{"id":32204363,"url":"https://github.com/alexisderumigny/boundedgeworth","last_synced_at":"2026-02-21T18:04:25.960Z","repository":{"id":59133212,"uuid":"513491165","full_name":"AlexisDerumigny/BoundEdgeworth","owner":"AlexisDerumigny","description":"Numerical bounds for Edgeworth expansions","archived":false,"fork":false,"pushed_at":"2025-12-02T13:18:21.000Z","size":136,"stargazers_count":1,"open_issues_count":2,"forks_count":0,"subscribers_count":1,"default_branch":"main","last_synced_at":"2026-01-29T07:36:32.854Z","etag":null,"topics":["edgeworth-expansion","probability-bounds","r-package","r-pkg"],"latest_commit_sha":null,"homepage":"","language":"R","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":null,"status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/AlexisDerumigny.png","metadata":{"files":{"readme":"README.Rmd","changelog":"NEWS.md","contributing":null,"funding":null,"license":null,"code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null,"governance":null,"roadmap":null,"authors":null,"dei":null,"publiccode":null,"codemeta":null,"zenodo":null,"notice":null,"maintainers":null,"copyright":null,"agents":null,"dco":null,"cla":null}},"created_at":"2022-07-13T11:17:57.000Z","updated_at":"2025-12-01T13:38:26.000Z","dependencies_parsed_at":"2025-09-08T16:33:57.916Z","dependency_job_id":null,"html_url":"https://github.com/AlexisDerumigny/BoundEdgeworth","commit_stats":null,"previous_names":[],"tags_count":2,"template":false,"template_full_name":null,"purl":"pkg:github/AlexisDerumigny/BoundEdgeworth","repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/AlexisDerumigny%2FBoundEdgeworth","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/AlexisDerumigny%2FBoundEdgeworth/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/AlexisDerumigny%2FBoundEdgeworth/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/AlexisDerumigny%2FBoundEdgeworth/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/AlexisDerumigny","download_url":"https://codeload.github.com/AlexisDerumigny/BoundEdgeworth/tar.gz/refs/heads/main","sbom_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/AlexisDerumigny%2FBoundEdgeworth/sbom","scorecard":null,"host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":286080680,"owners_count":29689644,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2026-02-21T15:51:39.154Z","status":"ssl_error","status_checked_at":"2026-02-21T15:49:03.425Z","response_time":107,"last_error":"SSL_connect returned=1 errno=0 peeraddr=140.82.121.5:443 state=error: unexpected eof while reading","robots_txt_status":"success","robots_txt_updated_at":"2025-07-24T06:49:26.215Z","robots_txt_url":"https://github.com/robots.txt","online":false,"can_crawl_api":true,"host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":["edgeworth-expansion","probability-bounds","r-package","r-pkg"],"created_at":"2025-10-22T04:54:21.813Z","updated_at":"2026-02-21T18:04:25.954Z","avatar_url":"https://github.com/AlexisDerumigny.png","language":"R","funding_links":[],"categories":[],"sub_categories":[],"readme":"---\noutput: github_document\nmath_method: \"default\"\n---\n\n\u003c!-- README.md is generated from README.Rmd. Please edit that file --\u003e\n\n```{r, include = FALSE}\nknitr::opts_chunk$set(\n  collapse = TRUE,\n  comment = \"#\u003e\",\n  fig.path = \"man/figures/README-\",\n  out.width = \"100%\"\n)\nrequire(\"BoundEdgeworth\")\n```\n\n# BoundEdgeworth\n\n\u003c!-- badges: start --\u003e\n\u003c!-- badges: end --\u003e\n\n\nThis package implements the computation of the bounds described in the article\nDerumigny, Girard, and Guyonvarch (2023), Explicit non-asymptotic bounds for the distance to the first-order Edgeworth expansion, Sankhya A. \n[doi:10.1007/s13171-023-00320-y](https://doi.org/10.1007/s13171-023-00320-y) \n[arxiv:2101.05780](https://arxiv.org/abs/2101.05780).\n\n\n## How to install\n\nYou can install the release version from the CRAN:\n```r\ninstall.packages(\"BoundEdgeworth\")\n```\n\nor the development version from [GitHub](https://github.com/AlexisDerumigny/BoundEdgeworth):\n\n```r\n# install.packages(\"remotes\")\nremotes::install_github(\"AlexisDerumigny/BoundEdgeworth\")\n```\n\n\n## Available bounds\n\nLet $X_1, \\dots, X_n$ be $n$ independent centered variables,\nand $S_n$ be their normalized sum, in the sense that\n$$S_n := \\sum_{i=1}^n X_i / \\text{sd} \\Big(\\sum_{i=1}^n X_i \\Big).$$\n\nThe goal of this package is to compute values of $\\delta_n \u003e 0$\nsuch that bounds of the form\n\n$$\n\\sup_{x \\in \\mathbb{R}}\n\\left| \\textrm{Prob}(S_n \\leq x) - \\Phi(x) \\right|\n\\leq \\delta_n,\n$$\n\nor of the form\n\n$$\n\\sup_{x \\in \\mathbb{R}}\n\\left| \\textrm{Prob}(S_n \\leq x) - \\Phi(x) - \\frac{\\lambda_{3,n}}{6\\sqrt{n}}(1-x^2) \\varphi(x) \\right|\n\\leq \\delta_n,\n$$\n\nare valid. Here $\\lambda_{3,n}$ denotes the average skewness of the\nvariables $X_1, \\dots, X_n$, $\\Phi$ denotes the cumulative distribution\nfunction (cdf) of the standard Gaussian distribution, and $\\varphi$\ndenotes its density.\n\nThe first type of bounds is returned by the function `Bound_BE()`\n(Berry-Esseen-type bound) and the second type (Edgeworth expansion-type\nbound) is returned by the function `Bound_EE1()`.\n\nSuch bounds are useful because they can help to control uniformly the\ndistance between the cdf of a normalized sum $\\textrm{Prob}(S_n \\leq x)$\nand its limit $\\Phi(x)$ (which is known by the central limit theorem).\nThe second type of bound is more precise, and give a control of the\nuniform distance between $\\textrm{Prob}(S_n \\leq x)$ and its first-order\nEdgeworth expansion, i.e. the limit from the central limit theorem\n$\\Phi(x)$ plus the next term\n$\\frac{\\lambda_{3,n}}{6\\sqrt{n}}(1-x^2) \\varphi(x)$.\n\nNote that these bounds depends on the assumptions made on\n$(X_1, \\dots, X_n)$ and especially on $K4$, the average kurtosis of the\nvariables $X_1, \\dots, X_n$. In all cases, they need to have finite\nfourth moment and to be independent. To get improved bounds, several\nadditional assumptions can be added:\n\n- the variables $X_1, \\dots, X_n$ are identically distributed,\n- the skewness (normalized third moment) of $X_1, \\dots, X_n$ are all $0$.\n- the distribution of $X_1, \\dots, X_n$ admits a continuous component.\n\n\n### Example\n\n```{r}\nsetup = list(continuity = FALSE, iid = TRUE, no_skewness = FALSE)\n\nBound_EE1(setup = setup, n = 1000, K4 = 9)\n```\nThis shows that\n\n$$\n\\sup_{x \\in \\mathbb{R}}\n\\left| \\textrm{Prob}(S_n \\leq x) - \\Phi(x) - \\frac{\\lambda_{3,n}}{6\\sqrt{n}}(1-x^2) \\varphi(x) \\right|\n\\leq `r Bound_EE1(setup = setup, n = 1000, K4 = 9)`,\n$$\n\nas soon as the variables $X_1, \\dots, X_{1000}$ are i.i.d. with a kurtosis smaller than $9$.\n\nAdding one more regularity assumption on the distribution of the $X_i$ helps to achieve a better bound:\n```{r}\nsetup = list(continuity = TRUE, iid = TRUE, no_skewness = FALSE)\n\nBound_EE1(setup = setup, n = 1000, K4 = 9, regularity = list(kappa = 0.99))\n```\n\nThis shows that\n\n$$\n\\sup_{x \\in \\mathbb{R}}\n\\left| \\textrm{Prob}(S_n \\leq x) - \\Phi(x) - \\frac{\\lambda_{3,n}}{6\\sqrt{n}}(1-x^2) \\varphi(x) \\right|\n\\leq `r Bound_EE1(setup = setup, n = 1000, K4 = 9, regularity = list(kappa = 0.99))`,\n$$\n\nin this case.\n\n\n## Applications to testing\n\nThis package also includes the function `Gauss_test_powerAnalysis()`,\nthat computes a uniformly valid power for the Gauss test that is valid\nover a large class of non-Gaussian distribution. This uniform validity\nis a consequence of the above-mentioned bounds.\n\n\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Falexisderumigny%2Fboundedgeworth","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Falexisderumigny%2Fboundedgeworth","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Falexisderumigny%2Fboundedgeworth/lists"}