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題名 模糊樣本資料之新統計檢定程序與決策
其他題名 New Statistical Testing Methods for Fuzzy Data and Fuzzy Decision
作者 吳柏林
貢獻者 國立政治大學應用數學學系
行政院國家科學委員會
關鍵詞 模糊期望值檢定;模糊變異數檢定;模糊χ 2 檢定;模糊決策模式;軟計算方法;區間時間數列;隨機區間;區間眾數;ARIMA 區間預測法;平均區間誤差平方和
Testing of fuzzy expected value and variance;fuzzy χ 2 testing;fuzzy decision processing;softcomputing;fuzzy nonparametric tests;fuzzy liner regression;interval time series;randominterval;ARIMA interval forecasting method
日期 2008
上傳時間 24-Oct-2012 16:14:35 (UTC+8)
摘要 要分析一組抽樣資料X 1 , X 2 , …,X n 的集中趨勢與分散程度，傳統統計經常用樣本平均數與變異數去檢定母體平均數與母體變異數。但是如果抽樣的資料是一群模糊(或區間)的形式，兩母體的平均數(也是模糊或區間形式)要如何比較大小呢？母體變異數又該如何去檢定呢?有一些文獻提出有關於模糊數比大小的問題,但似乎較欠缺在模糊資料上實證意義,甚至模糊隸屬度的探討也欠缺。本研究針對模糊資料特質研究,並與其他人的觀點作比較,最後想就這些方面討論區間的計算該如何訂定才比較符合統計上的意義及如何訂定區間或模糊數比大小的檢定問題。並將此結果應用在區間樣本分類問題上。本研究將提出模糊檢定與決策模式及其相關性質與證明，並探討區間統計與軟計算方法。希望經由這些性質的討論和模糊統計分析，將其應用於管理科學與市場調查分析上。期能將市場差異性與趨勢更精確地表達出來。本計畫目標針對市場調查領域中的模糊樣本或不明確資料進行模糊統計檢定與決策分析。對已提出的無母數參數或特徵檢定。研究動機源自很多實務問題，例如上市產品定價與市場區隔策略，環保補償金，社會問項共識，兩岸投資環境差異等市場研究。古典的統計檢定必須陳列明確的假設. 比方當我們想檢定兩母體平均數是否有差異時，事先(虛無)假設:兩個平均數相等。然而有時我們想要知道的只是兩平均值是否非常逼近, 此時傳統的檢定方法並不適用於這種包含不確定性的假設檢定。傳統的統計方法檢定都假定資料來自於某個分配，但若假設檢定包含著不確定性時，有關模糊數的假設檢定有其重要性。由此可知，模糊統計推論已逐漸受到重視，這是符合現在複雜的社會現象所自然發展的結果。針對模糊資料，本文嘗試以簡易的計算配合模糊理論，定義出模糊數及模糊區間的排序方法，並將此方法應用在檢定上。即針對傳統無母數檢定方法，在無法解決參數假設為模糊數或是模糊區間值的情形下，為改進此一缺點，本文提出模糊Kruskal-Wallis 檢定和Run test 檢定。由實証的例子顯示，本文提出的檢定方法能有效解決模糊樣本問題。再者，傳統的統計迴歸模式，假設觀察值的不確定性來自於隨機現象，但模糊迴歸則考慮不確定性來自於多重隸屬現象。因而以無母數統計方法，配合模糊迴歸理論，進而提出模糊無母數迴歸法，並應用實際的例子，以顯示其存在的實質意義。近年來，隨著科技的進步與工商業的發展，預測技術的創新與改進愈來愈受到重視，相對地，對於預測準確度的要求也愈來愈高。尤其在經濟建設、經營規畫、管理控制等問題上，預測更是決策過程中不可或缺的重要資訊。以證券市場為例，期指或選擇權收盤價這個數字的本身具有不確定性與模糊性，再加上影響此數值的因素眾多，如成交量、匯率等。因此，若僅考慮前一日的收盤價為其決定因素來建構模式以進行預測，不但會錯估未來市場走勢，且將造成不必要的損失。有鑑於此，本研究乃嘗試藉以區間運算推導，結合區間中心點及其長度，提出區間時間數列建構過程及模式理論架構。首先，藉由模擬方式設計出數組穩定及非穩定之區間時間數列，以本文所提供的預測方法：區間移動平均、區間加權移動平均、ARIMA 區間預測等方法，進行區間預測，再以平均區間預測誤差平方和，平均相對區間誤差和來作預測效果之比較。最後，以近十年來的財金(月)指標分析，將當期指標最高價與最低價視為變動區間，建立區間時間數列模式，並進行預測。在預測效率性的比較上，初步發現ARIMA 區間預測提供了較有彈性的預測結果。這將使得投資者在正確的資訊下，做出更客觀的判斷。對於財務金融的未來市場走勢將深具意義。
In tradition statistical testing hypothesis, we usually use sample mean and sample variance to test the population mean and population variance for a set of sample { X1,..., X n }. But if the sample exhibits the interval type, how to make an appropriated test for mean and variance is still a controversial problems. In this research, we start with a detailed investigation about soft computing for fuzzy data. We discuss such that it fits statistical meaning and testing problem for comparing intervals or discrete fuzzy numbers. Then we propose decision process on the testing hypothesis of mean and variance for fuzzy data.. In this research, the ordination technique, based on the fuzzy data, of fuzzy numbers and intervals will be defined by simple computations with fuzzy theories, and this technique will be applied to statistical testing. This project aims at developing a realistic fuzzy decision system and fuzzy statistical hypothesis testing for management sciences research. The motivation stems from the fact that in many practical problems such as price of a new merchandize, social agreement and difference in the educational topics property, pollution penalty, people』s tendency for public topics etc. During the survey, people are often encountered with uncertainty or imprecision problems. We will propose the procedure of fuzzy statistical testing for expected value, variance as well as fuzzy χ 2 testing and investigate their related properties. We will also work on empirical studies to illustrate the new techniques. We hope these pioneer methods will make the corresponding fuzzy statistical analysis more practical and efficient in the future study of management science and marketing research. Traditional nonparametric statistical hypothesis testing could not deal with the data from fuzzy numbers or intervals. To be successful for this, we provide fuzzy nonparametric tests in this research. The testing techniques mentioned by this research could solve the limitation of fuzzy data. Some empirical examples will be given to show for this. Furthermore, traditional statistical regression models assume that the uncertainty of the observed values is from random sampling. Nevertheless, fuzzy statistical regression models assume that the uncertainty of the observed data is from the phenomenon of multiple membership. Therefore we bring up fuzzy nonparametric regression model considering nonparametric statistical testing techniques. Point forecasting gives important information during decision-making processes, especially on economic developments, population policies, management planning or financial controls. Nevertheless, its drawbacks still include: (1) it is not efficient in the marketing application due to the inaccurate forecasting; (2) the model constructed only by the closing price may not illustrate the whole process of daily or monthly trend. The causes of this regretful situation are that the business marketing is full of uncertainty and human being』s manipulation. In this paper, we proposes interval forecasting approaches, such as the interval moving average, the weighted interval moving average, and ARIMA interval forecasting. We generate interval time series by simulation and apply the proposed forecasting approaches to carry out the interval forecasting. The forecast results are compared by the mean squared interval error and the mean relative interval error. Finally, we take the monthly trading prices of China Steel stock as a case study. In the comparison of forecasting performance, it is found that ARIMA interval forecasting provides more efficiency and flexibility than the traditional ones do.
關聯 基礎研究
學術補助
研究期間:9708~ 9807
研究經費:753仟元
資料類型 report
dc.contributor 國立政治大學應用數學學系en_US
dc.contributor 行政院國家科學委員會en_US
dc.creator (作者) 吳柏林zh_TW
dc.date (日期) 2008en_US
dc.date.accessioned 24-Oct-2012 16:14:35 (UTC+8)-
dc.date.available 24-Oct-2012 16:14:35 (UTC+8)-
dc.date.issued (上傳時間) 24-Oct-2012 16:14:35 (UTC+8)-
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/54074-
dc.description.abstract (摘要) 要分析一組抽樣資料X 1 , X 2 , …,X n 的集中趨勢與分散程度，傳統統計經常用樣本平均數與變異數去檢定母體平均數與母體變異數。但是如果抽樣的資料是一群模糊(或區間)的形式，兩母體的平均數(也是模糊或區間形式)要如何比較大小呢？母體變異數又該如何去檢定呢?有一些文獻提出有關於模糊數比大小的問題,但似乎較欠缺在模糊資料上實證意義,甚至模糊隸屬度的探討也欠缺。本研究針對模糊資料特質研究,並與其他人的觀點作比較,最後想就這些方面討論區間的計算該如何訂定才比較符合統計上的意義及如何訂定區間或模糊數比大小的檢定問題。並將此結果應用在區間樣本分類問題上。本研究將提出模糊檢定與決策模式及其相關性質與證明，並探討區間統計與軟計算方法。希望經由這些性質的討論和模糊統計分析，將其應用於管理科學與市場調查分析上。期能將市場差異性與趨勢更精確地表達出來。本計畫目標針對市場調查領域中的模糊樣本或不明確資料進行模糊統計檢定與決策分析。對已提出的無母數參數或特徵檢定。研究動機源自很多實務問題，例如上市產品定價與市場區隔策略，環保補償金，社會問項共識，兩岸投資環境差異等市場研究。古典的統計檢定必須陳列明確的假設. 比方當我們想檢定兩母體平均數是否有差異時，事先(虛無)假設:兩個平均數相等。然而有時我們想要知道的只是兩平均值是否非常逼近, 此時傳統的檢定方法並不適用於這種包含不確定性的假設檢定。傳統的統計方法檢定都假定資料來自於某個分配，但若假設檢定包含著不確定性時，有關模糊數的假設檢定有其重要性。由此可知，模糊統計推論已逐漸受到重視，這是符合現在複雜的社會現象所自然發展的結果。針對模糊資料，本文嘗試以簡易的計算配合模糊理論，定義出模糊數及模糊區間的排序方法，並將此方法應用在檢定上。即針對傳統無母數檢定方法，在無法解決參數假設為模糊數或是模糊區間值的情形下，為改進此一缺點，本文提出模糊Kruskal-Wallis 檢定和Run test 檢定。由實証的例子顯示，本文提出的檢定方法能有效解決模糊樣本問題。再者，傳統的統計迴歸模式，假設觀察值的不確定性來自於隨機現象，但模糊迴歸則考慮不確定性來自於多重隸屬現象。因而以無母數統計方法，配合模糊迴歸理論，進而提出模糊無母數迴歸法，並應用實際的例子，以顯示其存在的實質意義。近年來，隨著科技的進步與工商業的發展，預測技術的創新與改進愈來愈受到重視，相對地，對於預測準確度的要求也愈來愈高。尤其在經濟建設、經營規畫、管理控制等問題上，預測更是決策過程中不可或缺的重要資訊。以證券市場為例，期指或選擇權收盤價這個數字的本身具有不確定性與模糊性，再加上影響此數值的因素眾多，如成交量、匯率等。因此，若僅考慮前一日的收盤價為其決定因素來建構模式以進行預測，不但會錯估未來市場走勢，且將造成不必要的損失。有鑑於此，本研究乃嘗試藉以區間運算推導，結合區間中心點及其長度，提出區間時間數列建構過程及模式理論架構。首先，藉由模擬方式設計出數組穩定及非穩定之區間時間數列，以本文所提供的預測方法：區間移動平均、區間加權移動平均、ARIMA 區間預測等方法，進行區間預測，再以平均區間預測誤差平方和，平均相對區間誤差和來作預測效果之比較。最後，以近十年來的財金(月)指標分析，將當期指標最高價與最低價視為變動區間，建立區間時間數列模式，並進行預測。在預測效率性的比較上，初步發現ARIMA 區間預測提供了較有彈性的預測結果。這將使得投資者在正確的資訊下，做出更客觀的判斷。對於財務金融的未來市場走勢將深具意義。en_US
dc.description.abstract (摘要) In tradition statistical testing hypothesis, we usually use sample mean and sample variance to test the population mean and population variance for a set of sample { X1,..., X n }. But if the sample exhibits the interval type, how to make an appropriated test for mean and variance is still a controversial problems. In this research, we start with a detailed investigation about soft computing for fuzzy data. We discuss such that it fits statistical meaning and testing problem for comparing intervals or discrete fuzzy numbers. Then we propose decision process on the testing hypothesis of mean and variance for fuzzy data.. In this research, the ordination technique, based on the fuzzy data, of fuzzy numbers and intervals will be defined by simple computations with fuzzy theories, and this technique will be applied to statistical testing. This project aims at developing a realistic fuzzy decision system and fuzzy statistical hypothesis testing for management sciences research. The motivation stems from the fact that in many practical problems such as price of a new merchandize, social agreement and difference in the educational topics property, pollution penalty, people』s tendency for public topics etc. During the survey, people are often encountered with uncertainty or imprecision problems. We will propose the procedure of fuzzy statistical testing for expected value, variance as well as fuzzy χ 2 testing and investigate their related properties. We will also work on empirical studies to illustrate the new techniques. We hope these pioneer methods will make the corresponding fuzzy statistical analysis more practical and efficient in the future study of management science and marketing research. Traditional nonparametric statistical hypothesis testing could not deal with the data from fuzzy numbers or intervals. To be successful for this, we provide fuzzy nonparametric tests in this research. The testing techniques mentioned by this research could solve the limitation of fuzzy data. Some empirical examples will be given to show for this. Furthermore, traditional statistical regression models assume that the uncertainty of the observed values is from random sampling. Nevertheless, fuzzy statistical regression models assume that the uncertainty of the observed data is from the phenomenon of multiple membership. Therefore we bring up fuzzy nonparametric regression model considering nonparametric statistical testing techniques. Point forecasting gives important information during decision-making processes, especially on economic developments, population policies, management planning or financial controls. Nevertheless, its drawbacks still include: (1) it is not efficient in the marketing application due to the inaccurate forecasting; (2) the model constructed only by the closing price may not illustrate the whole process of daily or monthly trend. The causes of this regretful situation are that the business marketing is full of uncertainty and human being』s manipulation. In this paper, we proposes interval forecasting approaches, such as the interval moving average, the weighted interval moving average, and ARIMA interval forecasting. We generate interval time series by simulation and apply the proposed forecasting approaches to carry out the interval forecasting. The forecast results are compared by the mean squared interval error and the mean relative interval error. Finally, we take the monthly trading prices of China Steel stock as a case study. In the comparison of forecasting performance, it is found that ARIMA interval forecasting provides more efficiency and flexibility than the traditional ones do.en_US
dc.language.iso en_US-
dc.relation (關聯) 基礎研究en_US
dc.relation (關聯) 學術補助en_US
dc.relation (關聯) 研究期間:9708~ 9807en_US
dc.relation (關聯) 研究經費:753仟元en_US
dc.subject (關鍵詞) 模糊期望值檢定;模糊變異數檢定;模糊χ 2 檢定;模糊決策模式;軟計算方法;區間時間數列;隨機區間;區間眾數;ARIMA 區間預測法;平均區間誤差平方和en_US
dc.subject (關鍵詞) Testing of fuzzy expected value and variance;fuzzy χ 2 testing;fuzzy decision processing;softcomputing;fuzzy nonparametric tests;fuzzy liner regression;interval time series;randominterval;ARIMA interval forecasting methoden_US
dc.title (題名) 模糊樣本資料之新統計檢定程序與決策zh_TW
dc.title.alternative (其他題名) New Statistical Testing Methods for Fuzzy Data and Fuzzy Decisionen_US
dc.type (資料類型) reporten