Annals of Statistics最新文献_第7页

Hypothesis testing for high-dimensional time series via self-normalization 高维时间序列的自归一化假设检验

IF 4.5 1区数学

Annals of Statistics Pub Date : 2020-10-01 DOI: 10.1214/19-AOS1904

Runmin Wang, X. Shao

引用次数: 18

Valid post-selection inference in model-free linear regression 无模型线性回归中的有效后选择推理

IF 4.5 1区数学

Annals of Statistics Pub Date : 2020-10-01 DOI: 10.1214/19-AOS1917

Arun K. Kuchibhotla, L. Brown, A. Buja, Junhui Cai, E. George, Linda H. Zhao

{"title":"Valid post-selection inference in model-free linear regression","authors":"Arun K. Kuchibhotla, L. Brown, A. Buja, Junhui Cai, E. George, Linda H. Zhao","doi":"10.1214/19-AOS1917","DOIUrl":"https://doi.org/10.1214/19-AOS1917","url":null,"abstract":"S.1. Simulations Continued. The simulation setting in this section is the same as in Section 9. We first describe the reason for using the null situation β0 0p in the model. If β0 is an arbitrary non-zero vector, then, for fixed covariates, XiYi cannot be identically distributed and hence only (asymptotically) conservative inference is possible. In simulations this conservativeness confounds with the simultaneity so that the coverage becomes close to 1 (if not 1). In the main manuscript, we have shown plots comparing our method with Berk et al. (2013) and selective inference. We label our confidence region R̂:n,M (12) as “UPoSI,” the projected confidence region B̂ n,M (28) as “UPoSIBox”, and Berk et al. (2013) as “PoSI.” Tables 1, 2, and 3 show exact numbers for the comparison of our method with Berk et al. (2013). Note that size of each dot in the row plot of Figure 9 indicates the proportion of confidence regions of that volume among same-sized models. In Setting A and B, the confidence region volumes of same-sized models are the same. In Setting C, volumes of confidence regions of Berk and PoSI Box enlarge (hence smaller logpVolq{|M |q if the last covariate is included. Tables 4 and 5 show the numbers for the comparison of our method with selective inference when the selection procedure is forward stepwise and LARS, respectively. Sample splitting is a simple procedure that provides valid inference after selection as discussed in Section 1.3. We stress here that this is valid only for independent observations and that the model selected in the first split half could be different from the one selected in the full data. The comparison results with n 1000, p 500 and selection methods forward stepwise, LARS and BIC are summarized in Figure S.1. For sample splitting we have used the Bonferroni correction to obtain simultaneous inference for all coefficients in a model. Table 6 shows the comparison of our method with sample splitting.","PeriodicalId":8032,"journal":{"name":"Annals of Statistics","volume":"48 1","pages":"2953-2981"},"PeriodicalIF":4.5,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66077588","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 20

Asymptotic distribution and detection thresholds for two-sample tests based on geometric graphs 基于几何图的两样本检验的渐近分布和检测阈值

IF 4.5 1区数学

Annals of Statistics Pub Date : 2020-10-01 DOI: 10.1214/19-AOS1913

B. Bhattacharya

引用次数: 5

Asymptotic risk and phase transition of $l_{1}$-penalized robust estimator $l_{1}$惩罚鲁棒估计的渐近风险和相变

IF 4.5 1区数学

Annals of Statistics Pub Date : 2020-10-01 DOI: 10.1214/19-AOS1923

Hanwen Huang

引用次数: 7

Which bridge estimator is the best for variable selection? 哪种桥接估计器最适合变量选择？

IF 4.5 1区数学

Annals of Statistics Pub Date : 2020-10-01 DOI: 10.1214/19-AOS1906

Shuaiwen Wang, Haolei Weng, A. Maleki

引用次数: 18

Estimation and inference for precision matrices of nonstationary time series 非平稳时间序列精度矩阵的估计与推理

IF 4.5 1区数学

Annals of Statistics Pub Date : 2020-08-01 DOI: 10.1214/19-aos1894

Xiucai Ding, Zhou Zhou

引用次数: 9

Extending the validity of frequency domain bootstrap methods to general stationary processes 将频域自举方法的有效性推广到一般平稳过程

IF 4.5 1区数学

Annals of Statistics Pub Date : 2020-08-01 DOI: 10.1214/19-aos1892

M. Meyer, E. Paparoditis, Jens-Peter Kreiss

引用次数: 11

Double-slicing assisted sufficient dimension reduction for high-dimensional censored data 双切片有助于对高维截尾数据进行充分的降维

IF 4.5 1区数学

Annals of Statistics Pub Date : 2020-08-01 DOI: 10.1214/19-aos1880

Shanshan Ding, W. Qian, Lan Wang

{"title":"Double-slicing assisted sufficient dimension reduction for high-dimensional censored data","authors":"Shanshan Ding, W. Qian, Lan Wang","doi":"10.1214/19-aos1880","DOIUrl":"https://doi.org/10.1214/19-aos1880","url":null,"abstract":"This paper provides a unified framework and an efficient algorithm for analyzing high-dimensional survival data under weak modeling assumptions. In particular, it imposes neither parametric distributional assumption nor linear regression assumption. It only assumes that the survival time T depends on a high-dimensional covariate vector X through low-dimensional linear combinations of covariates ΓX. The censoring time is allowed to be conditionally independent of the survival time given the covariates. This general framework includes many popular parametric and semiparametric survival regression models as special cases. The proposed algorithm produces a number of practically useful outputs with theoretical guarantees, including a consistent estimate of the sufficient dimension reduction subspace of T |X, a uniformly consistent Kaplan-Meier type estimator of the conditional distribution function of T and a consistent estimator of the conditional quantile survival time. Our asymptotic results significantly extend the classical theory of sufficient dimension reduction for censored data (particularly that of Li et al. 1999) and the celebrated nonparametric Kaplan-Meier estimator to the setting where the number of covariates p diverges exponentially fast with the sample size n. We demonstrate the promising performance of the proposed new estimators through simulations and a real data example.","PeriodicalId":8032,"journal":{"name":"Annals of Statistics","volume":"48 1","pages":"2132-2154"},"PeriodicalIF":4.5,"publicationDate":"2020-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44672142","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 5

Beyond HC: More sensitive tests for rare/weak alternatives 超越HC：罕见/弱替代品的更敏感测试

IF 4.5 1区数学

Annals of Statistics Pub Date : 2020-08-01 DOI: 10.1214/19-aos1885

Thomas Porter, M. Stewart

{"title":"Beyond HC: More sensitive tests for rare/weak alternatives","authors":"Thomas Porter, M. Stewart","doi":"10.1214/19-aos1885","DOIUrl":"https://doi.org/10.1214/19-aos1885","url":null,"abstract":"Higher criticism (HC) is a popular method for large-scale inference problems based on identifying unusually high proportions of small pvalues. It has been shown to enjoy a lower-order optimality property in a simple normal location mixture model which is shared by the ‘tailor-made’ parametric generalised likelihood ratio test (GLRT) for the same model, however HC has also been shown to perform well outside this ‘narrow’ model. We develop a higher-order framework for analysing the power of these and similar procedures, which reveals the perhaps unsurprising fact that the GLRT enjoys an edge in power over HC for the normal location mixture model. We also identify a similar parametric mixture model to which HC is similarly ‘tailor-made’ and show that the situation is (at least partly) reversed there. We also show that in the normal location mixture model a procedure based on the empirical moment-generating function enjoys the same local power properties as the GLRT and may be recommended as an easy to implement (and interpret), complementary procedure to HC. Some other practical advice regarding the implementation of these procedures is provided. Finally we provide some simulation results to help interpret our theoretical findings.","PeriodicalId":8032,"journal":{"name":"Annals of Statistics","volume":"48 1","pages":"2230-2252"},"PeriodicalIF":4.5,"publicationDate":"2020-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44608637","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 5

Bayesian analysis of the covariance matrix of a multivariate normal distribution with a new class of priors 具有一类新先验的多元正态分布协方差矩阵的贝叶斯分析

IF 4.5 1区数学

Annals of Statistics Pub Date : 2020-08-01 DOI: 10.1214/19-aos1891

J. Berger, Dongchu Sun, Chengyuan Song

{"title":"Bayesian analysis of the covariance matrix of a multivariate normal distribution with a new class of priors","authors":"J. Berger, Dongchu Sun, Chengyuan Song","doi":"10.1214/19-aos1891","DOIUrl":"https://doi.org/10.1214/19-aos1891","url":null,"abstract":"Bayesian analysis for the covariance matrix of a multivariate normal distribution has received a lot of attention in the last two decades. In this paper, we propose a new class of priors for the covariance matrix, including both inverse Wishart and reference priors as special cases. The main motivation for the new class is to have available priors – both subjective and objective – that do not “force eigenvalues apart,” which is a criticism of inverse Wishart and Jeffreys priors. Extensive comparison of these ‘shrinkage priors’ with inverse Wishart and Jeffreys priors is undertaken, with the new priors seeming to have considerably better performance. A number of curious facts about the new priors are also observed, such as that the posterior distribution will be proper with just three vector observations from the multivariate normal distribution – regardless of the dimension of the covariance matrix – and that useful inference about features of the covariance matrix can be possible. Finally, a new MCMC algorithm is developed for this class of priors and is shown to be computationally effective for matrices of up to 100 dimensions.","PeriodicalId":8032,"journal":{"name":"Annals of Statistics","volume":"48 1","pages":"2381-2403"},"PeriodicalIF":4.5,"publicationDate":"2020-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48597865","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 7