What is Nonparametric Statistics?
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Nonparametric statistics refers to a statistical method in which the data are not assumed to come from prescribed models that are determined by a small number of parameters; examples of such models include the normal distribution model and the linear regression model. Nonparametric statistics sometimes uses data that is ordinal, meaning it does not rely on numbers, but rather on a ranking or order of sorts. For example, a survey conveying consumer preferences ranging from like to dislike would be considered ordinal data.Nonparametric statistics includes nonparametric descriptive statistics, statistical models, inference, and statistical tests. The model structure of nonparametric models is not specified but is instead determined from data. The term is not meant to imply that such models completely lack parameters, but rather that the number and nature of the parameters are flexible and not fixed in advance. A histogram is an example of a nonparametric estimate of a probability distribution.
Definition
Non-parametric statistics refer to statistical methods that do not assume data comes from a predetermined model defined by a small number of parameters, such as normal distribution models and linear regression models. Non-parametric statistics sometimes use ordinal data, meaning they rely on ranking or ordering rather than numerical values.
Origin
The origin of non-parametric statistics dates back to the early 20th century when statisticians began to recognize the limitations of traditional parametric methods, especially when dealing with data that did not fit specific distribution assumptions. With the advancement of computational power, non-parametric methods became more widely used in the mid-20th century.
Categories and Features
Non-parametric statistics include non-parametric descriptive statistics, statistical models, inference, and statistical tests. Their main feature is that the structure of the model is not specified in advance but is determined by the data. This flexibility makes non-parametric statistics particularly useful for handling data that do not meet traditional assumptions. A histogram is an example of a non-parametric probability distribution.
Case Studies
A typical case involves using non-parametric tests to analyze consumer preference survey data, which are often ordinal. Another example is using kernel density estimation to analyze the distribution of stock market returns, a method that does not assume returns follow a normal distribution.
Common Issues
Investors may encounter issues such as selecting the appropriate non-parametric method and interpreting the results when applying non-parametric statistics. A common misconception is that non-parametric statistics involve no parameters at all, whereas in reality, their parameters are flexible.
