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利用双重机器学习估计平均偏效应AI 解读

Single-parameter summaries of variable effects in regression settings are desirable for ease of interpretation. However, (partially) linear models, for example, which would deliver these, may fit poorly to the data. On the other hand, an interpretable summary of the contribution of a given predictor is provided by the so-called average partial effect—the average slope of the regression function with respect to the predictor of interest. Although one can construct a doubly…

Testing the significance of a variable or group of variables X for predicting a response Y, given additional covariates Z, is a ubiquitous task in statistics. A simple but common approach is to specify a linear model, and then test whether the regression coefficient for X is nonzero. However, when the model is misspecified, the test may have poor power, for example, when X is involved in complex interactions, or lead to many false rejections. In this work, we study the…

高维混杂下平均处理效应的去偏逆倾向得分加权AI 解读

We consider estimation of average treatment effects given observational data with high-dimensional pretreatment variables. Existing methods for this problem typically assume some form of sparsity for the regression functions. In this work, we introduce a debiased inverse propensity score weighting (DIPW) scheme for average treatment effect estimation that delivers n-consistent estimates when the propensity score follows a sparse logistic regression model; the outcome…

Hilbert 空间中的条件独立检验及函数型数据应用AI 解读

Abstract We study the problem of testing the null hypothesis that X and Y are conditionally independent given Z, where each of X, Y and Z may be functional random variables. This generalises testing the significance of X in a regression model of scalar response Y on functional regressors X and Z. We show, however, that even in the idealised setting where additionally (X, Y, Z) has a Gaussian distribution, the power of any test cannot exceed its size. Further modelling…

利用非凸融合惩罚建模高维分类数据AI 解读

Abstract We propose a method for estimation in high-dimensional linear models with nominal categorical data. Our estimator, called SCOPE, fuses levels together by making their corresponding coefficients exactly equal. This is achieved using the minimax concave penalty on differences between the order statistics of the coefficients for a categorical variable, thereby clustering the coefficients. We provide an algorithm for exact and efficient computation of the global minimum…

高维广义线性模型的拟合优度检验AI 解读

Summary We propose a family of tests to assess the goodness of fit of a high dimensional generalized linear model. Our framework is flexible and may be used to construct an omnibus test or directed against testing specific non-linearities and interaction effects, or for testing the significance of groups of variables. The methodology is based on extracting left-over signal in the residuals from an initial fit of a generalized linear model. This can be achieved by predicting…

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…

右奇异向量投影图：潜在混杂下的快速高维协方差估计AI 解读

Summary We consider the problem of estimating a high dimensional p × p covariance matrix Σ, given n observations of confounded data with covariance Σ+ΓΓT, where Γ is an unknown p × q matrix of latent factor loadings. We propose a simple and scalable estimator based on the projection onto the right singular vectors of the observed data matrix, which we call right singular vector projection (RSVP). Our theoretical analysis of this method reveals that, in contrast with…

高维线性模型的拟合优度检验AI 解读

Summary We propose a framework for constructing goodness-of-fit tests in both low and high dimensional linear models. We advocate applying regression methods to the scaled residuals following either an ordinary least squares or lasso fit to the data, and using some proxy for prediction error as the final test statistic. We call this family residual prediction tests. We show that simulation can be used to obtain the critical values for such tests in the low dimensional…

带错误控制的变量选择：再论稳定性选择AI 解读

Summary Stability selection was recently introduced by Meinshausen and Bühlmann as a very general technique designed to improve the performance of a variable selection algorithm. It is based on aggregating the results of applying a selection procedure to subsamples of the data. We introduce a variant, called complementary pairs stability selection, and derive bounds both on the expected number of variables included by complementary pairs stability selection that have low…