Journal of Statistical Planning and Inference最新文献

{"title":"D4R: Doubly robust reduced rank regression in high dimension","authors":"Xiaoyan Ma ,&nbsp;Lili Wei ,&nbsp;Wanfeng Liang","doi":"10.1016/j.jspi.2024.106162","DOIUrl":"https://doi.org/10.1016/j.jspi.2024.106162","url":null,"abstract":"<div><p>In this paper, we study high-dimensional reduced rank regression and propose a doubly robust procedure, called <span><math><mi>D4R</mi></math></span>, 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 <span><math><mi>D4R</mi></math></span> 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 <span><math><mi>D4R</mi></math></span> is better than that of several existing estimation methods.</p></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"232 ","pages":"Article 106162"},"PeriodicalIF":0.9,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139985505","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On card guessing with two types of cards","authors":"Markus Kuba ,&nbsp;Alois Panholzer","doi":"10.1016/j.jspi.2024.106160","DOIUrl":"10.1016/j.jspi.2024.106160","url":null,"abstract":"<div><p>We consider a card guessing strategy for a stack of cards with two different types of cards, say <span><math><msub><mrow><mi>m</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> cards of type red (heart or diamond) and <span><math><msub><mrow><mi>m</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> cards of type black (clubs or spades). Given a deck of <span><math><mrow><mi>M</mi><mo>=</mo><msub><mrow><mi>m</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>+</mo><msub><mrow><mi>m</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math></span> cards, we propose a refined counting of the number of correct colour guesses, when the guesser is provided with complete information, in other words, when the numbers <span><math><msub><mrow><mi>m</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>m</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> and the colour of each drawn card are known. We decompose the correct guessed cards into three different types by taking into account the probability of making a correct guess, and provide joint distributional results for the underlying random variables as well as joint limit laws.</p></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"232 ","pages":"Article 106160"},"PeriodicalIF":0.9,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139924736","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Feature screening via concordance indices for left-truncated and right-censored survival data","authors":"Li-Pang Chen","doi":"10.1016/j.jspi.2024.106153","DOIUrl":"10.1016/j.jspi.2024.106153","url":null,"abstract":"<div><p>Ultrahigh-dimensional data analysis has been a popular topic in decades. In the framework of ultrahigh-dimensional setting, feature screening methods are key techniques to retain informative covariates and screen out non-informative ones when the dimension of covariates is extremely larger than the sample size. In the presence of incomplete data caused by censoring, several valid methods have also been developed to deal with ultrahigh-dimensional covariates for time-to-event data. However, little approach is available to handle feature screening for survival data subject to biased sample, which is usually induced by left-truncation. In this paper, we extend the C-index estimation proposed by Hartman et al. (2023) to develop a valid feature screening procedure to deal with left-truncated and right-censored survival data subject to ultrahigh-dimensional covariates. The sure screening property is also rigorously established to justify the proposed method. Numerical results also verify the validity of the proposed procedure.</p></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"232 ","pages":"Article 106153"},"PeriodicalIF":0.9,"publicationDate":"2024-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139816268","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A new non-parametric estimation of the expected shortfall for dependent financial losses","authors":"Khouzeima Moutanabbir ,&nbsp;Mohammed Bouaddi","doi":"10.1016/j.jspi.2024.106151","DOIUrl":"10.1016/j.jspi.2024.106151","url":null,"abstract":"<div><p>In this paper, we address the problem of kernel estimation of the Expected Shortfall (ES) risk measure for financial losses that satisfy the <span><math><mi>α</mi></math></span>-mixing conditions. First, we introduce a new non-parametric estimator for the ES measure using a kernel estimation. Given that the ES measure is the sum of the Value-at-Risk and the mean-excess function, we provide an estimation of the ES as a sum of the estimators of these two components. Our new estimator has a closed-form expression that depends on the choice of the kernel smoothing function, and we derive these expressions in the case of Gaussian, Uniform, and Epanechnikov kernel functions. We study the asymptotic properties of this new estimator and compare it to the Scaillet estimator. Capitalizing on the properties of these two estimators, we combine them to create a new estimator for the ES which reduces the bias and lowers the mean square error. The combined estimator shows better stability with respect to the choice of the kernel smoothing parameter. Our findings are illustrated through some numerical examples that help us to assess the small sample properties of the different estimators considered in this paper.</p></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"232 ","pages":"Article 106151"},"PeriodicalIF":0.9,"publicationDate":"2024-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0378375824000089/pdfft?md5=41ea07fd0d26fc2bbea00de05c1c0468&pid=1-s2.0-S0378375824000089-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139680115","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Scale tests for a multilevel step-stress model with exponential lifetimes under Type-II censoring","authors":"Maria Kateri,&nbsp;Nikolay I. Nikolov","doi":"10.1016/j.jspi.2024.106152","DOIUrl":"10.1016/j.jspi.2024.106152","url":null,"abstract":"<div><p>Step-stress is a special type of accelerated life-testing procedure that allows the experimenter to test the units of interest under various stress conditions changed (usually increased) at different intermediate time points. In this paper, we study the problem of testing hypothesis for the scale parameter of a simple step-stress model with exponential lifetimes and under Type-II censoring. We consider several modifications of the log-likelihood ratio statistic and eliminate the distributional dependence on the unknown lifetime parameters by exploiting the scale invariant properties of the normalized failure spacings. The presented results and the ratio statistic are further generalized to the multilevel step-stress case under the log-link assumption. We compare the power performance of the proposed tests via Monte Carlo simulations. As an illustration, the described procedures are applied to a real data example from the literature.</p></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"232 ","pages":"Article 106152"},"PeriodicalIF":0.9,"publicationDate":"2024-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0378375824000090/pdfft?md5=cae47c9c8ceeff2301a8594614cd022f&pid=1-s2.0-S0378375824000090-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139678740","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Construction of high-dimensional high-separation distance designs","authors":"Xu He ,&nbsp;Fasheng Sun","doi":"10.1016/j.jspi.2024.106150","DOIUrl":"10.1016/j.jspi.2024.106150","url":null,"abstract":"<div><p>Space-filling designs that possess high separation distance are useful for computer experiments. We propose a novel method to construct high-dimensional high-separation distance designs. The construction involves taking the Kronecker product of sub-Hadamard matrices and rotation. In addition to possessing better separation distance than most existing types of space-filling designs, our newly proposed designs enjoy orthogonality and projection uniformity and are more flexible in the numbers of runs and factors than that from most algebraic constructions. From numerical results, such designs are excellent in Gaussian process emulation of high-dimensional computer experiments. An R package on design construction is available online.</p></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"232 ","pages":"Article 106150"},"PeriodicalIF":0.9,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139663836","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Calibrating multi-dimensional complex ODE from noisy data via deep neural networks","authors":"Kexuan Li ,&nbsp;Fangfang Wang ,&nbsp;Ruiqi Liu ,&nbsp;Fan Yang ,&nbsp;Zuofeng Shang","doi":"10.1016/j.jspi.2024.106147","DOIUrl":"10.1016/j.jspi.2024.106147","url":null,"abstract":"<div><p><span>Ordinary differential equations<span> (ODEs) are widely used to model complex dynamics that arise in biology, chemistry, engineering, finance, physics, etc. Calibration of a complicated ODE system using noisy data is generally challenging. In this paper, we propose a two-stage nonparametric approach to address this problem. We first extract the de-noised data and their higher order derivatives using boundary kernel method, and then feed them into a sparsely connected </span></span>deep neural network<span> with rectified linear unit (ReLU) activation function. Our method is able to recover the ODE system without being subject to the curse of dimensionality and the complexity of the ODE structure. We have shown that our method is consistent if the ODE possesses a general modular structure with each modular component involving only a few input variables, and the network architecture is properly chosen. Theoretical properties are corroborated by an extensive simulation study that also demonstrates the effectiveness of the proposed method in finite samples. Finally, we use our method to simultaneously characterize the growth rate of COVID-19 cases from the 50 states of the United States.</span></p></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"232 ","pages":"Article 106147"},"PeriodicalIF":0.9,"publicationDate":"2024-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139588540","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An empirical likelihood-based unified test for the integer-valued AR(1) models","authors":"Jing Zhang ,&nbsp;Bo Li ,&nbsp;Yu Wang ,&nbsp;Xinyi Wei ,&nbsp;Xiaohui Liu","doi":"10.1016/j.jspi.2024.106149","DOIUrl":"10.1016/j.jspi.2024.106149","url":null,"abstract":"<div><p>In this paper, we suggest an empirical likelihood-based test for the autoregressive coefficient of an integer-valued AR(1) model, i.e., INAR(1). We derive the limit distributions of the resulting test statistic under both null and alternative hypotheses. It turns out that regardless of whether the INAR process is stable or unstable, the statistic is always chi-squared distributed asymptotically under the null hypothesis, and as a result, it can offer unified inferences for the autoregressive coefficient. The performance of its finite sample is also demonstrated using simulations and an empirical example.</p></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"232 ","pages":"Article 106149"},"PeriodicalIF":0.9,"publicationDate":"2024-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0378375824000065/pdfft?md5=1c6d378b469788f0758b1d5699e2f871&pid=1-s2.0-S0378375824000065-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139588927","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Hilbert space-valued fractionally integrated autoregressive moving average processes with long memory operators","authors":"Amaury Durand ,&nbsp;François Roueff","doi":"10.1016/j.jspi.2024.106146","DOIUrl":"10.1016/j.jspi.2024.106146","url":null,"abstract":"<div><p><span>Fractionally integrated autoregressive moving average (FIARMA) processes have been widely and successfully used to model and predict univariate time series exhibiting long range dependence. Vector and functional extensions of these processes have also been considered more recently. Here we study these processes by relying on a spectral domain approach in the case where the processes are valued in a separable Hilbert space </span><span><math><msub><mrow><mi>H</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>. In this framework, the usual univariate long memory parameter <span><math><mi>d</mi></math></span> is replaced by a long memory <em>operator</em> <span><math><mi>D</mi></math></span> acting on <span><math><msub><mrow><mi>H</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>, leading to a class of <span><math><msub><mrow><mi>H</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>-valued FIARMA(<span><math><mrow><mi>D</mi><mo>,</mo><mi>p</mi><mo>,</mo><mi>q</mi></mrow></math></span>) processes, where <span><math><mi>p</mi></math></span> and <span><math><mi>q</mi></math></span> are the degrees of the AR and MA polynomials. When <span><math><mi>D</mi></math></span> is a normal operator, we provide a necessary and sufficient condition for the <span><math><mi>D</mi></math></span>-fractional integration of an <span><math><msub><mrow><mi>H</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>-valued ARMA(<span><math><mrow><mi>p</mi><mo>,</mo><mi>q</mi></mrow></math></span><span>) process to be well defined. Then, we derive the best predictor for a class of causal FIARMA processes and study how this best predictor can be consistently estimated from a finite sample of the process. To this end, we provide a general result on quadratic functionals of the periodogram, which incidentally yields a result of independent interest. Namely, for any ergodic stationary process valued in </span><span><math><msub><mrow><mi>H</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> with a finite second moment, the empirical autocovariance operator converges, in trace-norm, to the true autocovariance operator almost surely at each lag.</p></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"231 ","pages":"Article 106146"},"PeriodicalIF":0.9,"publicationDate":"2024-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139552069","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Fast and asymptotically-efficient estimation in an autoregressive process with fractional type noise","authors":"Samir Ben Hariz ,&nbsp;Alexandre Brouste ,&nbsp;Chunhao Cai ,&nbsp;Marius Soltane","doi":"10.1016/j.jspi.2024.106148","DOIUrl":"10.1016/j.jspi.2024.106148","url":null,"abstract":"<div><p>This paper considers the joint estimation of the parameters of a first-order fractional autoregressive model. A one-step procedure is considered in order to obtain an asymptotically-efficient estimator with an initial guess estimator with convergence speed lower than <span><math><msqrt><mrow><mi>n</mi></mrow></msqrt></math></span> and singular asymptotic joint distribution. This estimator is computed faster than the maximum likelihood estimator or the Whittle estimator and therefore allows for faster inference on large samples. The paper also illustrates the performance of this method on finite-size samples via Monte Carlo simulations.</p></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"232 ","pages":"Article 106148"},"PeriodicalIF":0.9,"publicationDate":"2024-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139588396","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}