Annals of Statistics最新文献_第6页

Sharp minimax distribution estimation for current status censoring with or without missing 有或没有缺失的当前状态审查的尖锐极小最大值分布估计

IF 4.5 1区数学

Annals of Statistics Pub Date : 2021-02-01 DOI: 10.1214/20-AOS1970

S. Efromovich

{"title":"Sharp minimax distribution estimation for current status censoring with or without missing","authors":"S. Efromovich","doi":"10.1214/20-AOS1970","DOIUrl":"https://doi.org/10.1214/20-AOS1970","url":null,"abstract":"Nonparametric estimation of the cumulative distribution function and the probability density of a lifetime X modified by a current status censoring (CSC), including cases of right and left missing data, is a classical ill-posed problem with biased data. The biased nature of CSC data may preclude us from consistent estimation unless the biasing function is known or may be estimated, and its ill-posed nature slows down rates of convergence. Under a traditionally studied CSC, we observe a sample from $(Z,Delta )$ where a continuous monitoring time $Z$ is independent of $X$, $Delta :=I(Xleq Z)$ is the status, and the bias of observations is created by the density of $Z$ which is estimable. In presence of right or left missing, we observe corresponding samples from $(Delta Z,Delta )$ or $((1-Delta )Z,Delta )$; the data are again biased but now the density of $Z$ cannot be estimated from the data. As a result, to solve the estimation problem, either the density of $Z$ must be known (like in a controlled study) or an extra cross-sectional sampling of $Z$, which is typically simpler than an underlying CSC study, be conducted. The main aim of the paper is to develop for this biased and ill-posed problem the theory of efficient (sharp-minimax) estimation which is inspired by known results for the case of directly observed $X$. Among interesting aspects of the developed theory: (i) While sharp-minimax analysis of missing CSC may follow the classical Pinsker’s methodology, analysis of CSC requires a more complicated estimation procedure based on a special smoothing in both frequency and time domains; (ii) Efficient estimation requires solving an old-standing problem of approximating aperiodic Sobolev functions; (iii) If smoothness of the cdf of $X$ is known, then its rate-minimax estimation is possible even if the density of $Z$ is rougher. Real and simulated examples, as well as extensions of the core models to dependent $X$ and Z and case-control CSC, are presented.","PeriodicalId":8032,"journal":{"name":"Annals of Statistics","volume":null,"pages":null},"PeriodicalIF":4.5,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49238602","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: 1

Inference for conditional value-at-risk of a predictive regression 预测回归的条件风险值推断

IF 4.5 1区数学

Annals of Statistics Pub Date : 2020-12-01 DOI: 10.1214/19-aos1937

Yi He, Yanxi Hou, L. Peng, Haipeng Shen

{"title":"Inference for conditional value-at-risk of a predictive regression","authors":"Yi He, Yanxi Hou, L. Peng, Haipeng Shen","doi":"10.1214/19-aos1937","DOIUrl":"https://doi.org/10.1214/19-aos1937","url":null,"abstract":"Conditional value-at-risk is a popular risk measure in risk management. We study the inference problem of conditional value-at-risk under a linear predictive regression model. We derive the asymptotic distribution of the least squares estimator for the conditional value-at-risk. Our results relax the model assumptions made in Chun et al. (2012) and correct their mistake in the asymptotic variance expression. We show that the asymptotic variance depends on the quantile density function of the unobserved error and whether the model has a predictor with infinite variance, which makes it challenging to actually quantify the uncertainty of the conditional risk measure. To make the inference feasible, we then propose a smooth empirical likelihood based method for constructing a confidence interval for the conditional value-at-risk based on either independent errors or GARCH errors. Our approach not only bypasses the challenge of directly estimating the asymptotic variance but also does not need to know whether there exists an infinite variance predictor in the predictive model. Furthermore, we apply the same idea to the quantile regression method, which allows infinite variance predictors and generalizes the parameter estimation in Whang (2006) to conditional value-at-risk in the supplementary material. We demonstrate the finite sample performance of the derived confidence intervals through numerical studies before applying them to real data.","PeriodicalId":8032,"journal":{"name":"Annals of Statistics","volume":null,"pages":null},"PeriodicalIF":4.5,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48812460","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: 10

Nonparametric drift estimation for i.i.d. paths of stochastic differential equations 随机微分方程i.i.d.路径的非参数漂移估计

IF 4.5 1区数学

Annals of Statistics Pub Date : 2020-12-01 DOI: 10.1214/19-aos1933

F. Comte, V. Genon-Catalot

引用次数: 22

Irreducibility and geometric ergodicity of Hamiltonian Monte Carlo 哈密顿蒙特卡罗的不可约性和几何遍历性

IF 4.5 1区数学

Annals of Statistics Pub Date : 2020-12-01 DOI: 10.1214/19-aos1941

Alain Durmus, É. Moulines, E. Saksman

引用次数: 11

Fréchet change-point detection 变点检测

IF 4.5 1区数学

Annals of Statistics Pub Date : 2020-12-01 DOI: 10.1214/19-AOS1930

Paromita Dubey, H. Müller

引用次数: 26

Assessment of the extent of corroboration of an elaborate theory of a causal hypothesis using partial conjunctions of evidence factors 利用证据因素的部分连词对因果假设的详细理论的确证程度进行评估

IF 4.5 1区数学

Annals of Statistics Pub Date : 2020-12-01 DOI: 10.1214/19-aos1929

B. Karmakar, Dylan S. Small

{"title":"Assessment of the extent of corroboration of an elaborate theory of a causal hypothesis using partial conjunctions of evidence factors","authors":"B. Karmakar, Dylan S. Small","doi":"10.1214/19-aos1929","DOIUrl":"https://doi.org/10.1214/19-aos1929","url":null,"abstract":"An elaborate theory of predictions of a causal hypothesis consists of several falsifiable statements derived from the causal hypothesis. Statistical tests for the various pieces of the elaborate theory help to clarify how much the causal hypothesis is corroborated. In practice, the degree of corroboration of the causal hypothesis has been assessed by a verbal description of which of the several tests provides evidence for which of the several predictions. This verbal approach can miss quantitative patterns. In this paper, we develop a quantitative approach. We first decompose these various tests of the predictions into independent factors with different sources of potential biases. Support for the causal hypothesis is enhanced when many of these evidence factors support the predictions. A sensitivity analysis is used to assess the potential bias that could make the finding of the tests spurious. Along with this multi-parameter sensitivity analysis, we consider the partial conjunctions of the tests. These partial conjunctions quantify the evidence supporting various fractions of the collection of predictions. A partial conjunction test involves combining tests of the components in the partial conjunction. We find the asymptotically optimal combination of tests in the context of a sensitivity analysis. Our analysis of an elaborate theory of a causal hypothesis controls for the familywise error rate.","PeriodicalId":8032,"journal":{"name":"Annals of Statistics","volume":null,"pages":null},"PeriodicalIF":4.5,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43683533","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

TEST OF SIGNIFICANCE FOR HIGH-DIMENSIONAL LONGITUDINAL DATA. 高维纵向数据的显著性检验。

IF 4.5 1区数学

Annals of Statistics Pub Date : 2020-10-01 Epub Date: 2020-09-19 DOI: 10.1214/19-aos1900

Ethan X Fang, Yang Ning, Runze Li

{"title":"TEST OF SIGNIFICANCE FOR HIGH-DIMENSIONAL LONGITUDINAL DATA.","authors":"Ethan X Fang, Yang Ning, Runze Li","doi":"10.1214/19-aos1900","DOIUrl":"10.1214/19-aos1900","url":null,"abstract":"<p><p>This paper concerns statistical inference for longitudinal data with ultrahigh dimensional covariates. We first study the problem of constructing confidence intervals and hypothesis tests for a low dimensional parameter of interest. The major challenge is how to construct a powerful test statistic in the presence of high-dimensional nuisance parameters and sophisticated within-subject correlation of longitudinal data. To deal with the challenge, we propose a new quadratic decorrelated inference function approach, which simultaneously removes the impact of nuisance parameters and incorporates the correlation to enhance the efficiency of the estimation procedure. When the parameter of interest is of fixed dimension, we prove that the proposed estimator is asymptotically normal and attains the semiparametric information bound, based on which we can construct an optimal Wald test statistic. We further extend this result and establish the limiting distribution of the estimator under the setting with the dimension of the parameter of interest growing with the sample size at a polynomial rate. Finally, we study how to control the false discovery rate (FDR) when a vector of high-dimensional regression parameters is of interest. We prove that applying the Storey (2002)'s procedure to the proposed test statistics for each regression parameter controls FDR asymptotically in longitudinal data. We conduct simulation studies to assess the finite sample performance of the proposed procedures. Our simulation results imply that the newly proposed procedure can control both Type I error for testing a low dimensional parameter of interest and the FDR in the multiple testing problem. We also apply the proposed procedure to a real data example.</p>","PeriodicalId":8032,"journal":{"name":"Annals of Statistics","volume":null,"pages":null},"PeriodicalIF":4.5,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8277154/pdf/nihms-1614211.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"39189359","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

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":null,"pages":null},"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