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    政大機構典藏 > 商學院 > 統計學系 > 學位論文 >  Item 140.119/152129


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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: 2024-07-01 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
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    [10] Scott, D. W., and Terrell, G. R. Biased and unbiased cross-validation in density
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    [11] Scott, D. W. On optimal and data-based histograms. Biometrika, 66(3):605-610,
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    [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,
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    [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
    顯示於類別:[統計學系] 學位論文

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