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通过近似留一交叉验证高效估计样本外预测误差AI 解读

Summary The paper considers the problem of out-of-sample risk estimation under the high dimensional settings where standard techniques such as K-fold cross-validation suffer from large biases. Motivated by the low bias of the leave-one-out cross-validation method, we propose a computationally efficient closed form approximate leave-one-out formula ALO for a large class of regularized estimators. Given the regularized estimate, calculating ALO requires a minor computational…

通过去噪矩方法最优估计高斯混合分布AI 解读

The method of moments (Philos. Trans. R. Soc. Lond. Ser. A 185 (1894) 71–110) is one of the most widely used methods in statistics for parameter estimation, by means of solving the system of equations that match the population and estimated moments. However, in practice and especially for the important case of mixture models, one frequently needs to contend with the difficulties of non-existence or nonuniqueness of statistically meaningful solutions, as well as the high…

非参数工具变量回归及其他病态模型中的诚实置信集AI 解读

Abstract This article develops inferential methods for a very general class of ill-posed models in econometrics encompassing the nonparametric instrumental variable regression, various functional regressions, and the density deconvolution. We focus on uniform confidence sets for the parameter of interest estimated with Tikhonov regularization, as in Darolles et al. (2011, Econometrica 79, 1541–1565). Since it is impossible to have inferential methods based on the central…

用收缩方法、实时扩散指数与模型组合预测利率AI 解读

Summary In the context of predicting the term structure of interest rates, we explore the marginal predictive content of real‐time macroeconomic diffusion indexes extracted from a “data rich” real‐time data set, when used in dynamic Nelson–Siegel (NS) models of the variety discussed in Svensson (NBER technical report, 1994; NSS) and Diebold and Li ( Journal of Econometrics , 2006, 130 , 337–364; DNS). Our diffusion indexes are constructed using principal component analysis…

模型简化与变量选择：复现 Hendry 的英国通胀模型AI 解读

Summary In this paper, we revisit the well‐known UK inflation model by Hendry ( Journal of Applied Econometrics , 2001, 16 , 255–275. We replicate the results in a narrow sense using the gretl and PcGive programs. In a wide sense, we extend the study of model uncertainty using the Bayesian averaging of classical estimates (BACE) approach as an automatic model reduction strategy. We consider three different specifications to compare BACE variable selection with Hendry's…

模型不确定性与参数不稳定性下的股票收益预测AI 解读

Summary We compare several representative sophisticated model averaging and variable selection techniques of forecasting stock returns. When estimated traditionally, our results confirm that the simple combination of individual predictors is superior. However, sophisticated models improve dramatically once we combine them with the historical average and take parameter instability into account. An equal weighted combination of the historical average with the standard…

建模研究间异质性以提高基因特征选择与临床预测的可重复性AI 解读

In the genomic era, the identification of gene signatures associated with disease is of significant interest. Such signatures are often used to predict clinical outcomes in new patients and aid clinical decision-making. However, recent studies have shown that gene signatures are often not replicable. This occurrence has practical implications regarding the generalizability and clinical applicability of such signatures. To improve replicability, we introduce a novel approach…

无需插补的块缺失多模态数据最优稀疏线性预测AI 解读

In modern scientific research, data are often collected from multiple modalities. Since different modalities could provide complementary information, statistical prediction methods using multi-modality data could deliver better prediction performance than using single modality data. However, one special challenge for using multi-modality data is related to block-missing data. In practice, due to dropouts or the high cost of measures, the observations of a certain modality…

复杂分组高维多响应模型的典型相关搜索特征选择AI 解读

High-dimensional multiresponse models with complex group structures in both the response variables and the covariates arise from current researches in important fields such as genetics and medicine. However, no enough research has been done on such models. One of a few researches, if not the only one, is the article by Li, Nan, and Zhu where the sparse group Lasso approach is extended to such models. In this article, we propose a novel approach named the sequential canonical…

用 D 概率比较和加权不完美模型AI 解读

), relying on evaluating parametric models relative to a nonparametric Bayesian reference using Kullback-Leibler divergence. D-probabilities are useful in goodness-of-fit assessments, in comparing imperfect models, and in providing model weights to be used in model aggregation. D-probabilities avoid some of the disadvantages of Bayesian model probabilities, such as large sensitivity to prior choice, and tend to place higher weight on a greater diversity of models. In an…

空间滞后模型中空间权重矩阵的估计与选择AI 解读

Spatial econometric models allow for interactions among variables through the specification of a spatial weight matrix. Practitioners often face the risk of misspecification of such a matrix. In many problems a number of potential specifications exist, such as geographic distances, or various economic quantities among variables. We propose estimating the best linear combination of these specifications, added with a potentially sparse adjustment matrix. The coefficients in…

基于正则化奇异值分解的时间序列季节调整AI 解读

We propose a new seasonal adjustment method based on the Regularized Singular Value Decomposition (RSVD) of the matrix obtained by reshaping the seasonal time series data. The method is flexible enough to capture two kinds of seasonality: the fixed seasonality that does not change over time and the time-varying seasonality that varies from one season to another. RSVD represents the time-varying seasonality by a linear combination of several seasonal patterns. The right…

高维工具变量回归的统计推断AI 解读

This paper concerns statistical inference for the components of a high-dimensional regression parameter despite possible endogeneity of each regressor. Given a first-stage linear model for the endogenous regressors and a second-stage linear model for the dependent variable, we develop a novel adaptation of the parametric one-step update to a generic second-stage estimator. We provide conditions under which the scaled update is asymptotically normal. We then introduce a…

特征值的 Lasso 收缩AI 解读

Summary The properties of penalized sample covariance matrices depend on the choice of the penalty function. In this paper, we introduce a class of nonsmooth penalty functions for the sample covariance matrix and demonstrate how their use results in a grouping of the estimated eigenvalues. We refer to the proposed method as lassoing eigenvalues, or the elasso.

利用 K 近邻融合套索的自适应非参数回归AI 解读

Summary The fused lasso, also known as total-variation denoising, is a locally adaptive function estimator over a regular grid of design points. In this article, we extend the fused lasso to settings in which the points do not occur on a regular grid, leading to a method for nonparametric regression. This approach, which we call the $K$-nearest-neighbours fused lasso, involves computing the $K$-nearest-neighbours graph of the design points and then performing the fused lasso…

高维 Hotelling T² 检验的自适应推广AI 解读

We propose a two-sample test for detecting the difference between mean vectors in a high-dimensional regime based on a ridge-regularized Hotelling’s $T^{2}$. To choose the regularization parameter, a method is derived that aims at maximizing power within a class of local alternatives. We also propose a composite test that combines the optimal tests corresponding to a specific collection of local alternatives. Weak convergence of the stochastic process corresponding to the…

条件独立性检验的困难与广义协方差度量AI 解读

It is a common saying that testing for conditional independence, that is, testing whether whether two random vectors $X$ and $Y$ are independent, given $Z$, is a hard statistical problem if $Z$ is a continuous random variable (or vector). In this paper, we prove that conditional independence is indeed a particularly difficult hypothesis to test for. Valid statistical tests are required to have a size that is smaller than a pre-defined significance level, and different tests…

GRID：高维非参数回归的变量选择与结构发现方法AI 解读

We consider nonparametric regression in high dimensions where only a relatively small subset of a large number of variables are relevant and may have nonlinear effects on the response. We develop methods for variable selection, structure discovery and estimation of the true low-dimensional regression function, allowing any degree of interactions among the relevant variables that need not be specified a-priori. The proposed method, called the GRID, combines empirical…

Knockoff 方法的稳健推断AI 解读

We consider the variable selection problem, which seeks to identify important variables influencing a response $Y$ out of many candidate features $X_{1},\ldots ,X_{p}$. We wish to do so while offering finite-sample guarantees about the fraction of false positives—selected variables $X_{j}$ that in fact have no effect on $Y$ after the other features are known. When the number of features $p$ is large (perhaps even larger than the sample size $n$), and we have no prior…

多维扩散过程漂移向量场的非参数统计推断AI 解读

The problem of determining a periodic Lipschitz vector field $b=(b_{1},\ldots ,b_{d})$ from an observed trajectory of the solution $(X_{t}:0\le t\le T)$ of the multi-dimensional stochastic differential equation \begin{equation*}dX_{t}=b(X_{t})\,dt+dW_{t},\quad t\geq 0,\end{equation*} where $W_{t}$ is a standard $d$-dimensional Brownian motion, is considered. Convergence rates of a penalised least squares estimator, which equals the maximum a posteriori (MAP) estimate…

直接插值：无岭惩罚核回归也能泛化AI 解读

In the absence of explicit regularization, Kernel “Ridgeless” Regression with nonlinear kernels has the potential to fit the training data perfectly. It has been observed empirically, however, that such interpolated solutions can still generalize well on test data. We isolate a phenomenon of implicit regularization for minimum-norm interpolated solutions which is due to a combination of high dimensionality of the input data, curvature of the kernel function and favorable…

识别协整面板中的潜在分组模式AI 解读

We consider a panel cointegration model with latent group structures that allows for heterogeneous long-run relationships across groups. We extend Su, Shi, and Phillips (2016, Econometrica 84(6), 2215–2264) classifier-Lasso (C-Lasso) method to the nonstationary panels and allow for the presence of endogeneity in both the stationary and nonstationary regressors in the model. In addition, we allow the dimension of the stationary regressors to diverge with the sample size. We…

大型似不相关回归系统：惩罚准极大似然估计AI 解读

In this article, using a shrinkage estimator, we propose a penalized quasi-maximum likelihood estimator (PQMLE) to estimate a large system of equations in seemingly unrelated regression models, where the number of equations is large relative to the sample size. We develop the asymptotic properties of the PQMLE for both the error covariance matrix and model coefficients. In particular, we derive the asymptotic distribution of the coefficient estimator and the convergence rate…

存在出口时的企业生产率估计：中国制造业证据AI 解读

Summary Motivated by the long‐standing interest of economists in understanding the nexus between firm productivity and export behavior, this paper develops a novel structural framework for control‐function‐based nonparametric identification of the gross production function and latent firm productivity in the presence of endogenous export opportunities that is robust to recent unidentification critiques of proxy estimators. We provide a workable identification strategy,…