Journal of Statistical Planning and Inference最新文献

Model selection for network data is an open area of research. Using the $\beta$-model as a convenient starting point, we propose a simple and non-asymptotic approach to model selection of $\beta$-models with and without constraints. Simulations indicate that the proposed model selection approach selects the data-generating model with high probability, in contrast to classical and extended Bayesian Information Criteria. We conclude with an application to the Enron email network, which has 181,831 connections among 36,692 employees.

In this paper, we consider the following regression model: $y(kT/n)=f\star g(kT/n)+{\varepsilon }_k,k=-n,\dots ,n-1$, $T$ fixed, where $g$ is known and $f$ is the unknown function to be estimated. The errors ${\left({\varepsilon }_k\right)}_{-n\le k\le n-1}$ are independent and identically distributed centered with finite known variance. Two adaptive estimation methods for $f$ are considered by exploiting the properties of the Hermite basis. We study the quadratic risk of each estimator. If $f$ belongs to Sobolev regularity spaces, we derive rates of convergence. Adaptive procedures to select the relevant parameter inspired by the Goldenshluger and Lepski method are proposed and we prove that the resulting estimators satisfy oracle inequalities for sub-Gaussian $\varepsilon$’s. Finally, we illustrate numerically these approaches.

We analyze the generalization properties of two-layer neural networks in the neural tangent kernel (NTK) regime, trained with gradient descent (GD). For early stopped GD we derive fast rates of convergence that are known to be minimax optimal in the framework of non-parametric regression in reproducing kernel Hilbert spaces. On our way, we precisely keep track of the number of hidden neurons required for generalization and improve over existing results. We further show that the weights during training remain in a vicinity around initialization, the radius being dependent on structural assumptions such as degree of smoothness of the regression function and eigenvalue decay of the integral operator associated to the NTK.

Literature reviews reveal that there is a very close connection between experimental design and coding theory. Based on a code mapping transformation, this paper provides a new method to construct a class of mixed designs with two- and four-level. A general construction method is described and some theoretical results of obtained designs are given. Analytic connections are established between the generated and the initial designs in terms of aberration criteria and discrepancies. Sharp lower bounds of the wrap-around $L_2$- and Lee discrepancies are obtained and used as the benchmarks to measure the uniformity of the generated designs. Examples are provided to illustrate the effectiveness of the construction and lend our results further support.

Detecting the correlation between two random variables is widely used in many empirical problems in economics. Among them, Pearson’s correlation can be used to quantify the degree of dependence between variables. However, it cannot handle asymmetric correlations. To deal with this situation, we proposed a pair of widely applicable measures of conditional dependence ($MCDs$), which can not only account for the asymmetry but also the linear or nonlinear conditional dependencies in the presence of multiple variables. We give instances: when the paired measures are the same, resulting in symmetric correlation measures that are equivalent to the square of the Pearson coefficient; when no condition variables are given, $MCDs$ are used to assess the relationship between two variables. Consequently, Pearson’s correlation is a particular instance of $MCDs$. Theoretical attributes of $MCDs$ show that they have wide applicability. In statistical inference, we develop the joint asymptotics of kernel-based estimators for $MCDs$, which can be applied to determine whether two randomly generated variables exhibit symmetric conditional dependence in the presence of confounding variables. In the simulation, we verify the efficacy of the proposed $MCDs$. Then we use real data to analyze the asymmetric impact of $MCDs$ on stock market movements.

Problems of large-scale multiple testing are often encountered in modern scientific research. Conventional multiple testing procedures usually suffer considerable loss of testing efficiency when correlations among tests are ignored. In fact, appropriate use of correlation information not only enhances the efficacy of the testing procedure, but also improves the interpretability of the results. Since the disease- or trait-related single nucleotide polymorphisms (SNPs) tend to be clustered and exhibit serial correlations, hidden Markov model (HMM) based multiple testing procedures have been successfully applied in genome-wide association studies (GWAS). However, modeling the entire chromosome using a single HMM is somewhat rough. To overcome this issue, this paper employs the hierarchical hidden Markov model (HHMM) to describe local correlations among tests, and develops a multiple testing procedure that can automatically divide different class of chromosome regions, while taking into account local correlations among tests. We first propose an oracle procedure that is shown theoretically to be valid, and in fact optimal in some sense. We then develop a date-driven procedure to mimic the oracle version. Extensive simulations and a real data example show that the novel multiple testing procedure outperforms its competitors.

The modified Cholesky decomposition (MCD) method is commonly used in precision matrix estimation assuming that the random variables have a specified order. In this paper, we develop a permutation-based refitted cross validation (PRCV) estimation procedure for ultrahigh dimensional precision matrix based on the MCD, which does not rely on the order of variables. The consistency of the proposed estimator is established under the Frobenius norm without normal distribution assumption. Simulation studies present satisfactory performance of in various scenarios. The proposed method is also applied to analyze a real data. We provide the complete code at https://github.com/lwfwhunanhero/PRCV.

In this paper, we perform deep neural networks for learning stationary $\psi$-weakly dependent processes. Such weak-dependence property includes a class of weak dependence conditions such as mixing, association$\cdots$ and the setting considered here covers many commonly used situations such as: regression estimation, time series prediction, time series classification$\cdots$ The consistency of the empirical risk minimization algorithm in the class of deep neural networks predictors is established. We achieve the generalization bound and obtain an asymptotic learning rate, which is less than $O\left(n^{-1/\alpha }\right)$, for all $\alpha >2$. A bound of the excess risk, for a wide class of target functions, is also derived. Applications to binary time series classification and prediction in affine causal models with exogenous covariates are carried out. Some simulation results are provided, as well as an application to the US recession data.

In this paper, we study high-dimensional reduced rank regression and propose a doubly robust procedure, called $\mathrm{D4R}$, meaning concurrent robustness to both outliers in predictors and heavy-tailed random noise. The proposed method uses the composite gradient descent based algorithm to solve the nonconvex optimization problem resulting from combining Tukey’s biweight loss with spectral regularization. Both theoretical and numerical properties of $\mathrm{D4R}$ are investigated. We establish non-asymptotic estimation error bounds under both the Frobenius norm and the nuclear norm in the high-dimensional setting. Simulation studies and real example show that the performance of $\mathrm{D4R}$ is better than that of several existing estimation methods.