# Nonparametric statistics

**non-parametricnonparametricnon-parametric statisticsnonparametric testnon-parametric modelnonparametric methodsnon-parametric testnon-parametric methodsdistribution-freenon-parametric method**

Nonparametric statistics is the branch of statistics that is not based solely on parametrized families of probability distributions (common examples of parameters are the mean and variance).wikipedia

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### Ranking

**rankrankedrankings**

The use of non-parametric methods may be necessary when data have a ranking but no clear numerical interpretation, such as when assessing preferences.

Analysis of data obtained by ranking commonly requires non-parametric statistics.

### Descriptive statistics

**descriptivedescriptive statisticstatistics**

Nonparametric statistics includes both descriptive statistics and statistical inference.

This generally means that descriptive statistics, unlike inferential statistics, is not developed on the basis of probability theory, and are frequently nonparametric statistics.

### Statistical inference

**inferenceinferential statisticsinferences**

Nonparametric statistics includes both descriptive statistics and statistical inference.

Non-parametric: The assumptions made about the process generating the data are much less than in parametric statistics and may be minimal. For example, every continuous probability distribution has a median, which may be estimated using the sample median or the Hodges–Lehmann–Sen estimator, which has good properties when the data arise from simple random sampling.

### Ordinal data

**ordinalordinal variable**

In terms of levels of measurement, non-parametric methods result in ordinal data.

Nonparametric methods have been proposed as the most appropriate procedures for inferential statistics involving ordinal data, especially those developed for the analysis of ranked measurements.

### Kernel density estimation

**kernelkernel densitykernel density estimate**

Kernel density estimation provides better estimates of the density than histograms.

In statistics, kernel density estimation (KDE) is a non-parametric way to estimate the probability density function of a random variable.

### Power (statistics)

**statistical powerpowerpowerful**

The wider applicability and increased robustness of non-parametric tests comes at a cost: in cases where a parametric test would be appropriate, non-parametric tests have less power.

In addition, the concept of power is used to make comparisons between different statistical testing procedures: for example, between a parametric test and a nonparametric test of the same hypothesis.

### Parametric statistics

**parametricparametric testparametric inference**

Non-parametric models differ from parametric models in that the model structure is not specified a priori but is instead determined from data.

Since a parametric model relies on a fixed parameter set, it assumes more about a given population than non-parametric methods do.

### Data envelopment analysis

Data envelopment analysis provides efficiency coefficients similar to those obtained by multivariate analysis without any distributional assumption.

Data envelopment analysis (DEA) is a nonparametric method in operations research and economics for the estimation of production frontiers.

### K-nearest neighbors algorithm

**k-nearest neighbor algorithmk-nearest neighbork-nearest neighbors**

KNNs classify the unseen instance based on the K points in the training set which are nearest to it.

In pattern recognition, the k-nearest neighbors algorithm (k-NN) is a non-parametric method used for classification and regression.

### Kernel (statistics)

**kernelkernelskernel estimation**

Nonparametric regression and semiparametric regression methods have been developed based on kernels, splines, and wavelets.

In nonparametric statistics, a kernel is a weighting function used in non-parametric estimation techniques.

### Sign test

Early nonparametric statistics include the median (13th century or earlier, use in estimation by Edward Wright, 1599; see ) and the sign test by John Arbuthnot (1710) in analyzing the human sex ratio at birth (see ).

The sign test is a non-parametric test which makes very few assumptions about the nature of the distributions under test – this means that it has very general applicability but may lack the statistical power of the alternative tests.

### Nonparametric regression

**non-parametric regressionnonparametricnon-parametric**

Nonparametric regression and semiparametric regression methods have been developed based on kernels, splines, and wavelets.

Non-parametric statistics

### Jean D. Gibbons

**Gibbons, J.D.Gibbons, Jean DickinsonJean Dickinson Gibbons**

Gibbons, Jean Dickinson; Chakraborti, Subhabrata (2003). Nonparametric Statistical Inference, 4th Ed. CRC Press. ISBN: 0-8247-4052-1.

Jean Dickinson Gibbons (née Dickinson, born 1938) is an American statistician, an expert in nonparametric statistics and an author of books on statistics.

### John Arbuthnot

**ArbuthnotDr John ArbuthnotArbuthnot, John**

Early nonparametric statistics include the median (13th century or earlier, use in estimation by Edward Wright, 1599; see ) and the sign test by John Arbuthnot (1710) in analyzing the human sex ratio at birth (see ).

This is credited as "… the first use of significance tests …", the first example of reasoning about statistical significance and moral certainty, and "… perhaps the first published report of a nonparametric test …".

### Resampling (statistics)

**resamplingstatistical supportstrongly supported**

Resampling (statistics)

Permutation tests are a subset of non-parametric statistics.

### Human sex ratio

**Sex ratioGender ratiogender imbalance**

Early nonparametric statistics include the median (13th century or earlier, use in estimation by Edward Wright, 1599; see ) and the sign test by John Arbuthnot (1710) in analyzing the human sex ratio at birth (see ).

This is credited as "… the first use of significance tests …" the first example of reasoning about statistical significance and moral certainty, and "… perhaps the first published report of a nonparametric test …"; see details at.

### CDF-based nonparametric confidence interval

**Cumulative distribution function-based nonparametric confidence interval**

CDF-based nonparametric confidence interval

Non-parametric statistics

### Statistics

**statisticalstatistical analysisstatistician**

Nonparametric statistics is the branch of statistics that is not based solely on parametrized families of probability distributions (common examples of parameters are the mean and variance).

### Statistical parameter

**parametersparameterparametrization**

Nonparametric statistics is the branch of statistics that is not based solely on parametrized families of probability distributions (common examples of parameters are the mean and variance).

### Probability distribution

**distributioncontinuous probability distributiondiscrete probability distribution**

Nonparametric statistics is the branch of statistics that is not based solely on parametrized families of probability distributions (common examples of parameters are the mean and variance).

### Number

**number systemnumericalnumeric**

The use of non-parametric methods may be necessary when data have a ranking but no clear numerical interpretation, such as when assessing preferences.

### Preference

**preferencespenchantpreferential**

The use of non-parametric methods may be necessary when data have a ranking but no clear numerical interpretation, such as when assessing preferences.

### Level of measurement

**quantitativescaleinterval scale**

In terms of levels of measurement, non-parametric methods result in ordinal data.

### Robust statistics

**robustbreakdown pointrobustness**

The wider applicability and increased robustness of non-parametric tests comes at a cost: in cases where a parametric test would be appropriate, non-parametric tests have less power. Also, due to the reliance on fewer assumptions, non-parametric methods are more robust.

### Histogram

**histogramsbin sizebin**

A histogram is a simple nonparametric estimate of a probability distribution.