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題名 無母數密度函數之信賴帶建構及適合度檢定
Confidence Bands of Nonparametric Probability Density Functions and Goodness-of-Fit Tests
作者 蕭名妍
Hsiao, Ming-Yan
貢獻者 黃子銘
Huang, Tzee-Ming
蕭名妍
Hsiao, Ming-Yan
關鍵詞 無母數
密度函數估計
信賴帶
適合度檢定
Nonparametric
Density estimation
Confidence bands
Goodness-of-fit test
日期 2024
上傳時間 1-Jul-2024 13:27:30 (UTC+8)
摘要 本文考慮了二種構建機率密度函數信賴帶的方法。一種是基於分段估計，另一種則是基於核估計式。這篇論文提出針對第二種方法的修改版本，並比較這些信賴帶的覆蓋率。此外，分別基於修改後的信賴帶和聯合機率的信賴區間構建適合度檢定，並根據模擬實驗檢驗型一誤差和檢定力。結果顯示，基於信賴區間構建的檢定相對於基於信賴帶構建的檢定，具有較高的檢定力。
In this thesis, two approaches for constructing the confidence bands of probability density functions are considered. One is based on interpolation density estimators, and the other is based on kernel estimators. In this thesis, a modified version of the second approach is proposed. The coverage rates of those confidence bands are compared. In addition, goodness-of-fit tests are constructed based on the modified confidence bands and the confidence intervals of joint probabilities, respectively. Type I error probability and the power of those tests are examined based on simulation experiments. The results show that the test constructed based on confidence intervals has higher power than the ones based on confidence bands.
參考文獻 [1] D’Agostino, R. and Stephens, M. Goodness of Fit Techniques. Marcel Dekker, New York, 1986. [2] Hall, P., and Titterington, D. M. On confidence bands in nonparametric density estimation and regression. Journal of Multivariate Analysis, 27(1):228-254, 1988. [3] Hall, P., and Horowitz, J. A simple bootstrap method for constructing nonparametric confidence bands for functions. The Annals of Statistics, 1892-1921, 2013. [4] Rosenblatt, M. Remarks on Some Nonparametric Estimates of a Density Function. The Annals of Mathematical Statistics, 27(3):832-837, 1956. [5] Parzen, E. On estimation of a probability density function and mode. The Annals of Mathematical Statistics, 33(3):1065-1076, 1962. [6] Sha, M., and Xie, Y. The study of different types of kernel density estimators. 2nd International Conference on Electronics, Network and Computer Engineering (ICENCE 2016), Atlantis Press, 336-340, 2016. [7] Silverman, B. Density Estimation for Statistics and Data Analysis. New York: Chapman and Hall/CRC, 1986. [8] Bowman, A. W. An Alternative Method of Cross-validation for the Smoothing of Density Estimates. Biometrika, 71:353-360, 1984. [9] Rudemo, M. Empirical Choice of Histograms and Kernel Estimators. Scandinavian Journal of Statistics, 9:65-78, 1982. [10] Scott, D. W., and Terrell, G. R. Biased and unbiased cross-validation in density estimation. Journal of the american Statistical association, 82(400):1131-1146, 1987. [11] Scott, D. W. On optimal and data-based histograms. Biometrika, 66(3):605-610, 1979. [12] Sison, C. P., and Glaz, J. Simultaneous confidence intervals and sample size determination for multinomial proportions. Journal of the American Statistical Association, 90(429):366-369, 1995. [13] Levin, B. A representation for multinomial cumulative distribution functions. The Annals of Statistics, 1123-1126, 1981. [14] May, W. L., and Johnson, W. D. Constructing two-sided simultaneous confidence intervals for multinomial proportions for small counts in a large number of cells. Journal of statistical software, 5:1-24, 2000. [15] De Boor, C. On calculating with B-splines. Journal of Approximation theory, 6(1):50-62, 1972. [16] Kolmogorov, A. N. Sulla determinazione empirica di una legge di distribuzione. Giornale dell’Istituto Italiano degli Attuari. Journal of Approximation theory, 4(1):83-91, 1933. [17] Smirnov, N. Table for estimating the goodness of fit of empirical distributions. The Annals of Mathematical Statistics, 19(2):279-281, 1948.
描述 碩士
國立政治大學
統計學系
111354003
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0111354003
資料類型 thesis
dc.contributor.advisor 黃子銘zh_TW
dc.contributor.advisor Huang, Tzee-Mingen_US
dc.contributor.author (Authors) 蕭名妍zh_TW
dc.contributor.author (Authors) Hsiao, Ming-Yanen_US
dc.creator (作者) 蕭名妍zh_TW
dc.creator (作者) Hsiao, Ming-Yanen_US
dc.date (日期) 2024en_US
dc.date.accessioned 1-Jul-2024 13:27:30 (UTC+8)-
dc.date.available 1-Jul-2024 13:27:30 (UTC+8)-
dc.date.issued (上傳時間) 1-Jul-2024 13:27:30 (UTC+8)-
dc.identifier (Other Identifiers) G0111354003en_US
dc.identifier.uri (URI) https://nccur.lib.nccu.edu.tw/handle/140.119/152129-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 統計學系zh_TW
dc.description (描述) 111354003zh_TW
dc.description.abstract (摘要) 本文考慮了二種構建機率密度函數信賴帶的方法。一種是基於分段估計，另一種則是基於核估計式。這篇論文提出針對第二種方法的修改版本，並比較這些信賴帶的覆蓋率。此外，分別基於修改後的信賴帶和聯合機率的信賴區間構建適合度檢定，並根據模擬實驗檢驗型一誤差和檢定力。結果顯示，基於信賴區間構建的檢定相對於基於信賴帶構建的檢定，具有較高的檢定力。zh_TW
dc.description.abstract (摘要) In this thesis, two approaches for constructing the confidence bands of probability density functions are considered. One is based on interpolation density estimators, and the other is based on kernel estimators. In this thesis, a modified version of the second approach is proposed. The coverage rates of those confidence bands are compared. In addition, goodness-of-fit tests are constructed based on the modified confidence bands and the confidence intervals of joint probabilities, respectively. Type I error probability and the power of those tests are examined based on simulation experiments. The results show that the test constructed based on confidence intervals has higher power than the ones based on confidence bands.en_US
dc.description.tableofcontents 1 緒論 8 2 文獻回顧及背景介紹 9 2.1 基於分段估計的信賴帶 9 2.2 基於核估計的信賴帶 10 2.2.1 核密度函數估計 10 2.2.2 信賴帶建構 11 2.3 多項分布之信賴區間建構 12 2.4 Spline 函數 13 2.5 科摩哥洛夫 - 史密諾夫檢定（K-S 檢定） 14 3 研究方法 16 3.1 信賴帶建構方式與評估 16 3.2 適合度檢定 21 3.2.1 基於信賴帶的檢定 21 3.2.2 基於信賴區間 21 4 模擬實驗 23 4.1 信賴帶 23 4.2 適合度檢定 24 5 結論 30 參考文獻 31zh_TW
dc.format.extent 3792447 bytes-
dc.format.mimetype application/pdf-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0111354003en_US
dc.subject (關鍵詞) 無母數zh_TW
dc.subject (關鍵詞) 密度函數估計zh_TW
dc.subject (關鍵詞) 信賴帶zh_TW
dc.subject (關鍵詞) 適合度檢定zh_TW
dc.subject (關鍵詞) Nonparametricen_US
dc.subject (關鍵詞) Density estimationen_US
dc.subject (關鍵詞) Confidence bandsen_US
dc.subject (關鍵詞) Goodness-of-fit testen_US
dc.title (題名) 無母數密度函數之信賴帶建構及適合度檢定zh_TW
dc.title (題名) Confidence Bands of Nonparametric Probability Density Functions and Goodness-of-Fit Testsen_US
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) [1] D’Agostino, R. and Stephens, M. Goodness of Fit Techniques. Marcel Dekker, New York, 1986. [2] Hall, P., and Titterington, D. M. On confidence bands in nonparametric density estimation and regression. Journal of Multivariate Analysis, 27(1):228-254, 1988. [3] Hall, P., and Horowitz, J. A simple bootstrap method for constructing nonparametric confidence bands for functions. The Annals of Statistics, 1892-1921, 2013. [4] Rosenblatt, M. Remarks on Some Nonparametric Estimates of a Density Function. The Annals of Mathematical Statistics, 27(3):832-837, 1956. [5] Parzen, E. On estimation of a probability density function and mode. The Annals of Mathematical Statistics, 33(3):1065-1076, 1962. [6] Sha, M., and Xie, Y. The study of different types of kernel density estimators. 2nd International Conference on Electronics, Network and Computer Engineering (ICENCE 2016), Atlantis Press, 336-340, 2016. [7] Silverman, B. Density Estimation for Statistics and Data Analysis. New York: Chapman and Hall/CRC, 1986. [8] Bowman, A. W. An Alternative Method of Cross-validation for the Smoothing of Density Estimates. Biometrika, 71:353-360, 1984. [9] Rudemo, M. Empirical Choice of Histograms and Kernel Estimators. Scandinavian Journal of Statistics, 9:65-78, 1982. [10] Scott, D. W., and Terrell, G. R. Biased and unbiased cross-validation in density estimation. Journal of the american Statistical association, 82(400):1131-1146, 1987. [11] Scott, D. W. On optimal and data-based histograms. Biometrika, 66(3):605-610, 1979. [12] Sison, C. P., and Glaz, J. Simultaneous confidence intervals and sample size determination for multinomial proportions. Journal of the American Statistical Association, 90(429):366-369, 1995. [13] Levin, B. A representation for multinomial cumulative distribution functions. The Annals of Statistics, 1123-1126, 1981. [14] May, W. L., and Johnson, W. D. Constructing two-sided simultaneous confidence intervals for multinomial proportions for small counts in a large number of cells. Journal of statistical software, 5:1-24, 2000. [15] De Boor, C. On calculating with B-splines. Journal of Approximation theory, 6(1):50-62, 1972. [16] Kolmogorov, A. N. Sulla determinazione empirica di una legge di distribuzione. Giornale dell’Istituto Italiano degli Attuari. Journal of Approximation theory, 4(1):83-91, 1933. [17] Smirnov, N. Table for estimating the goodness of fit of empirical distributions. The Annals of Mathematical Statistics, 19(2):279-281, 1948.zh_TW