论文检索

大规模交叉随机效应回归的回拟合算法AI 解读

Regression models with crossed random effect errors can be very expensive to compute. The cost of both generalized least squares and Gibbs sampling can easily grow as N3/2 (or worse) for N observations. Papaspiliopoulos, Roberts and Zanella (Biometrika 107 (2020) 25–40) present a collapsed Gibbs sampler that costs O(N), but under an extremely stringent sampling model. We propose a backfitting algorithm to compute a generalized least squares estimate and prove that it costs…

促进时间治愈模型的一种扩展AI 解读

We consider the problem of estimating the distribution of time-to-event data that is subject to censoring and for which the event of interest might never occur, that is, some subjects are cured. To model this kind of data in the presence of covariates, one of the leading semiparametric models is the promotion time cure model (Stochastic Models of Tumor Latency and Their Biostatistical Applications (1996) World Scientific), which adapts the Cox model to the presence of cured…

多变量纵向与生存数据的半参数潜在类别模型AI 解读

In long-term follow-up studies, data are often collected on repeated measures of multivariate response variables as well as on time to the occurrence of a certain event. To jointly analyze such longitudinal data and survival time, we propose a general class of semiparametric latent-class models that accommodates a heterogeneous study population with flexible dependence structures between the longitudinal and survival outcomes. We combine nonparametric maximum likelihood…

非稀疏高维线性回归的典范阈值估计AI 解读

We consider a high-dimensional linear regression problem. Unlike many papers on the topic, we do not require sparsity of the regression coefficients; instead, our main structural assumption is a decay of eigenvalues of the covariance matrix of the data. We propose a new family of estimators, called the canonical thresholding estimators, which pick largest regression coefficients in the canonical form. The estimators admit an explicit form and can be linked to LASSO and…

纯量子态的极小极大非参数估计AI 解读

In classical statistics, Pinsker’s theorem provides an exact asymptotic minimax bound in nonparametric estimation, improving upon optimal rates of convergence results. We obtain a quantum version of the theorem by establishing asymptotic minimax results for estimation of the displacement vector in a quantum Gaussian white noise model, given by a sequence of shifted vacuum states. Analogous results are then obtained for estimation of a general pure state from an ensemble of…

凸约束高斯序列模型中似然比检验的高维渐近理论AI 解读

In the Gaussian sequence model Y=μ+ξ, we study the likelihood ratio test (LRT) for testing H0:μ=μ0 versus H1:μ∈K, where μ0∈K, and K is a closed convex set in Rn. In particular, we show that under the null hypothesis, normal approximation holds for the log-likelihood ratio statistic for a general pair (μ0,K), in the high-dimensional regime where the estimation error of the associated least squares estimator diverges in an appropriate sense. The normal approximation further…

未知排列下的保序回归：统计、计算与自适应AI 解读

Motivated by models for multiway comparison data, we consider the problem of estimating a coordinatewise isotonic function on the domain [0,1]d from noisy observations collected on a uniform lattice, but where the design points have been permuted along each dimension. While the univariate and bivariate versions of this problem have received significant attention, our focus is on the multivariate case d≥3. We study both the minimax risk of estimation (in empirical L2 loss)…

未知噪声分布下多元信号的反卷积AI 解读

This paper considers the deconvolution problem in the case where the target signal is multidimensional and no information is known about the noise distribution. More precisely, no assumption is made on the noise distribution and no samples are available to estimate it: the deconvolution problem is solved based only on observations of the corrupted signal. We establish the identifiability of the model up to translation when the signal has a Laplace transform with an…

异方差与重尾误差下的最小二乘估计AI 解读

We consider least squares estimation in a general nonparametric regression model where the error is allowed to depend on the covariates. The rate of convergence of the least squares estimator (LSE) for the unknown regression function is well studied when the errors are sub-Gaussian. We find upper bounds on the rates of convergence of the LSE when the error has a uniformly bounded conditional variance and has only finitely many moments. Our upper bound on the rate of…

凸惩罚高维回归的根本障碍AI 解读

In high-dimensional regression, we attempt to estimate a parameter vector β0∈Rp from n≲p observations {(yi,xi)}i≤n, where xi∈Rp is a vector of predictors and yi is a response variable. A well-established approach uses convex regularizers to promote specific structures (e.g., sparsity) of the estimate βˆ while allowing for practical algorithms. Theoretical analysis implies that convex penalization schemes have nearly optimal estimation properties in certain settings. However,…

模式图：非单调缺失数据的图形化方法AI 解读

We introduce the concept of pattern graphs–directed acyclic graphs representing how response patterns are associated. A pattern graph represents an identifying restriction that is nonparametrically identified/saturated and is often a missing not at random restriction. We introduce a selection model and a pattern mixture model formulations using the pattern graphs and show that they are equivalent. A pattern graph leads to an inverse probability weighting estimator as well as…

基于弱条件矩的函数型数据降维AI 解读

We develop a general theory and estimation methods for functional linear sufficient dimension reduction, where both the predictor and the response can be random functions, or even vectors of functions. Unlike the existing dimension reduction methods, our approach does not rely on the estimation of conditional mean and conditional variance. Instead, it is based on a new statistical construction—the weak conditional expectation, which is based on Carleman operators and their…

稀疏贝叶斯预测密度估计的极小极大最优性AI 解读

We study predictive density estimation under Kullback–Leibler loss in ℓ0-sparse Gaussian sequence models. We propose proper Bayes predictive density estimates and establish asymptotic minimaxity in sparse models. Fundamental for this is a new risk decomposition for sparse, or spike-and-slab priors. A surprise is the existence of a phase transition in the future-to-past variance ratio r. For r

极端事件的空间依赖与时空趋势AI 解读

The statistical theory of extremes is extended to independent multivariate observations that are non-stationary both over time and across space. The non-stationarity over time and space is controlled via the scedasis (tail scale) in the marginal distributions. Spatial dependence stems from multivariate extreme value theory. We establish asymptotic theory for both the weighted sequential tail empirical process and the weighted tail quantile process based on all observations,…

广义张量估计的统计与计算最优框架AI 解读

This paper describes a flexible framework for generalized low-rank tensor estimation problems that includes many important instances arising from applications in computational imaging, genomics, and network analysis. The proposed estimator consists of finding a low-rank tensor fit to the data under generalized parametric models. To overcome the difficulty of nonconvexity in these problems, we introduce a unified approach of projected gradient descent that adapts to the…

近线性时间内均值向量的稳健次高斯估计AI 解读

We construct an algorithm for estimating the mean of a heavy-tailed random variable when given an adversarial corrupted sample of N independent observations. The only assumption we make on the distribution of the noncorrupted (or informative) data is the existence of a covariance matrix Σ, unknown to the statistician. Our algorithm outputs μˆ, which is robust to the presence of |O| adversarial outliers and satisfies (1)‖μˆ−μ‖2≲ Tr(Σ) N+ ‖Σ‖opK N with probability at least…

旋转不变矩阵的近似消息传递算法AI 解读

Approximate Message Passing (AMP) algorithms have seen widespread use across a variety of applications. However, the precise forms for their Onsager corrections and state evolutions depend on properties of the underlying random matrix ensemble, limiting the extent to which AMP algorithms derived for white noise may be applicable to data matrices that arise in practice. In this work, we study more general AMP algorithms for random matrices W that satisfy orthogonal rotational…

异方差主成分分析：算法、最优性与应用AI 解读

A general framework for principal component analysis (PCA) in the presence of heteroskedastic noise is introduced. We propose an algorithm called HeteroPCA, which involves iteratively imputing the diagonal entries of the sample covariance matrix to remove estimation bias due to heteroskedasticity. This procedure is computationally efficient and provably optimal under the generalized spiked covariance model. A key technical step is a deterministic robust perturbation analysis…

利用分布不连续协变量检验基于可观测变量的选择假设AI 解读

We present a test of the selection on observables assumption that neither requires instruments nor excluded covariates from the structural function. Instead, we rely on the presence of a discontinuously distributed variable among the set of controls. We develop formal testing procedures for a non-parametric additively separable model for binary and finite treatment variables. We also outline a nonparametric nonseparable extension. Our test is easy to implement and should be…

完全信息有序反应博弈中的推断AI 解读

We study inference in complete information games with discrete strategy spaces. Unlike binary games, we allow for rich strategy spaces and we only assume that they are ordinal in nature. We derive observable implications of equilibrium play under mild shape restrictions on payoff functions, and we characterize sharp identified sets for model parameters. We propose a novel inference method based on a test statistic that embeds conditional moment inequalities implied by…

参数存在跳跃不连续的面板模型：小波方法AI 解读

While a substantial literature on structural break change point analysis exists for univariate time series, research on large panel data models has not been as extensive. In this paper, a novel method for estimating panel models with multiple structural changes is proposed. The breaks are allowed to occur at unknown points in time and may affect the multivariate slope parameters individually. Our method adapts Haar wavelets to the structure of the observed variables in order…

半参数模型系数的识别及集体家庭模型应用AI 解读

We prove identification of coefficients for a set of semiparametric specifications that are related to multiple index models. Potential applications of these results include models of observed heterogeneity in production functions and in consumer demand systems. We then generalize these results to identify a class of collective household consumption models. We extend the existing literature by proving point identification, rather than the weaker generic identification, of…

不可观测选择集下的多项选择模型估计AI 解读

This paper proposes a new approach to estimating multinomial choice models when each consumer’s actual choice set is unobservable but could be bounded by two known sets, i.e., the largest and smallest possible choice sets. The bounds on choice set, combined with a monotonicity property derived from utility maximization, imply a system of inequality restrictions on observed choice probabilities that could be used to identify and estimate the model. A key insight is that the…

由数学规划定义的估计量的统计推断AI 解读

We propose an inference procedure for a class of estimators defined as the solutions to linear and convex quadratic programming problems in which the coefficients in both the objective function and the constraints of the problem are estimated from data and hence involve sampling error. We argue that the Karush–Kuhn–Tucker conditions that characterize the solutions to these programming problems can be treated as moment conditions; by doing so, we transform the problem of…