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高维分类中的非参数特征增广与选择：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…

高维线性回归中的样条 LassoAI 解读

We consider a high-dimensional linear regression problem, where the covariates (features) are ordered in some meaningful way, and the number of covariates p can be much larger than the sample size n. The fused lasso of Tibshirani et al. is designed especially to tackle this type of problems; it yields sparse coefficients and selects grouped variables, and encourages local constant coefficient profile within each group. However, in some applications, the effects of different…

序贯条件独立下中介效应估计量的有限样本表现AI 解读

Using a comprehensive simulation study based on empirical data, this article investigates the finite sample properties of different classes of parametric and semiparametric estimators of (natural) direct and indirect causal effects used in mediation analysis under sequential conditional independence assumptions. The estimators are based on regression, inverse probability weighting, and combinations thereof. Our simulation design uses a large population of Swiss jobseekers…

非同步含噪资产价格的平顶已实现核二次协变差估计AI 解读

This article develops a general multivariate additive noise model for synchronized asset prices and provides a multivariate extension of the generalized flat-top realized kernel estimators, analyzed earlier by Varneskov (2014), to estimate its quadratic covariation. The additive noise model allows for α-mixing dependent exogenous noise, random sampling, and an endogenous noise component that encompasses synchronization errors, lead-lag relations, and diurnal…

密度众数的非参数推断AI 解读

Summary We derive non-parametric confidence intervals for the eigenvalues of the Hessian at modes of a density estimate. This provides information about the strength and shape of modes and can also be used as a significance test. We use a data-splitting approach in which potential modes are identified by using the first half of the data and inference is done with the second half of the data. To obtain valid confidence sets for the eigenvalues, we use a bootstrap based on an…

误差分布未知时的非参数反卷积方法AI 解读

Summary In the non-parametric deconvolution problem, to estimate consistently a density or distribution from a sample of data contaminated by additive random noise, it is often assumed that the noise distribution is completely known or that an additional sample of replicated or validation data is available. Methods also have been suggested for estimating the scale of the error distribution, but they require somewhat restrictive smoothness assumptions on the signal…

利用重复测量非参数估计有限混合分布AI 解读

Summary This paper provides methods to estimate finite mixtures from data with repeated measurements non-parametrically. We present a constructive identification argument and use it to develop simple two-step estimators of the component distributions and all their functionals. We discuss a computationally efficient method for estimation and derive asymptotic theory. Simulation experiments suggest that our theory provides confidence intervals with good coverage in small…

病例对照研究二次分析中的半参数估计AI 解读

Summary We study the regression relationship between covariates in case–control data: an area known as the secondary analysis of case–control studies. The context is such that only the form of the regression mean is specified, so that we allow an arbitrary regression error distribution, which can depend on the covariates and thus can be heteroscedastic. Under mild regularity conditions we establish the theoretical identifiability of such models. Previous work in this context…

中等高维支持向量机的变量选择AI 解读

Summary The support vector machine (SVM) is a powerful binary classification tool with high accuracy and great flexibility. It has achieved great success, but its performance can be seriously impaired if many redundant covariates are included. Some efforts have been devoted to studying variable selection for SVMs, but asymptotic properties, such as variable selection consistency, are largely unknown when the number of predictors diverges to ∞. We establish a unified theory…

使用受约束多项式样条拟合数据包络AI 解读

Summary Estimation of support frontiers and boundaries often involves monotone and/or concave edge data smoothing. This estimation problem arises in various unrelated contexts, such as optimal cost and production assessments in econometrics and master curve prediction in the reliability programmes of nuclear reactors. Very few constrained estimators of the support boundary of a bivariate distribution have been introduced in the literature. They are based on simple…

存在内生性时的单调性检验AI 解读

This paper develops a test for monotonicity of nonparametric regression models under endogeneity, which in its generality is novel in the literature. The test statistic, which is built upon a second order U-process, introduces ‘correction terms’ based on control functions that purge the endogeneity. The test has a non-standard asymptotic distribution from which asymptotic critical values can directly be derived. Furthermore, the test statistic is extended to accommodate…

两个期权市场的定价核与波动率风险AI 解读

Using both S&P 500 option and recently introduced VIX option prices, we study pricing kernels and their dependence on multiple volatility factors. We first propose nonparametric estimates of marginal pricing kernels, conditional on the VIX and the slope of the variance swap term structure. Our estimates highlight the state-dependence nature of the pricing kernels. In particular, conditioning on volatility factors, the pricing kernel of market returns exhibit a downward…

含趋势协整模型的伪高斯与局部最优秩检验AI 解读

This paper provides pseudo-Gaussian and locally optimal rank-based tests for the cointegration rank in linear cointegrated error-correction models with common trends and i.i.d. elliptical innovations. The proposed tests are asymptotically distribution-free, hence their validity does not depend on the actual distribution of the innovations. The proposed rank-based tests depend on the choice of scores, associated with a reference density that can freely be chosen. Under…

横截面相关下的级数估计AI 解读

An asymptotic theory is developed for series estimation of nonparametric and semiparametric regression models for cross-sectional data under conditions on disturbances that allow for forms of cross-sectional dependence and heterogeneity, including conditional and unconditional heteroscedasticity, along with conditions on regressors that allow dependence and do not require existence of a density. The conditions aim to accommodate various settings plausible in economic…

价格与波动率的共同跳跃AI 解读

The nature of the dependence between discontinuities in prices and contemporaneous discontinuities in volatility (co-jumps) has been reported by many as being elusive, in terms of sign, magnitude, and statistical significance. Using a novel identification strategy in continuous time relying on trade-level information for spot variance estimation, as well as infinitesimal cross-moments, we document that a sizeable proportion of discontinuous changes in prices are associated…

金融网络动态与持久性的估计：英镑货币市场应用AI 解读

Summary We propose a novel methodology for dynamic econometric modelling of large financial networks subject to persistence, structural changes and sparsity. We estimate bivariate dynamic Tobit‐type models for each pair of banks, allowing for deterministic or stochastic time‐varying parameters, and then aggregate across all bank pairs. To tackle the high dimensionality of the model, we construct a few lagged variables that efficiently summarize the position of a bank pair in…

高频数据的广义积分矩方法AI 解读

We propose a semiparametric two‐step inference procedure for a finite‐dimensional parameter based on moment conditions constructed from high‐frequency data. The population moment conditions take the form of temporally integrated functionals of state‐variable processes that include the latent stochastic volatility process of an asset. In the first step, we nonparametrically recover the volatility path from high‐frequency asset returns. The nonparametric volatility estimator…

Statistical depth measures the centrality of a point with respect to a given distribution or data cloud. It provides a natural center-outward ordering of multivariate data points and yields a systematic nonparametric multivariate analysis scheme. In particular, the half-space depth is shown to have many desirable properties and broad applicability. However, the empirical half-space depth is zero outside the convex hull of the data. This property has rendered the empirical…

超高维广义半变系数模型的模型选择与结构识别AI 解读

In this paper, we study the model selection and structure specification for the generalised semi-varying coefficient models (GSVCMs), where the number of potential covariates is allowed to be larger than the sample size. We first propose a penalised likelihood method with the LASSO penalty function to obtain the preliminary estimates of the functional coefficients. Then, using the quadratic approximation for the local log-likelihood function and the adaptive group LASSO…

高维 Spearman 秩相关矩阵的谱统计及其应用AI 解读

Let $\mathbf{Q}=(Q_{1},\ldots,Q_{n})$ be a random vector drawn from the uniform distribution on the set of all $n!$ permutations of $\{1,2,\ldots,n\}$. Let $\mathbf{Z}=(Z_{1},\ldots,Z_{n})$, where $Z_{j}$ is the mean zero variance one random variable obtained by centralizing and normalizing $Q_{j}$, $j=1,\ldots,n$. Assume that $\mathbf{X}_{i},i=1,\ldots,p$ are i.i.d. copies of $\frac{1}{\sqrt{p}}\mathbf{Z}$ and $X=X_{p,n}$ is the $p\times n$ random matrix with $\mathbf{X}_{i}$…

点过程独立性的 Bootstrap 与置换检验AI 解读

Motivated by a neuroscience question about synchrony detection in spike train analysis, we deal with the independence testing problem for point processes. We introduce nonparametric test statistics, which are rescaled general $U$-statistics, whose corresponding critical values are constructed from bootstrap and randomization/permutation approaches, making as few assumptions as possible on the underlying distribution of the point processes. We derive general consistency…

半参数模型中光滑泛函的 Bernstein–von Mises 定理AI 解读

A Bernstein–von Mises theorem is derived for general semiparametric functionals. The result is applied to a variety of semiparametric problems in i.i.d. and non-i.i.d. situations. In particular, new tools are developed to handle semiparametric bias, in particular for nonlinear functionals and in cases where regularity is possibly low. Examples include the squared $L^{2}$-norm in Gaussian white noise, nonlinear functionals in density estimation, as well as functionals in…

达到最优收敛率的 Graphon 估计AI 解读

Network analysis is becoming one of the most active research areas in statistics. Significant advances have been made recently on developing theories, methodologies and algorithms for analyzing networks. However, there has been little fundamental study on optimal estimation. In this paper, we establish optimal rate of convergence for graphon estimation. For the stochastic block model with $k$ clusters, we show that the optimal rate under the mean squared error is $n^{-1}\log k+k^{2}/n^{2}$…

高维情形下的同时变点检验AI 解读

Consider $d$ dependent change point tests, each based on a CUSUM-statistic. We provide an asymptotic theory that allows us to deal with the maximum over all test statistics as both the sample size $n$ and $d$ tend to infinity. We achieve this either by a consistent bootstrap or an appropriate limit distribution. This allows for the construction of simultaneous confidence bands for dependent change point tests, and explicitly allows us to determine the location of the change…