非參數核迴歸於宗教捐獻研究之應用

Abstract

以往的參數估計方式由於對母體和資料的假設較多，在估計時經常必須 忽略資料違反假設的事實。非參數方法不需要給定和參數估計一樣多的假設，且可以對樣本資料提供更好的配適。而在宗教支出研究方面，非參數方法的應用研究相對不足。因此本文引進了非參數核迴歸的方法，估計台灣2013 年至2014 年的宗教捐獻資料，並比較了多元線性迴歸、Tobit 迴歸及非參數核迴歸的結果，檢視三個模型的配適度、殘差及變數顯著性後，可以看出非參數核迴歸模型得到了更小的殘差及更準確的模型，並且它係數的顯著性和另外兩種估計方式有著極大的不同。

The parametric estimation method used to make several assumptions on the population and data. In real case, however, researchers often have to ignore these violations. In non-parametric methods, researchers don’t have to make so many assumptions as they do in parametric estimation. In addition, using non-parametric methods, researchers can get a better fitted model for the data. The application of non-parametric methods in religious giving studies is quite rare, therefore in this study, we introduced the non-parametric kernel regression method to estimate the 2013~2014 religious giving amount of Taiwan. We compared the results of multiple linear regression, Tobit regression and non-parametric kernel regression and found that the kernel regression model shows the best fitting and the smallest RSE. Also, the significance of each coefficients in kernel regression is quite different from that in multiple regression and Tobit regression.