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高斯随机场驱动空间点过程的充分降维AI 解读

Summary We develop a sufficient dimension reduction paradigm for inhomogeneous spatial point processes driven by Gaussian random fields. Specifically, we introduce the notion of the kth-order central intensity subspace. We show that a central subspace can be defined as the combination of all central intensity subspaces. For many commonly used spatial point process models, we find that the central subspace is equivalent to the first-order central intensity subspace. To…

粒子 Markov 链 Monte Carlo 方法AI 解读

Summary Markov chain Monte Carlo and sequential Monte Carlo methods have emerged as the two main tools to sample from high dimensional probability distributions. Although asymptotic convergence of Markov chain Monte Carlo algorithms is ensured under weak assumptions, the performance of these algorithms is unreliable when the proposal distributions that are used to explore the space are poorly chosen and/or if highly correlated variables are updated independently. We show…

时间序列置信区间构造的自归一化方法AI 解读

Summary We propose a new method to construct confidence intervals for quantities that are associated with a stationary time series, which avoids direct estimation of the asymptotic variances. Unlike the existing tuning-parameter-dependent approaches, our method has the attractive convenience of being free of any user-chosen number or smoothing parameter. The interval is constructed on the basis of an asymptotically distribution-free self-normalized statistic, in which the…

弱依赖函数型数据AI 解读

Functional data often arise from measurements on fine time grids and are obtained by separating an almost continuous time record into natural consecutive intervals, for example, days. The functions thus obtained form a functional time series, and the central issue in the analysis of such data consists in taking into account the temporal dependence of these functional observations. Examples include daily curves of financial transaction data and daily patterns of geophysical…

最高密度区域估计的渐近理论与最优带宽选择AI 解读

We study kernel estimation of highest-density regions (HDR). Our main contributions are two-fold. First, we derive a uniform-in-bandwidth asymptotic approximation to a risk that is appropriate for HDR estimation. This approximation is then used to derive a bandwidth selection rule for HDR estimation possessing attractive asymptotic properties. We also present the results of numerical studies that illustrate the benefits of our theory and methodology.

Collaborative recommendation is an information-filtering technique that attempts to present information items that are likely of interest to an Internet user. Traditionally, collaborative systems deal with situations with two types of variables, users and items. In its most common form, the problem is framed as trying to estimate ratings for items that have not yet been consumed by a user. Despite wide-ranging literature, little is known about the statistical properties of…

Efron [Biometrika 58 (1971) 403–417] developed a restricted randomization procedure to promote balance between two treatment groups in a sequential clinical trial. He called this the biased coin design. He also introduced the concept of accidental bias, and investigated properties of the procedure with respect to both accidental and selection bias, balance, and randomization-based inference using the steady-state properties of the induced Markov chain. In this paper we…

可选 Pólya 树与贝叶斯推断AI 解读

We introduce an extension of the Pólya tree approach for constructing distributions on the space of probability measures. By using optional stopping and optional choice of splitting variables, the construction gives rise to random measures that are absolutely continuous with piecewise smooth densities on partitions that can adapt to fit the data. The resulting “optional Pólya tree” distribution has large support in total variation topology and yields posterior distributions…

高度或非高度相关协变量下的加性模型估计AI 解读

Motivated by normalizing DNA microarray data and by predicting the interest rates, we explore nonparametric estimation of additive models with highly correlated covariates. We introduce two novel approaches for estimating the additive components, integration estimation and pooled backfitting estimation. The former is designed for highly correlated covariates, and the latter is useful for nonhighly correlated covariates. Asymptotic normalities of the proposed estimators are…

具有高阶精度的调整经验似然AI 解读

Empirical likelihood is a popular nonparametric or semi-parametric statistical method with many nice statistical properties. Yet when the sample size is small, or the dimension of the accompanying estimating function is high, the application of the empirical likelihood method can be hindered by low precision of the chi-square approximation and by nonexistence of solutions to the estimating equations. In this paper, we show that the adjusted empirical likelihood is effective…

方向边界锥包估计量的渐近分布AI 解读

Nonparametric data envelopment analysis (DEA) estimators have been widely applied in analysis of productive efficiency. Typically they are defined in terms of convex-hulls of the observed combinations of inputs×outputs in a sample of enterprises. The shape of the convex-hull relies on a hypothesis on the shape of the technology, defined as the boundary of the set of technically attainable points in the inputs × outputs space. So far, only the statistical properties of the…

部分识别模型的经验似然推断：大偏差最优性与自助法有效性AI 解读

This paper addresses the issue of optimal inference for parameters that are partially identified in models with moment inequalities. There currently exists a variety of inferential methods for use in this setting. However, the question of choosing optimally among contending procedures is unresolved. In this paper, I first consider a canonical large deviations criterion for optimality and show that inference based on the empirical likelihood ratio statistic is optimal.…

聚焦平均导数的单指标限制检验AI 解读

This paper considers a situation where the violation of a single-index restriction is a concern only to the extent that it causes bias to the estimates of the average derivatives. We propose a method to construct tests that concentrate their asymptotic powers upon only such interesting alternatives. The test has a limiting distribution under the null hypothesis, and even accommodates the case where the parameter estimates have a convergence rate slower than as in the case of…

多元密度的指数级数估计量AI 解读

We present an Exponential Series Estimator (ESE) of multivariate densities, which has an appealing information-theoretic interpretation. For a d dimensional random variable with density p0, the ESE takes the form , where are some real-valued, linearly independent functions defined on the support of p0. We derive the convergence rate of the ESE in terms of the Kullback-Leibler Information Criterion, the integrated squared error and some other metrics. We also derive its…

Hausman 预检验对假设检验尺寸的影响：面板数据情形AI 解读

The size properties of a two-stage test in a panel data model are investigated where in the first stage a Hausman (1978) specification test is used as a pretest of the random effects specification and in the second stage, a simple hypothesis about a component of the parameter vector is tested, using a t-statistic that is based on either the random effects or the fixed effects estimator depending on the outcome of the Hausman pretest. It is shown that the asymptotic size of…

利用梯形核在 GMM 中同时选择和加权矩条件AI 解读

This paper proposes a novel procedure to estimate linear models when the number of instruments is large. At the heart of such models is the need to balance the trade off between attaining asymptotic efficiency, which requires more instruments, and minimizing bias, which is adversely affected by the addition of instruments. Two questions are of central concern: (1) What is the optimal number of instruments to use? (2) Should the instruments receive different weights? This…

序贯教育决策中的异质回报AI 解读

This paper presents a method for estimating returns to multiple schooling levels taking into account that returns may be heterogeneous among agents and that educational decisions are made sequentially. A sequential decision model explicitly considers that the level of education is the result of previous schooling choices and so, the variation of supply-side instruments over time will emerge as a source of identification of the desired parameters. A test for heterogeneity in…

两类半参数扩散模型的伪最大似然估计AI 解读

Two classes of semiparametric diffusion models are considered, where either the drift or the diffusion term is parameterized, while the other term is left unspecified. We propose a pseudo-maximum likelihood estimator (PMLE) of the parametric component that maximizes the likelihood with a preliminary estimator of the unspecified term plugged in. It is demonstrated how models and estimators can be used in a two-step specification testing strategy of semiparametric and fully…

利用混合总体证据为超高维聚类选择变量AI 解读

In this paper we develop a nonparametric approach to clustering very high-dimensional data, designed particularly for problems where the mixture nature of a population is expressed through multimodality of its density. Therefore, a technique based implicitly on mode testing can be particularly effective. In principle, several alternative approaches could be used to assess the extent of multimodality, but in the present problem the excess mass method has important advantages.…

调整协变量后的两个有序变量关联检验AI 解读

We propose a new set of test statistics to examine the association between two ordinal categorical variables X and Y after adjusting for continuous and/or categorical covariates Z. Our approach first fits multinomial (e.g., proportional odds) models of X and Y, separately, on Z. For each subject, we then compute the conditional distributions of X and Y given Z. If there is no relationship between X and Y after adjusting for Z, then these conditional distributions will be…

大数据集可数混合模型的后验模拟AI 解读

Mixture models, or convex combinations of a countable number of probability distributions, offer an elegant framework for inference when the population of interest can be subdivided into latent clusters having random characteristics that are heterogeneous between, but homogeneous within, the clusters. Traditionally, the different kinds of mixture models have been motivated and analyzed from very different perspectives, and their common characteristics have not been fully…

含半参数单指标交互的广义函数型线性模型AI 解读

We introduce a new class of functional generalized linear models, where the response is a scalar and some of the covariates are functional. We assume that the response depends on multiple covariates, a finite number of latent features in the functional predictor, and interaction between the two. To achieve parsimony, the interaction between the multiple covariates and the functional predictor is modeled semiparametrically with a single-index structure. We propose a two step…

部分线性变换模型的估计AI 解读

We study a general class of partially linear transformation models, which extend linear transformation models by incorporating nonlinear covariate effects in survival data analysis. A new martingale-based estimating equation approach, consisting of both global and kernel-weighted local estimation equations, is developed for estimating the parametric and nonparametric covariate effects in a unified manner. We show that with a proper choice of the kernel bandwidth parameter,…

高斯随机函数的二阶比较与 DNA 微环几何AI 解读

Given two samples of continuous zero-mean iid Gaussian processes on [0,1], we consider the problem of testing whether they share the same covariance structure. Our study is motivated by the problem of determining whether the mechanical properties of short strands of DNA are significantly affected by their base-pair sequence; though expected to be true, had so far not been observed in three-dimensional electron microscopy data. The testing problem is seen to involve aspects…