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| Title: | 混合變數之互信息的假設檢定
Hypotheses testing of the mutual information of two mixed-type variables |
| Authors: | 王俞惠
Wang, Yu-Hui |
| Contributors: | 薛慧敏
Hsueh, Huey-Ming
王俞惠
Wang, Yu-Hui |
| Keywords: | 互信息
相關性檢定
漸近原理
排列檢定
檢定力
型一錯誤率
Mutual information
Test of dependence
Asymptotic theory
Permutation test
Power
Type one error rate |
| Date: | 2022 |
| Issue Date: | 2022-10-05 09:01:50 (UTC+8) |
| Abstract: | 在大數據時代，很多實務資料同時涵蓋連續型與離散型變數（稱為混合型變數），在資料分析過程中常牽涉測量這些變數間的相關性。文獻上有許多方法以檢定連續型變數之間或離散型變數之間的獨立性，本研究則針對混合型變數之間相關性的檢定問題，我們將資訊理論中的互信息量延伸至此問題用以測量混合型變數間的相關性。Beknazaryan et al.(2018)定義混合型變數之互信息並且提出無母數估計方法，作者們並推導出該估計量的漸近常態性質。本研究延續該研究成果發展相關的檢定方法，包括常態漸近檢定和排列檢定。透過模擬實驗觀察到漸近檢定表現並不好，其型一誤差率遠低於顯著水準。我們進一步發現即便增加樣本數至3000時，該無母數估計量的抽樣分配與常態分配仍有相當歧異。相反地排列檢定的表現則過度激進，其型一誤差率無法有效控制在顯著水準下。為參考起見，模擬中也發現兩個檢定方法在特定對立假設下都有良好檢定力以偵測混合變數的相關性。本研究將所發展的統計檢定應用至一組羽球實證資料。本研究的結論是這兩個方法都有待改進。
In the generation of big data, many practical data including both continuous and discrete variables (also known as mixed variables), and an analytical procedure often involves measuring the dependence between mixed variables. In literatures, many methods are developed to measure and test the dependence among continuous variables or among discrete variables. In this study, we focus on the test of the dependence between mixed variables. We extend the mutual information criterion in information theory to describe dependence between mixed variables. In the study of Beknazaryan et al. (2018), the authors defined the mutual information of mixed variables and proposed a nonparametric estimation method which employed kernel estimation. Further, the authors showed the asymptotic normality of the estimator. In this study, we follow their research and develop two correspondent hypothesis tests: an asymptotic test and permutation test. Through simulation experiments, it is seen that the two testing procedures do not have satisfactory performance in controlling the type I error rate, the asymptotic test is too conservative and the permutation test is too liberal. Further, we find that even when the sample size is increased to 3000, the sampling distribution of the nonparametric estimator is still deviated from a normal distribution. However, we find that both tests have good power to detect two dependent mixed variables under certain alternative hypothetical scenarios in the simulation. The two tests are applied to a real badminton data set for demonstration. We conclude that both methods have room for improvement. |
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| Description: | 碩士
國立政治大學
統計學系
109354002 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0109354002 |
| Data Type: | thesis |
| DOI: | 10.6814/NCCU202201498 |
| Appears in Collections: | [統計學系] 學位論文
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