nonparametric statistic, 無母數統計,不需要模型假設的統計

在實際上應用，機率或統計最為人詬病的，一直是模型假設的問題。通常許多結果被批評，都是因為假設機率分配為常態分配，或是假設模型是線性模型。

那有沒有什麼方法可以拿掉這些假設呢??  有的，這就是無母數統計學。

In practicality, wrong assuming our model is the main critics for statistics. Wrong assuming model is linear or normal distribution causes  lots of disasters in Finance and other areas.

Is there a way to overcome the drawbacks of statistics? Yes, that is nonparametric statistics !!

"粗略的正確好過精准的錯誤"

-- 凱因斯

 "It is better to be roughly right than precisely wrong"

-- john maynard keynes

無母數統計，顧名思義，是一種不需要母體假設的統計。好處是可以忠實呈現資料的訊息，不用加太多人為的假設在資料上。壞處是無法提供一個能解釋現象的模型，而且需要比傳統統計方法更多的樣本，才能達到一樣的精確程度。

無母數統計，背後的直覺，可以想像成直方圖。直方圖，可以告訴我們模型大略的情況和形狀，但是沒有解釋性，然後也比較大略。現代無母數統計，就是循著這路思維去發展出來的技術，已經可以證明如果資料夠多，那可以離真實模型無限靠近。

Nonparametric statistics, follow by the name, is another approach in statistics without assuming particular distribution or model, so it does not need any parameters. The advantages are avoiding the wrong assumptions at first and presenting the information in data correctly. The drawbacks are lacking of interpretations and can't do further inference.

The tuition behind is bar chart. We can use bar chart to understand our data at first, but need more information to do precise analysis. The good news is that we can have consistent estimators in modern nonparametric methods. It can guarantee the results we got will be closed to true when sample size going to infinite. 

通常無母數統計，都是當作探查資料型態的一開始手段，有賴於這種方法可以涵蓋各種傳統模型，提供最廣義的結果，所以在沒有任何明確的模型時，當作初步的模型是最適切的。在某些複雜領域，可能真實的模型太過複雜，無法明確地描繪出來時，無母數統計就是很好的一種解決辦法。

In general, nonparametric statistics is using for exploratory data analysis. We can give a roughly initial model and look deeply before having some thoughts about data. In some areas, true models may be too complicate to formulate clearly. The models offered by nonparametric statistics may be appropriate. 

最後，無母數模型，還是有一些科學上的基本假設。像是我們必須去假設真實的模型的跳動程度，像是真實模型是幾次可微分。因為如果真實模型是像魏爾斯特拉曲線(下圖)，這種處處連續，但是處處不可微分的奇怪模型，那也沒有人能用統計估得出來了......

Finally, there are still some assumptions in nonparametric statistics. We need to assume the smoothness of true model. If true model is too strange, like Weierstrass function. We can do nothing  about it......

https://en.wikipedia.org/wiki/Weierstrass_function