Journal of Statistical Planning and Inference最新文献_第7页

IF 0.9 4区数学

Journal of Statistical Planning and Inference Pub Date : 2024-04-26 DOI: 10.1016/j.jspi.2024.106187

Namhyun Kim , Pipat Wongsa-art , Yingcun Xia

{"title":"A dynamic count process","authors":"Namhyun Kim , Pipat Wongsa-art , Yingcun Xia","doi":"10.1016/j.jspi.2024.106187","DOIUrl":"https://doi.org/10.1016/j.jspi.2024.106187","url":null,"abstract":"<div>The current paper aims to complement the recent development of the observation-driven models of dynamic counts with a parametric-driven one for a general case, particularly discrete two parameters exponential family distributions. The current paper proposes a finite semiparametric exponential mixture of SETAR processes of the conditional mean of counts to capture the nonlinearity and complexity. Because of the intrinsic latency of the conditional mean, the general additive state-space representation of dynamic counts is firstly proposed then stationarity and geometric ergodicity are established under a mild set of conditions. We also propose to estimate the unknown parameters by using quasi maximum likelihood estimation and establishes the asymptotic properties of the quasi maximum likelihood estimators (QMLEs), particularly <math><msqrt><mrow><mi>T</mi></mrow></msqrt></math>-consistency and normality under the relatively mild set of conditions. Furthermore, the finite sample properties of the QMLEs are investigated via simulation exercises and an illustration of the proposed process is presented by applying the proposed method to the intraday transaction counts per minute of AstraZeneca stock.</div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"233 ","pages":"Article 106187"},"PeriodicalIF":0.9,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140894991","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}

引用次数: 0

Consistency of the maximum likelihood estimator of population tree in a coalescent framework 聚合框架中种群树最大似然估计的一致性

IF 0.9 4区数学

Journal of Statistical Planning and Inference Pub Date : 2024-04-21 DOI: 10.1016/j.jspi.2024.106172

Arindam RoyChoudhury

引用次数: 0

Augmented projection Wasserstein distances: Multi-dimensional projection with neural surface 增强投影瓦瑟斯坦距离：带神经表面的多维投影

IF 0.9 4区数学

Journal of Statistical Planning and Inference Pub Date : 2024-04-19 DOI: 10.1016/j.jspi.2024.106185

Miyu Sugimoto , Ryo Okano , Masaaki Imaizumi

{"title":"Augmented projection Wasserstein distances: Multi-dimensional projection with neural surface","authors":"Miyu Sugimoto , Ryo Okano , Masaaki Imaizumi","doi":"10.1016/j.jspi.2024.106185","DOIUrl":"https://doi.org/10.1016/j.jspi.2024.106185","url":null,"abstract":"<div>The Wasserstein distance is a fundamental tool for comparing probability distributions and has found broad applications in various fields, including image generation using generative adversarial networks. Despite its useful properties, the performance of the Wasserstein distance decreases when data is high-dimensional, known as the curse of dimensionality. To mitigate this issue, an extension of the Wasserstein distance has been developed, such as the sliced Wasserstein distance using one-dimensional projection. However, such an extension loses information on the original data, due to the linear projection onto the one-dimensional space. In this paper, we propose novel distances named augmented projection Wasserstein distances (APWDs) to address these issues, which utilize multi-dimensional projection with a nonlinear surface by a neural network. The APWDs employ a two-step procedure; it first maps data onto a nonlinear surface by a neural network, then linearly projects the mapped data into a multidimensional space. We also give an algorithm to select a subspace for the multi-dimensional projection. The APWDs are computationally effective while preserving nonlinear information of data. We theoretically confirm that the APWDs mitigate the curse of dimensionality from data. Our experiments demonstrate the APWDs’ outstanding performance and robustness to noise, particularly in the context of nonlinear high-dimensional data.</div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"233 ","pages":"Article 106185"},"PeriodicalIF":0.9,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0378375824000429/pdfft?md5=d9eef2f8ec0fb76099ca4281dc2a0b63&pid=1-s2.0-S0378375824000429-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140632638","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}

引用次数: 0

Distributed optimal subsampling for quantile regression with massive data 海量数据量化回归的分布式最优子采样

IF 0.9 4区数学

Journal of Statistical Planning and Inference Pub Date : 2024-04-18 DOI: 10.1016/j.jspi.2024.106186

Yue Chao, Xuejun Ma, Boya Zhu

引用次数: 0

Entropic regularization of neural networks: Self-similar approximations 神经网络的熵正则化：自相似近似

IF 0.9 4区数学

Journal of Statistical Planning and Inference Pub Date : 2024-04-16 DOI: 10.1016/j.jspi.2024.106181

Amir R. Asadi, Po-Ling Loh

引用次数: 0

Multiplier subsample bootstrap for statistics of time series 用于时间序列统计的乘数子样本自举法

IF 0.9 4区数学

Journal of Statistical Planning and Inference Pub Date : 2024-04-15 DOI: 10.1016/j.jspi.2024.106183

Ruru Ma, Shibin Zhang

引用次数: 0

A unified Fourier slice method to derive ridgelet transform for a variety of depth-2 neural networks 为各种深度-2 神经网络推导小岭变换的统一傅立叶切片法

IF 0.9 4区数学

Journal of Statistical Planning and Inference Pub Date : 2024-04-15 DOI: 10.1016/j.jspi.2024.106184

Sho Sonoda , Isao Ishikawa , Masahiro Ikeda

{"title":"A unified Fourier slice method to derive ridgelet transform for a variety of depth-2 neural networks","authors":"Sho Sonoda , Isao Ishikawa , Masahiro Ikeda","doi":"10.1016/j.jspi.2024.106184","DOIUrl":"https://doi.org/10.1016/j.jspi.2024.106184","url":null,"abstract":"<div>To investigate neural network parameters, it is easier to study the distribution of parameters than to study the parameters in each neuron. The ridgelet transform is a pseudo-inverse operator that maps a given function <math><mi>f</mi></math> to the parameter distribution <math><mi>γ</mi></math> so that a network <math><mrow><mstyle><mi>N</mi><mi>N</mi></mstyle><mrow><mo>[</mo><mi>γ</mi><mo>]</mo></mrow></mrow></math> reproduces <math><mi>f</mi></math>, i.e. <math><mrow><mstyle><mi>N</mi><mi>N</mi></mstyle><mrow><mo>[</mo><mi>γ</mi><mo>]</mo></mrow><mo>=</mo><mi>f</mi></mrow></math>. For depth-2 fully-connected networks on a Euclidean space, the ridgelet transform has been discovered up to the closed-form expression, thus we could describe how the parameters are distributed. However, for a variety of modern neural network architectures, the closed-form expression has not been known. In this paper, we explain a systematic method using Fourier expressions to derive ridgelet transforms for a variety of modern networks such as networks on finite fields <math><msub><mrow><mi>F</mi></mrow><mrow><mi>p</mi></mrow></msub></math>, group convolutional networks on abstract Hilbert space <math><mi>H</mi></math>, fully-connected networks on noncompact symmetric spaces <math><mrow><mi>G</mi><mo>/</mo><mi>K</mi></mrow></math>, and pooling layers, or the <math><mi>d</mi></math>-plane ridgelet transform.</div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"233 ","pages":"Article 106184"},"PeriodicalIF":0.9,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0378375824000417/pdfft?md5=98e3c89ff86925f67f13c56d174f0109&pid=1-s2.0-S0378375824000417-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140618803","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}

引用次数: 0

Robust nonparametric regression based on deep ReLU neural networks 基于深度 ReLU 神经网络的鲁棒非参数回归

IF 0.9 4区数学

Journal of Statistical Planning and Inference Pub Date : 2024-04-15 DOI: 10.1016/j.jspi.2024.106182

Juntong Chen

{"title":"Robust nonparametric regression based on deep ReLU neural networks","authors":"Juntong Chen","doi":"10.1016/j.jspi.2024.106182","DOIUrl":"https://doi.org/10.1016/j.jspi.2024.106182","url":null,"abstract":"<div>In this paper, we consider robust nonparametric regression using deep neural networks with ReLU activation function. While several existing theoretically justified methods are geared towards robustness against identical heavy-tailed noise distributions, the rise of adversarial attacks has emphasized the importance of safeguarding estimation procedures against systematic contamination. We approach this statistical issue by shifting our focus towards estimating conditional distributions. To address it robustly, we introduce a novel estimation procedure based on <math><mi>ℓ</mi></math>-estimation. Under a mild model assumption, we establish general non-asymptotic risk bounds for the resulting estimators, showcasing their robustness against contamination, outliers, and model misspecification. We then delve into the application of our approach using deep ReLU neural networks. When the model is well-specified and the regression function belongs to an <math><mi>α</mi></math>-Hölder class, employing <math><mi>ℓ</mi></math>-type estimation on suitable networks enables the resulting estimators to achieve the minimax optimal rate of convergence. Additionally, we demonstrate that deep <math><mi>ℓ</mi></math>-type estimators can circumvent the curse of dimensionality by assuming the regression function closely resembles the composition of several Hölder functions. To attain this, new deep fully-connected ReLU neural networks have been designed to approximate this composition class. This approximation result can be of independent interest.</div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"233 ","pages":"Article 106182"},"PeriodicalIF":0.9,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0378375824000399/pdfft?md5=79a5bc36ebe3d6024d39b9f8adf1f910&pid=1-s2.0-S0378375824000399-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140649412","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}

引用次数: 0

Convergence guarantees for forward gradient descent in the linear regression model 线性回归模型中前向梯度下降的收敛保证

IF 0.9 4区数学

Journal of Statistical Planning and Inference Pub Date : 2024-04-06 DOI: 10.1016/j.jspi.2024.106174

Thijs Bos , Johannes Schmidt-Hieber

{"title":"Convergence guarantees for forward gradient descent in the linear regression model","authors":"Thijs Bos , Johannes Schmidt-Hieber","doi":"10.1016/j.jspi.2024.106174","DOIUrl":"https://doi.org/10.1016/j.jspi.2024.106174","url":null,"abstract":"<div>Renewed interest in the relationship between artificial and biological neural networks motivates the study of gradient-free methods. Considering the linear regression model with random design, we theoretically analyze in this work the biologically motivated (weight-perturbed) forward gradient scheme that is based on random linear combination of the gradient. If <math><mi>d</mi></math> denotes the number of parameters and <math><mi>k</mi></math> the number of samples, we prove that the mean squared error of this method converges for <math><mrow><mi>k</mi><mo>≳</mo><msup><mrow><mi>d</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>log</mo><mrow><mo>(</mo><mi>d</mi><mo>)</mo></mrow></mrow></math> with rate <math><mrow><msup><mrow><mi>d</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>log</mo><mrow><mo>(</mo><mi>d</mi><mo>)</mo></mrow><mo>/</mo><mi>k</mi></mrow></math>. Compared to the dimension dependence <math><mi>d</mi></math> for stochastic gradient descent, an additional factor <math><mrow><mi>d</mi><mo>log</mo><mrow><mo>(</mo><mi>d</mi><mo>)</mo></mrow></mrow></math> occurs.</div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":"233 ","pages":"Article 106174"},"PeriodicalIF":0.9,"publicationDate":"2024-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0378375824000314/pdfft?md5=fc5918288c472da3301b467d899078ad&pid=1-s2.0-S0378375824000314-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140536571","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}

引用次数: 0

Toward improved inference for Krippendorff’s Alpha agreement coefficient 改进克里彭多夫阿尔法一致系数的推断方法

IF 0.9 4区数学

Journal of Statistical Planning and Inference Pub Date : 2024-04-05 DOI: 10.1016/j.jspi.2024.106170

John Hughes

引用次数: 0