{
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  "Title": "Confidence Intervals Utilizing Uncertain Prior Information",
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  "Authors@R": "c(person(\"Paul\", \"Kabaila\", email = \"P.Kabaila@latrobe.edu.au\", \nrole = c(\"aut\", \"cre\")),\nperson(\"Rheanna\", \"Mainzer\", role = c(\"aut\")),\nperson(\"Ayesha\", \"Perera\", role = c(\"ctb\")))",
  "Author": "Paul Kabaila [aut, cre], Rheanna Mainzer [aut], Ayesha Perera\n[ctb]",
  "Maintainer": "Paul Kabaila <P.Kabaila@latrobe.edu.au>",
  "Description": "Computes a confidence interval for a specified linear\ncombination of the regression parameters in a linear regression\nmodel with iid normal errors with known variance when there is\nuncertain prior information that a distinct specified linear\ncombination of the regression parameters takes a given value.\nThis confidence interval, found by numerical nonlinear\nconstrained optimization, has the required minimum coverage and\nutilizes this uncertain prior information through desirable\nexpected length properties. This confidence interval has the\nfollowing three practical applications. Firstly, if the error\nvariance has been accurately estimated from previous data then\nit may be treated as being effectively known. Secondly, for\nsufficiently large (dimension of the response vector) minus\n(dimension of regression parameter vector), greater than or\nequal to 30 (say), if we replace the assumed known value of the\nerror variance by its usual estimator in the formula for the\nconfidence interval then the resulting interval has, to a very\ngood approximation, the same coverage probability and expected\nlength properties as when the error variance is known. Thirdly,\nsome more complicated models can be approximated by the linear\nregression model with error variance known when certain unknown\nparameters are replaced by estimates. This confidence interval\nis described in Mainzer, R. and Kabaila, P. (2019)\n<doi:10.32614/RJ-2019-026>, and is a member of the family of\nconfidence intervals proposed by Kabaila, P. and Giri, K.\n(2009) <doi:10.1016/j.jspi.2009.03.018>.",
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  "Date/Publication": "2024-06-19 02:43:33 UTC",
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  "_assets": [
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    "extra/citation.html",
    "extra/citation.json",
    "extra/citation.txt",
    "extra/ciuupi.html",
    "extra/contents.json",
    "manual.pdf"
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      "date": "2019-01-15"
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    "acX_to_rho",
    "bs_ciuupi",
    "bsspline",
    "ci_standard",
    "ciuupi_observed_value",
    "cpciuupi",
    "plot_b",
    "plot_cp",
    "plot_s",
    "plot_squared_sel",
    "selciuupi"
  ],
  "_datasets": [
    {
      "name": "bs.list.example",
      "title": "The list that specifies the CIUUPI for the example",
      "object": "bs.list.example",
      "class": [
        "list"
      ],
      "fields": [],
      "table": false,
      "tojson": true
    }
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  "_help": [
    {
      "page": "acX_to_rho",
      "title": "Computes the known correlation rho between \\widehat{theta} and \\widehat{tau} from the p-vectors a and c and the design matrix X",
      "topics": [
        "acX_to_rho"
      ]
    },
    {
      "page": "bs_ciuupi",
      "title": "Computes the the functions b and s that specify the CIUUPI for all possible values of sigma and the observed response vector",
      "topics": [
        "bs_ciuupi"
      ]
    },
    {
      "page": "bs.list.example",
      "title": "The list that specifies the CIUUPI for the example",
      "topics": [
        "bs.list.example"
      ]
    },
    {
      "page": "bsspline",
      "title": "Evaluate the functions b and s at 'x'",
      "topics": [
        "bsspline"
      ]
    },
    {
      "page": "ci_standard",
      "title": "For given observed response vector y, compute the standard 1 - alpha confidence interval",
      "topics": [
        "ci_standard"
      ]
    },
    {
      "page": "ciuupi_observed_value",
      "title": "For given observed response vector y, compute the confidence interval that utilizes the uncertain prior information (CIUUPI)",
      "topics": [
        "ciuupi_observed_value"
      ]
    },
    {
      "page": "cpciuupi",
      "title": "Compute the coverage probability of the CIUUPI",
      "topics": [
        "cpciuupi"
      ]
    },
    {
      "page": "plot_b",
      "title": "Plot the graph of the odd function b used in the specification of the CIUUPI",
      "topics": [
        "plot_b"
      ]
    },
    {
      "page": "plot_cp",
      "title": "Plot the graph of the coverage probability of the CIUUPI",
      "topics": [
        "plot_cp"
      ]
    },
    {
      "page": "plot_s",
      "title": "Plot the graph of the even function s used in the specification of the CIUUPI",
      "topics": [
        "plot_s"
      ]
    },
    {
      "page": "plot_squared_sel",
      "title": "Plot the graph of the squared scaled expected length of the CIUUPI",
      "topics": [
        "plot_squared_sel"
      ]
    },
    {
      "page": "selciuupi",
      "title": "Compute the scaled expected length of the CIUUPI",
      "topics": [
        "selciuupi"
      ]
    }
  ],
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    "nloptr",
    "pracma",
    "statmod"
  ],
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      "title": "Description of ciuupi",
      "author": "Paul Kabaila, Rheanna Mainzer and Ayesha Perera",
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      "headings": [
        "Description of the confidence interval that utilizes uncertain prior information (CIUUPI)",
        "Functions in this package",
        "acX_to_rho",
        "Compute the functions $b$ and $s$ that specify the CIUUPI",
        "bs_ciuupi",
        "Plot the graphs of the functions $b$ and $s$",
        "plot_b and plot_s",
        "The performance of the CIUUPI",
        "plot_cp and plot_squared_sel",
        "Computation of the observed value of the CIUUPI",
        "ciuupi_observed_value and ci_standard",
        "References"
      ],
      "created": "2024-06-19 02:43:33",
      "modified": "2024-06-19 02:43:33",
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    }
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