论文检索

高维分类中的非参数特征增强与选择：FANSAI 解读

We propose a high dimensional classification method that involves nonparametric feature augmentation. Knowing that marginal density ratios are the most powerful univariate classifiers, we use the ratio estimates to transform the original feature measurements. Subsequently, penalized logistic regression is invoked, taking as input the newly transformed or augmented features. This procedure trains models equipped with local complexity and global simplicity, thereby avoiding…

高维面板模型的推断及枪支管制应用AI 解读

We consider estimation and inference in panel data models with additive unobserved individual specific heterogeneity in a high dimensional setting. The setting allows the number of time varying regressors to be larger than the sample size. To make informative estimation and inference feasible, we require that the overall contribution of the time varying variables after eliminating the individual specific heterogeneity can be captured by a relatively small number of the…

稀疏结构的结构变化AI 解读

In the high-dimensional sparse modeling literature, it has been crucially assumed that the sparsity structure of the model is homogeneous over the entire population. That is, the identities of important regressors are invariant across the population and across the individuals in the collected sample. In practice, however, the sparsity structure may not always be invariant in the population, due to heterogeneity across different sub-populations. We consider a general,…

协变量辅助的筛选与估计AI 解读

Consider a linear model $Y=Xβ+z$, where $X=X_{n,p}$ and $z\sim N(0,I_n)$. The vector $β$ is unknown but is sparse in the sense that most of its coordinates are $0$. The main interest is to separate its nonzero coordinates from the zero ones (i.e., variable selection). Motivated by examples in long-memory time series (Fan and Yao [Nonlinear Time Series: Nonparametric and Parametric Methods (2003) Springer]) and the change-point problem (Bhattacharya [In Change-Point Problems…

极值子抽样：从块最大值到平滑尾部估计AI 解读

We study a new estimator for the tail index of a distribution in the Frechet domain of attraction that arises naturally by computing subsample maxima. This estimator is equivalent to taking a U-statistic over a Hill estimator with two order statistics. The estimator presents multiple advantages over the Hill estimator. In particular, it has asymptotically smooth sample paths as a function of the threshold k, making it considerably more stable than the Hill estimator. The…

重尾数据的半参数指数族建模AI 解读

We propose a semiparametric method for fitting the tail of a heavy-tailed population given a relatively small sample from that population and a larger sample from a related background population. We model the tail of the small sample as an exponential tilt of the better-observed large-sample tail, using a robust sufficient statistic motivated by extreme value theory. In particular, our method induces an estimator of the small-population mean, and we give theoretical and…

高维均值回归的稳健估计AI 解读

Data subject to heavy-tailed errors are commonly encountered in various scientific fields, especially in the modern era with explosion of massive data. To address this problem, procedures based on quantile regression and Least Absolute Deviation (LAD) regression have been devel- oped in recent years. These methods essentially estimate the conditional median (or quantile) function. They can be very different from the conditional mean functions when distributions are…

反集中性与诚实、自适应置信带AI 解读

Modern construction of uniform confidence bands for nonparametric densities (and other functions) often relies on the classical Smirnov-Bickel-Rosenblatt (SBR) condition; see, for example, Giné and Nickl [Probab. Theory Related Fields 143 (2009) 569-596]. This condition requires the existence of a limit distribution of an extreme value type for the supremum of a studentized empirical process (equivalently, for the supremum of a Gaussian process with the same covariance…

正特征函数的非参数识别AI 解读

Important features of certain economic models may be revealed by studying positive eigenfunctions of appropriately chosen linear operators. Examples include long-run risk-return relationships in dynamic asset pricing models and components of marginal utility in external habit formation models. This paper provides identification conditions for positive eigenfunctions in nonparametric models. Identification is achieved if the operator satisfies two mild positivity conditions…

经验过程上确界的高斯近似AI 解读

This paper develops a new direct approach to approximating suprema of general empirical processes by a sequence of suprema of Gaussian processes, without taking the route of approximating whole empirical processes in the sup-norm. We prove an abstract approximation theorem applicable to a wide variety of statistical problems, such as construction of uniform confidence bands for functions. Notably, the bound in the main approximation theorem is nonasymptotic and the theorem…

高维截面检验的功效增强AI 解读

We propose a novel technique to boost the power of testing a high-dimensional vector $H:\btheta=0$ against sparse alternatives where the null hypothesis is violated only by a couple of components. Existing tests based on quadratic forms such as the Wald statistic often suffer from low powers due to the accumulation of errors in estimating high-dimensional parameters. More powerful tests for sparse alternatives such as thresholding and extreme-value tests, on the other hand,…

利用分位数进行面板模型的非参数识别AI 解读

This paper considers identification and estimation of ceteris paribus effects of continuous regressors in nonseparable panel models with time homogeneity. The effects of interest are derivatives of the average and quantile structural functions of the model. We find that these derivatives are identified with two time periods for "stayers", i.e. for individuals with the same regressor values in two time periods. We show that the identification results carry over to models that…

固定效应主成分分析的置信区域AI 解读

PCA is often used to visualize data when the rows and the columns are both of interest. In such a setting there is a lack of inferential methods on the PCA output. We study the asymptotic variance of a fixed-effects model for PCA, and propose several approaches to assessing the variability of PCA estimates: a method based on a parametric bootstrap, a new cell-wise jackknife, as well as a computationally cheaper approximation to the jackknife. We visualize the confidence…

不交叉的分位数与概率曲线AI 解读

This paper proposes a method to address the longstanding problem of lack of monotonicity in estimation of conditional and structural quantile functions, also known as the quantile crossing problem. The method consists in sorting or monotone rearranging the original estimated non-monotone curve into a monotone rearranged curve. We show that the rearranged curve is closer to the true quantile curve in finite samples than the original curve, establish a functional delta method…

高维模型中的内生性AI 解读

Most papers on high-dimensional statistics are based on the assumption that none of the regressors are correlated with the regression error, namely, they are exogenous. Yet, endogeneity can arise incidentally from a large pool of regressors in a high-dimensional regression. This causes the inconsistency of the penalized least-squares method and possible false scientific discoveries. A necessary condition for model selection consistency of a general class of penalized…

非参数回归中基于平方根 Lasso 的枢轴估计AI 解读

We propose a self-tuning $\sqrt{\mathrm {Lasso}}$ method that simultaneously resolves three important practical problems in high-dimensional regression analysis, namely it handles the unknown scale, heteroscedasticity and (drastic) non-Gaussianity of the noise. In addition, our analysis allows for badly behaved designs, for example, perfectly collinear regressors, and generates sharp bounds even in extreme cases, such as the infinite variance case and the noiseless case, in…

混合数据的高维半参数潜在图模型AI 解读

Graphical models are commonly used tools for modeling multivariate random variables. While there exist many convenient multivariate distributions such as Gaussian distribution for continuous data, mixed data with the presence of discrete variables or a combination of both continuous and discrete variables poses new challenges in statistical modeling. In this paper, we propose a semiparametric model named latent Gaussian copula model for binary and mixed data. The observed…

维度递增的弯曲指数族中的后验推断AI 解读

This work studies the large sample properties of the posterior-based inference in the curved exponential family under increasing dimension. The curved structure arises from the imposition of various restrictions on the model, such as moment restrictions, and plays a fundamental role in econometrics and others branches of data analysis. We establish conditions under which the posterior distribution is approximately normal, which in turn implies various good properties of…

可能存在变点的高维回归中的 LassoAI 解读

We consider a high-dimensional regression model with a possible change-point due to a covariate threshold and develop the Lasso estimator of regression coefficients as well as the threshold parameter. Our Lasso estimator not only selects covariates but also selects a model between linear and threshold regression models. Under a sparsity assumption, we derive non-asymptotic oracle inequalities for both the prediction risk and the $\ell_1$ estimation loss for regression…

随机森林的置信区间：刀切法与无穷小刀切法AI 解读

We study the variability of predictions made by bagged learners and random forests, and show how to estimate standard errors for these methods. Our work builds on variance estimates for bagging proposed by Efron (1992, 2012) that are based on the jackknife and the infinitesimal jackknife (IJ). In practice, bagged predictors are computed using a finite number B of bootstrap replicates, and working with a large B can be computationally expensive. Direct applications of…

自适应稳健变量选择AI 解读

Heavy-tailed high-dimensional data are commonly encountered in various scientific fields and pose great challenges to modern statistical analysis. A natural procedure to address this problem is to use penalized quantile regression with weighted $L_1$-penalty, called weighted robust Lasso (WR-Lasso), in which weights are introduced to ameliorate the bias problem induced by the $L_1$-penalty. In the ultra-high dimensional setting, where the dimensionality can grow…

存在删失与内生性的分位数回归AI 解读

In this paper, we develop a new censored quantile instrumental variable (CQIV) estimator and describe its properties and computation. The CQIV estimator combines Powell (1986) censored quantile regression (CQR) to deal with censoring, with a control variable approach to incorporate endogenous regressors. The CQIV estimator is obtained in two stages that are non-additive in the unobservables. The first stage estimates a non-additive model with infinite dimensional parameters…

具有交互效应的面板数据模型：理论与方法AI 解读

This paper considers the maximum likelihood estimation of panel data models with interactive effects. Motivated by applications in economics and other social sciences, a notable feature of the model is that the explanatory variables are correlated with the unobserved effects. The usual within-group estimator is inconsistent. Existing methods for consistent estimation are either designed for panel data with short time periods or are less efficient. The maximum likelihood…

限制条件局部奇异时的 Wald 检验AI 解读

Wald-type tests are convenient because they allow one to test a wide array of linear and nonlinear restrictions from a single unrestricted estimator; we focus on the problem of implementing Wald-type tests for nonlinear restrictions. We provide examples showing that Wald statistics in non-regular cases can have several asymptotic distributions; the usual critical values based on a chi-square distribution can both lead to under-rejections and over-rejections; indeed, the Wald…