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核密度估计的双侧验证带宽选择AI 解读

Bandwidth selection in kernel density estimation is one of the fundamental model selection problems of mathematical statistics. The study of this problem took major steps forward with the articles of Hall and Marron (1987) and Hall and Johnstone (1992). Since then, the focus seems to have been on various versions of implementing the so-called plug-in method aimed at estimating the minimum mean integrated squared error (MISE). The most successful of these efforts still seems…

有限总体复杂抽样设计的直接自助法AI 解读

In complex designs, classical bootstrap methods result in a biased variance estimator when the sampling design is not taken into account. Resampled units are usually rescaled or weighted in order to achieve unbiasedness in the linear case. In the present article, we propose novel resampling methods that may be directly applied to variance estimation. These methods consist of selecting subsamples under a completely different sampling scheme from that which generated the…

半参数贝叶斯层级模型估计利率期限结构：公司债应用AI 解读

The term structure of interest rates is used to price defaultable bonds and credit derivatives, as well as to infer the quality of bonds for risk management purposes. We introduce a model that jointly estimates term structures by means of a Bayesian hierarchical model with a prior probability model based on Dirichlet process mixtures. The modeling methodology borrows strength across term structures for purposes of estimation. The main advantage of our framework is its…

体视学体积估计的分布估计量与置信区间AI 解读

Assessing the precision of volume estimates from systematic samples is a question of great practical importance, but statistically a challenging task due to the strong spatial dependence of the data and typically small sample sizes. The approach taken in this paper is more ambitious than earlier methodologies, the goal of which was estimation of the variance of a volume estimator v̂, rather than estimation of the distribution of v̂. We shall show that bootstrap methods yield…

条件资产定价模型的估计与评价AI 解读

ABSTRACT We find that several recently proposed consumption‐based models of stock returns, when evaluated using an optimal set of managed portfolios and the associated model‐implied conditional moment restrictions, fail to capture key features of risk premiums in equity markets. To arrive at these conclusions, we construct an optimal Generalized Method of Moments (GMM) estimator for models in which the stochastic discount factor (SDF) is a conditionally affine function of a…

作为病态逆问题的半参数需求分析AI 解读

In this paper we are concerned with analyzing the behavior of a semiparametric estimator that corrects for endogeneity in a nonparametric regression by assuming mean independence of residuals from instruments only. Because it is common in many applications, we focus on the case where endogenous regressors and additional instruments are jointly normal, conditional on exogenous regressors. This leads to a severely ill-posed inverse problem. In this setup, we show first how to…

未知连接函数加性模型的 Oracle 有效非参数估计AI 解读

This paper describes an estimator of the additive components of a nonparametric additive model with an unknown link function. When the additive components and link function are twice differentiable with sufficiently smooth second derivatives, the estimator is asymptotically normally distributed with a rate of convergence in probability of n −2/5 . This is true regardless of the (finite) dimension of the explanatory variable. Thus, the estimator has no curse of…

教育回报估计：基于正态混合的似然方法AI 解读

Abstract In this paper we develop likelihood‐based methods for statistical inference in a joint system of equations for the choice of length of schooling and earnings. The model for schooling choice is assumed to be an ordered probit model, whereas the earnings equation contains variables that are flexible transformations of schooling and experience, with corresponding coefficients that are allowed to be heterogeneous across individuals. Under the assumption that the…

含弱识别干扰参数的 GMM 新投影推断方法AI 解读

Projection-based tests for subsets of parameters are useful because they do not over-reject the true parameter values when either it is difficult to estimate the nuisance parameters or their identification status is questionable. However, they are also often criticized for being overly conservative. We overcome this conservativeness by introducing a new projection-based test that is more powerful than the traditional projection-based tests. The new test is even…

二元响应模型的一族经验似然函数与估计量AI 解读

The minimum discrimination information principle is used to identify an appropriate parametric family of probability distributions and the corresponding maximum likelihood estimators for binary response models. Estimators in the family subsume the conventional logit model and form the basis for a set of parametric estimation alternatives with the usual asymptotic properties. Sampling experiments are used to assess finite sample performance.

相对于给定函数的二阶随机占优半非参数检验AI 解读

In an expected utility framework, assuming a decision maker operates under utility k([dot operator][theta]), for two risky alternatives X and Y with respective distribution functions F and G, alternative X is said to dominate alternative Y with respect to k([dot operator][theta]) if for all y. Utilizing the empirical distribution functions of F and G, a statistical test is presented to test the null hypothesis of indifference between X and Y given k([dot operator][theta])…

双重差分模型中的分布恢复：选拔制与综合制中学教育比较AI 解读

We compare the effects of selective and nonselective secondary education on children's test scores, using British data from the National Child Development Study. Test scores are modeled as the output of an additive production function. An important input is the child's unobserved initial endowment, which may be correlated with the education system attended. In this model, we generalize the difference-in-differences approach and identify the entire counterfactual distribution…

高维矩阵降秩估计量的最优选择AI 解读

We introduce a new criterion, the Rank Selection Criterion (RSC), for selecting the optimal reduced rank estimator of the coefficient matrix in multivariate response regression models. The corresponding RSC estimator minimizes the Frobenius norm of the fit plus a regularization term proportional to the number of parameters in the reduced rank model. The rank of the RSC estimator provides a consistent estimator of the rank of the coefficient matrix; in general, the rank of…

The delta method is a popular and elementary tool for deriving limiting distributions of transformed statistics, while applications of asymptotic distributions do not allow one to obtain desirable accuracy of approximation for tail probabilities. The large and moderate deviation theory can achieve this goal. Motivated by the delta method in weak convergence, a general delta method in large deviations is proposed. The new method can be widely applied to driving the moderate…

偏序下的多元分位数AI 解读

This paper focuses on generalizing quantiles from the ordering point of view. We propose the concept of partial quantiles, which are based on a given partial order. We establish that partial quantiles are equivariant under order-preserving transformations of the data, robust to outliers, characterize the probability distribution if the partial order is sufficiently rich, generalize the concept of efficient frontier, and can measure dispersion from the partial order…

平面形状平均测地线的内蕴推断与基于叶片生长的树木区分AI 解读

For planar landmark based shapes, taking into account the non-Euclidean geometry of the shape space, a statistical test for a common mean first geodesic principal component (GPC) is devised which rests on one of two asymptotic scenarios. For both scenarios, strong consistency and central limit theorems are established, along with an algorithm for the computation of a Ziezold mean geodesic. In application, this allows to verify the geodesic hypothesis for leaf growth of…

含噪声与高维尺度下的低秩及近低秩矩阵估计AI 解读

We study an instance of high-dimensional inference in which the goal is to estimate a matrix Θ∗∈ℝm1×m2 on the basis of N noisy observations. The unknown matrix Θ∗ is assumed to be either exactly low rank, or “near” low-rank, meaning that it can be well-approximated by a matrix with low rank. We consider a standard M-estimator based on regularization by the nuclear or trace norm over matrices, and analyze its performance under high-dimensional scaling. We define the notion of…

复合假设检验、Hermite 多项式与非光滑泛函的最优估计AI 解读

A general lower bound is developed for the minimax risk when estimating an arbitrary functional. The bound is based on testing two composite hypotheses and is shown to be effective in estimating the nonsmooth functional (1/n)∑|θi| from an observation Y∼N(θ, In). This problem exhibits some features that are significantly different from those that occur in estimating conventional smooth functionals. This is a setting where standard techniques fail to yield sharp results. A…

自适应马尔可夫链蒙特卡洛的渐近方差核估计AI 解读

We study the asymptotic behavior of kernel estimators of asymptotic variances (or long-run variances) for a class of adaptive Markov chains. The convergence is studied both in Lp and almost surely. The results also apply to Markov chains and improve on the existing literature by imposing weaker conditions. We illustrate the results with applications to the GARCH(1, 1) Markov model and to an adaptive MCMC algorithm for Bayesian logistic regression.

估计逆回归函数的两阶段混合程序AI 解读

We consider a two-stage procedure (TSP) for estimating an inverse regression function at a given point, where isotonic regression is used at stage one to obtain an initial estimate and a local linear approximation in the vicinity of this estimate is used at stage two. We establish that the convergence rate of the second-stage estimate can attain the parametric n1/2 rate. Furthermore, a bootstrapped variant of TSP (BTSP) is introduced and its consistency properties studied.…

变阶可逆马尔可夫链的贝叶斯分析AI 解读

We define a conjugate prior for the reversible Markov chain of order r. The prior arises from a partially exchangeable reinforced random walk, in the same way that the Beta distribution arises from the exchangeable Polyá urn. An extension to variable-order Markov chains is also derived. We show the utility of this prior in testing the order and estimating the parameters of a reversible Markov model.

长时间区间内基于高频数据的 Lévy 过程估计AI 解读

In this paper, we study nonparametric estimation of the Lévy density for Lévy processes, with and without Brownian component. For this, we consider n discrete time observations with step Δ. The asymptotic framework is: n tends to infinity, Δ=Δn tends to zero while nΔn tends to infinity. We use a Fourier approach to construct an adaptive nonparametric estimator of the Lévy density and to provide a bound for the global ${\mathbb{L}}^{2}$-risk. Estimators of the drift and of…

含噪观测下波动率推断的渐近等价性AI 解读

We consider discrete-time observations of a continuous martingale under measurement error. This serves as a fundamental model for high-frequency data in finance, where an efficient price process is observed under microstructure noise. It is shown that this nonparametric model is in Le Cam’s sense asymptotically equivalent to a Gaussian shift experiment in terms of the square root of the volatility function σ and a nonstandard noise level. As an application, new rate-optimal…

可能非线性模型中的弱识别检验AI 解读

In this paper we propose a chi-square test for identification. Our proposed test statistic is based on the distance between two shrinkage extremum estimators. The two estimators converge in probability to the same limit when identification is strong, and their asymptotic distributions are different when identification is weak. The proposed test is consistent not only for the alternative hypothesis of no identification but also for the alternative of weak identification,…