Journal of Statistical Planning and Inference最新文献

{"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}

{"title":"Locally adaptive sparse additive quantile regression model with TV penalty","authors":"Yue Wang ,&nbsp;Hongmei Lin ,&nbsp;Zengyan Fan ,&nbsp;Heng Lian","doi":"10.1016/j.jspi.2024.106144","DOIUrl":"10.1016/j.jspi.2024.106144","url":null,"abstract":"<div><p><span>High-dimensional additive quantile regression<span> model via penalization provides a powerful tool for analyzing complex data in many contemporary applications. Despite the fast developments, how to combine the strengths of additive quantile regression with total variation penalty with theoretical guarantees still remains unexplored. In this paper, we propose a new methodology for sparse additive quantile regression model over bounded variation function classes via the empirical norm penalty and the total variation penalty for local adaptivity. Theoretically, we prove that the proposed method achieves the optimal convergence rate under mild assumptions. Moreover, an </span></span>alternating direction method of multipliers (ADMM) based algorithm is developed. Both simulation results and real data analysis confirm the effectiveness of our method.</p></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"232 ","pages":"Article 106144"},"PeriodicalIF":0.9,"publicationDate":"2024-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139499684","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 the adaptive Lasso estimator of AR(p) time series with applications to INAR(p) and Hawkes processes","authors":"Daniela De Canditiis,&nbsp;Giovanni Luca Torrisi","doi":"10.1016/j.jspi.2024.106145","DOIUrl":"10.1016/j.jspi.2024.106145","url":null,"abstract":"<div><p>We investigate the consistency and the rate of convergence of the adaptive Lasso estimator for the parameters of linear AR(p) time series with a white noise which is a strictly stationary and ergodic martingale difference. Roughly speaking, we prove that <span><math><mrow><mo>(</mo><mi>i</mi><mo>)</mo></mrow></math></span> If the white noise has a finite second moment, then the adaptive Lasso estimator is almost sure consistent <span><math><mrow><mo>(</mo><mi>i</mi><mi>i</mi><mo>)</mo></mrow></math></span><span> If the white noise has a finite fourth moment, then the error estimate converges to zero with the same rate as the regularizing parameters of the adaptive Lasso estimator. Such theoretical findings are applied to estimate the parameters of INAR(p) time series and to estimate the fertility function of Hawkes processes. The results are validated by some numerical simulations, which show that the adaptive Lasso estimator allows for a better balancing between bias and variance with respect to the Conditional Least Square estimator and the classical Lasso estimator.</span></p></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"231 ","pages":"Article 106145"},"PeriodicalIF":0.9,"publicationDate":"2024-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139499638","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":"Statistical inference for wavelet curve estimators of symmetric positive definite matrices","authors":"Daniel Rademacher ,&nbsp;Johannes Krebs ,&nbsp;Rainer von Sachs","doi":"10.1016/j.jspi.2023.106140","DOIUrl":"https://doi.org/10.1016/j.jspi.2023.106140","url":null,"abstract":"<div><p><span>In this paper we treat statistical inference<span> for a wavelet estimator of curves of symmetric positive definite (SPD) using the log-Euclidean distance. This estimator preserves positive-definiteness and enjoys permutation-equivariance, which is particularly relevant for covariance matrices. Our second-generation wavelet estimator is based on average-interpolation (AI) and allows the same powerful properties, including fast algorithms, known from nonparametric curve estimation with wavelets in standard Euclidean set-ups. The core of our work is the </span></span>proposition<span> of confidence sets for our AI wavelet estimator in a non-Euclidean geometry. We derive asymptotic normality<span> of this estimator, including explicit expressions of its asymptotic variance<span>. This opens the door for constructing asymptotic confidence regions which we compare with our proposed bootstrap scheme for inference. Detailed numerical simulations confirm the appropriateness of our suggested inference schemes.</span></span></span></p></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"231 ","pages":"Article 106140"},"PeriodicalIF":0.9,"publicationDate":"2024-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139433656","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":"Uniformly more powerful tests for a subset of the components of a Normal Mean Vector","authors":"Yining Wang ,&nbsp;Gang Li","doi":"10.1016/j.jspi.2023.106141","DOIUrl":"10.1016/j.jspi.2023.106141","url":null,"abstract":"<div><p>A class of tests that are uniformly more powerful than the likelihood ratio test<span> is derived for testing the hypothesis about the means of a subset of the components of a multivariate normal distribution<span> with unknown covariance matrix, when the means of the other subset of the components are known.</span></span></p></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"231 ","pages":"Article 106141"},"PeriodicalIF":0.9,"publicationDate":"2023-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139070464","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":"Sparse multiple kernel learning: Minimax rates with random projection","authors":"Wenqi Lu ,&nbsp;Zhongyi Zhu ,&nbsp;Rui Li ,&nbsp;Heng Lian","doi":"10.1016/j.jspi.2023.106142","DOIUrl":"10.1016/j.jspi.2023.106142","url":null,"abstract":"<div><p>In kernel-based learning, the random projection method, also called random sketching, has been successfully used in kernel ridge regression to reduce the computational burden in the big data setting, and at the same time retain the minimax convergence rate. In this work, we consider its use in sparse multiple kernel learning problems where a closed-form optimizer is not available, which poses significant technical challenges, for which the existing results do not carry over directly. Even when random projection is not used, our risk bound improves on the existing results in several aspects. We also illustrate the use of random projection via some numerical examples.</p></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"231 ","pages":"Article 106142"},"PeriodicalIF":0.9,"publicationDate":"2023-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139070664","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 First-Order mixture integer-valued threshold autoregressive process based on binomial thinning and negative binomial thinning","authors":"Danshu Sheng ,&nbsp;Dehui Wang ,&nbsp;Liuquan Sun","doi":"10.1016/j.jspi.2023.106143","DOIUrl":"10.1016/j.jspi.2023.106143","url":null,"abstract":"<div><p><span><span>In this paper, we introduce a new first-order mixture integer-valued threshold autoregressive process, based on the binomial and </span>negative binomial thinning operators. Basic probabilistic and statistical properties of this model are discussed. Conditional least squares (CLS) and conditional maximum likelihood (CML) estimators are derived and the </span>asymptotic properties<span> of the estimators are established. The inference for the threshold parameter is obtained based on the CLS and CML score functions<span>. Moreover, the Wald test is applied to detect the existence of the piecewise structure. Simulation studies are considered, along with an application: the number of criminal mischief incidents in the Pittsburgh dataset</span></span></p></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"231 ","pages":"Article 106143"},"PeriodicalIF":0.9,"publicationDate":"2023-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139070374","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":"Designs for half-diallel experiments with commutative orthogonal block structure","authors":"R.A. Bailey, Peter J. Cameron, Dário Ferreira, Sandra S. Ferreira, Célia Nunes","doi":"10.1016/j.jspi.2023.106139","DOIUrl":"https://doi.org/10.1016/j.jspi.2023.106139","url":null,"abstract":"<p>In some experiments, the experimental units are all pairs of individuals who have to undertake a given task together. The set of such pairs forms a triangular association scheme. Appropriate randomization then gives two non-trivial strata. The design is said to have commutative orthogonal block structure (COBS) if the best linear unbiased estimators of treatment contrasts do not depend on the stratum variances. There are precisely three ways in which such a design can have COBS. We give a complete description of designs for which all treatment contrasts are in the same stratum. Then we give a very general construction for designs with COBS which have some treatment contrasts in each stratum.</p>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"16 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139027909","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}