# Nonparametric Method

A mathematical approach for statistical inference that does not consider the underlying assumptions on the shape of the probability distribution of the observation under study

## What is a Nonparametric Method?

A nonparametric method is a mathematical approach for statistical inferences that do not consider the underlying assumptions on the shape of the probability distribution of the observation under study. It estimates relevant statistical quantities or offers a general method for testing and validating covariate data, under fewer conditions than the parametric method. The incurred measurement of covariate data is a common problem in statistical data analysis due to the use of imperfect surrogate covariates, errors in variables, or the problem of missing data.

### Summary

• A nonparametric method is a mathematical inference method that does not consider the underlying assumptions on the shape of the probability distribution of the population.
• The nonparametric method helps in the modeling of appropriate statistical methods as a model building tool in financial time series and econometrics.
• While the nonparametric method works under a few assumptions, it is considered less potent than the parametric approach.

### Conditions for the Nonparametric Method

The nonparametric method does not require the population under study to meet particular assumptions or specific parameters to characterize the observations, as is the case with parametric methods. To illustrate, conventional parametric methods, such as t-test and ANOVA, provide valid and reliable results only if the population under study satisfies certain assumptions.

A statistical method qualifies to be nonparametric if it meets the following assumption. First, the method is used with quantitative data when no assumption is made about the population. Second, the technique uses qualitative data in a rather informal way; therefore, the nonparametric method is a diagnostic tool for a model building where it tests, checks, estimates, and validates data.

Different types of data use either parametric or nonparametric methods. Whereas parametric data generally requires interval or ratio data, the nonparametric approach is concerned with nominal or ordinal data. Nominal data represents variables whose categories don’t demonstrate natural order or ranking order, and the order is non-essential. It is closely related to the ratio data, which possesses all the properties of an interval data, such as growth rate or a market segment.

On the other hand, interval data is one where there is a ranking order, and the difference between the two values is meaningful, such as market price. In ordinal data, the difference between values is not essential, but the ranking order is important – such as socio-economic status.

### Nonparametric Approach in Modeling Financial Time Series

The nonparametric method helps in the modeling of appropriate statistical methods, as a unified approach for statistical inference in financial time series. For example, it plays a growing role in orthogonal line estimators, local polynomial and kernel smoothing and smoothing splines, among others.

Nonparametric smoothing is the commonly used density estimation in time series analysis. The primary reason behind the concept in financial series is because of its lack of technical challenges when estimating.

Another common application of nonparametric methods is in financial econometrics, where it is used to estimate returns, bond yields, volatility, return, and state price densities of stock prices. For example, the method is preferred when examining the overtime variation of stock prices and bonds.

### Limitations of Using the Nonparametric Method for Estimation

The density estimation technique is affected by the curse of dimensionality problem. Ordinarily, estimating density function using the nonparametric method appears to be simple. Take, for example, a case of density estimation using a histogram.

As the data dimension increases, so does the complexity of estimation, courtesy of the dimension problem. Even with complicated nonparametric methods for estimation, the effect is inevitable. Such a phenomenon presents two significant challenges when using the technique. First, the difficulty with which to interpret results in a multivariate setting is a common challenge when employing the method.

Put another way, as the number of dimensions increases, the estimates do not display the critical features. The second challenge relates to forecasting, given that the method does not allow extrapolation. Such problems present drawbacks when making forecasts or analyzing policies whose chief objective is to provide insight into what can happen under the unavailable data.

### Practical Example of Nonparametric Tests

Assuming that a researcher seeks to determine the customer preference between two similar but competing products, A and B. The researcher will ask individuals in a sampled population to state their preference between the two products.

The “+” sign can be used to denote a preference of product A, while the “–” sign can be used to indicate a choice of product B. The researcher can then use the qualitative data in its current form, alongside the nonparametric method, to statistically establish whether a difference in preference between products A and B exist among the population.

Similarly, the sign test can be applied to test hypotheses on the value of a population median. Some of the common nonparametric tests that may be used include spearman’s rank-order correlation, Chi-Square, and Wilcoxon Rank Sum Test.

A nonparametric method is hailed for its advantage of working under a few assumptions. However, the concept is generally regarded as less powerful than the parametric approach. Regarding such a fact, statisticians recommend parametric methods in cases where both methods are applicable.