceedingly flexible and has a wide range of potential applications including hierarchical (mixed) settings, small area estimation, etc. A data-driven cross-validatory bandwidth selection method is proposed that can handle both the qualitative and…

用于贝叶斯与频率学派推断的默认先验AI 解读

Summary We investigate the choice of default priors for use with likelihood for Bayesian and frequentist inference. Such a prior is a density or relative density that weights an observed likelihood function, leading to the elimination of parameters that are not of interest and then a density-type assessment for a parameter of interest. For independent responses from a continuous model, we develop a prior for the full parameter that is closely linked to the original Bayes…

通过贝叶斯先验—后验转移拟合实现时间扭曲的多分辨率方法AI 解读

Summary Warping is an approach to the reduction and analysis of phase variability in functional observations, by applying a smooth bijection to the function argument. We propose a natural representation of warping functions in terms of a new type of elementary functions named ‘warping component functions’, or ‘warplets’, which are combined into the warping function by composition. The inverse warping function is trivial and explicit to obtain. A sequential Bayesian…

有偏抽样下右删失数据的非参数检验AI 解读

Summary Testing the equality of two survival distributions can be difficult in a prevalent cohort study when non-random sampling of subjects is involved. Owing to the biased sampling scheme, the independent censoring assumption is often violated. Although the issues about biased inference caused by length-biased sampling have been widely recognized in the statistical, epidemiological and economical literature, there is no satisfactory solution for efficient two-sample…