(*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 4.0, MathReader 4.0, or any compatible application. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). 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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. ***********************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 268264, 6883]*) (*NotebookOutlinePosition[ 269005, 6909]*) (* CellTagsIndexPosition[ 268961, 6905]*) (*WindowFrame->Normal*) Notebook[{ Cell[TextData[{ "\n", StyleBox["BootStrapPackage: A Package of Bootstrap Algorithms for Mean, \ Simple Linear Regression Models and Correlation Coefficient.", FontWeight->"Bold", FontColor->RGBColor[0.886732, 0.144533, 0.109377]] }], "Text", FontSize->20, FontColor->RGBColor[0, 0, 0.500008]], Cell["\<\ Enis SINIKSARAN\ \>", "Text", FontSize->14, FontWeight->"Bold"], Cell["\<\ Assistant Professor of Statistics Istanbul University, Faculty of Economics, Department of Econometrics Beyazit-Istanbul, Turkey saran@istanbul.edu.tr\ \>", "Text"], Cell["\<\ Created : June, 2001 \ \>", "Text"], Cell[TextData[{ "\n Assume that we wish to make an inference about a population \ parameter \[Theta] and let ", Cell[BoxData[ \(TraditionalForm\`\[Theta]\&\[And]\)]], " be an estimator of \[Theta]. In some cases , however, an analytic \ estimate of the standard error of ", Cell[BoxData[ \(TraditionalForm\`\[Theta]\&\[And]\)]], " is too difficult or impossible to obtain. In some other cases, we would \ not be satisfied with the results of the asymptotic theory as to the \ accuracy of ", Cell[BoxData[ \(TraditionalForm\`\[Theta]\&\[And]\)]], ". Bootstrap which is a\ncomputer-based method for statistical inference \ would be a remedy to these circumstances. The algorithm of the bootstrap \ methods is as follows. Let us have a sample of size n, say ", StyleBox["\[Chi]", FontWeight->"Bold"], " . Resample with replacement from this data to get a bootstrap sample, say \ ", Cell[BoxData[ FormBox[ StyleBox[\(\(\[Chi]\^*\)\_i\), FontWeight->"Bold"], TraditionalForm]]], ", of the same size as our original sample ", StyleBox["\[Chi]. 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If we wish to know , for instance, the standard error of ", Cell[BoxData[ \(TraditionalForm\`\[Theta]\&\[And]\)]], " we can use these B replications. 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Two methods may give different results depending on the structure of your \ data. Which model is more reliable? The answer depends on how far we trust the assumptions of our model. \ \>", "Text"] }, Closed]], Cell[CellGroupData[{ Cell[TextData[StyleBox["Bootstrapping Pairs", FontColor->RGBColor[0.886732, 0.144533, 0.109377]]], "Subsection", FontWeight->"Bold", FontSlant->"Plain"], Cell[CellGroupData[{ Cell[BoxData[ \(\(?BootRegPair\)\)], "Input"], Cell[BoxData[ \("BootRegPair[data,B] finds a bootstrap fit for simple linear \ regression model.The method is based on the bootstrapping pairs.The data must \ have the form {{x1, y1 },{x2, y2}, ... ,{xk , yk}}. B which is the number of \ bootstrap samples must be an integer.BootRegPair[list,B] returns a table \ which shows summary statistics for model parameters beta0 and beta1.It also \ gives histograms of B bootstrap replications of the estimates of the model \ parameters. Dashing lines indicate the estimates of the beta0 and beta1 for \ the original data"\)], "Print"] }, Open ]], Cell[TextData[{ "\n", StyleBox["150 Replications", FontSize->16] }], "Text", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], Cell[CellGroupData[{ Cell[BoxData[ \(BootRegPair[data, 150]\)], "Input"], Cell[BoxData[ InterpretationBox[\("*"\[InvisibleSpace]"*"\[InvisibleSpace]"Bootstrap \ Results for Paired Regression:"\[InvisibleSpace]\(150\ "Replications"\)\ \[InvisibleSpace]"*"\[InvisibleSpace]"*"\), SequenceForm[ "*", "*", "Bootstrap Results for Paired Regression:", Times[ 150, "Replications"], "*", "*"], Editable->False]], "Print"], Cell[BoxData[ \("Summary Statistics"\)], "Print"], Cell[BoxData[ TagBox[GridBox[{ {"\<\"\"\>", "\<\"observed\"\>", "\<\"bootstrap\"\>", \ "\<\"bias\"\>", "\<\"seboot\"\>"}, {"\<\"beta0\"\>", "35.45827244740526`", "35.43732346641022`", \(-0.020948980995036948`\), "0.5554162735960136`"}, {"\<\"beta1\"\>", "0.32160822467340966`", 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