# Category: Nonparametric statistics

Cohen's kappa
Cohen's kappa coefficient (κ, lowercase Greek kappa) is a statistic that is used to measure inter-rater reliability (and also intra-rater reliability) for qualitative (categorical) items. It is genera
Variance function
In statistics, the variance function is a smooth function which depicts the variance of a random quantity as a function of its mean. The variance function is a measure of heteroscedasticity and plays
Concordant pair
In statistics, a concordant pair is a pair of observations, each on two variables, (X1,Y1) and (X2,Y2), having the property that where "sgn" refers to whether a number is positive, zero, or negative (
Mann–Whitney U test
In statistics, the Mann–Whitney U test (also called the Mann–Whitney–Wilcoxon (MWW/MWU), Wilcoxon rank-sum test, or Wilcoxon–Mann–Whitney test) is a nonparametric test of the null hypothesis that, for
Mean integrated squared error
In statistics, the mean integrated squared error (MISE) is used in density estimation. The MISE of an estimate of an unknown probability density is given by where ƒ is the unknown density, ƒn is its e
Wilcoxon signed-rank test
The Wilcoxon signed-rank test is a non-parametric statistical hypothesis test used either to test the location of a population based on a sample of data, or to compare the locations of two populations
Price-Jones curve
A Price-Jones curve is a graph showing the distribution of diameters of red blood cells. Higher diameter may be seen in pernicious anaemia, while lower diameter may be seen after haemorrhage.
Siegel–Tukey test
In statistics, the Siegel–Tukey test, named after Sidney Siegel and John Tukey, is a non-parametric test which may be applied to data measured at least on an ordinal scale. It tests for differences in
Sign test
The sign test is a statistical method to test for consistent differences between pairs of observations, such as the weight of subjects before and after treatment. Given pairs of observations (such as
Van der Waerden test
Named after the Dutch mathematician Bartel Leendert van der Waerden, the Van der Waerden test is a statistical test that k population distribution functions are equal. The Van der Waerden test convert
Variable kernel density estimation
In statistics, adaptive or "variable-bandwidth" kernel density estimation is a form of kernel density estimation in which the size of the kernels used in the estimate are varieddepending upon either t
Ranking
A ranking is a relationship between a set of items such that, for any two items, the first is either "ranked higher than", "ranked lower than" or "ranked equal to" the second.In mathematics, this is k
Cramér–von Mises criterion
In statistics the Cramér–von Mises criterion is a criterion used for judging the goodness of fit of a cumulative distribution function compared to a given empirical distribution function , or for comp
Variational series
In statistics, a variational series is a non-decreasing sequence composed from an initial series of independent and identically distributed random variables . The members of the variational series for
Hoeffding's independence test
In statistics, Hoeffding's test of independence, named after Wassily Hoeffding, is a test based on the population measure of deviation from independence where is the joint distribution function of two
CDF-based nonparametric confidence interval
In statistics, cumulative distribution function (CDF)-based nonparametric confidence intervals are a general class of confidence intervals around statistical functionals of a distribution. To calculat
Resampling (statistics)
In statistics, resampling is the creation of new samples based on one observed sample.Resampling methods are: 1. * Permutation tests (also re-randomization tests) 2. * Bootstrapping 3. * Cross vali
Anderson–Darling test
The Anderson–Darling test is a statistical test of whether a given sample of data is drawn from a given probability distribution. In its basic form, the test assumes that there are no parameters to be
ANOVA on ranks
In statistics, one purpose for the analysis of variance (ANOVA) is to analyze differences in means between groups. The test statistic, F, assumes independence of observations, homogeneous variances, a
Kolmogorov–Smirnov test
In statistics, the Kolmogorov–Smirnov test (K–S test or KS test) is a nonparametric test of the equality of continuous (or discontinuous, see ), one-dimensional probability distributions that can be u
Semiparametric regression
In statistics, semiparametric regression includes regression models that combine parametric and nonparametric models. They are often used in situations where the fully nonparametric model may not perf
Order of a kernel
In statistics, the order of a kernel is the degree of the first non-zero moment of a kernel.
Durbin test
In the analysis of designed experiments, the Friedman test is the most common non-parametric test for complete block designs. The Durbin test is a nonparametric test for balanced incomplete designs th
Mantel test
The Mantel test, named after Nathan Mantel, is a statistical test of the correlation between two matrices. The matrices must be of the same dimension; in most applications, they are matrices of interr
U-statistic
In statistical theory, a U-statistic is a class of statistics that is especially important in estimation theory; the letter "U" stands for unbiased. In elementary statistics, U-statistics arise natura
Lepage test
In statistics, the Lepage test is an exactly distribution-free test (nonparametric test) for jointly monitoring the location (central tendency) and scale (variability) in two-sample treatment versus c
Nonparametric statistics
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). Nonparame
Record value
In statistics, a record value or record statistic is the largest or smallest value obtained from a sequence of random variables. The theory is closely related to that used in order statistics. The ter
L-estimator
In statistics, an L-estimator is an estimator which is a linear combination of order statistics of the measurements (which is also called an L-statistic). This can be as little as a single point, as i
Rank product
The rank product is a biologically motivated test for the detection of differentially expressed genes in replicated microarray experiments.It is a simple non-parametric statistical method based on ran
Cucconi test
In statistics, the Cucconi test is a nonparametric test for jointly comparing central tendency and variability (detecting location and scale changes) in two samples. Many rank tests have been proposed
Kendall's W
Kendall's W (also known as Kendall's coefficient of concordance) is a non-parametric statistic for rank correlation. It is a normalization of the statistic of the Friedman test, and can be used for as
Kernel smoother
A kernel smoother is a statistical technique to estimate a real valued function as the weighted average of neighboring observed data. The weight is defined by the kernel, such that closer points are g
Friedman test
The Friedman test is a non-parametric statistical test developed by Milton Friedman. Similar to the parametric repeated measures ANOVA, it is used to detect differences in treatments across multiple t
Empirical process
In probability theory, an empirical process is a stochastic process that describes the proportion of objects in a system in a given state.For a process in a discrete state space a population continuou
Fisher's exact test
Fisher's exact test is a statistical significance test used in the analysis of contingency tables. Although in practice it is employed when sample sizes are small, it is valid for all sample sizes. It
Multivariate kernel density estimation
Kernel density estimation is a nonparametric technique for density estimation i.e., estimation of probability density functions, which is one of the fundamental questions in statistics. It can be view
Cochran's Q test
In statistics, in the analysis of two-way randomized block designs where the response variable can take only two possible outcomes (coded as 0 and 1), Cochran's Q test is a non-parametric statistical
Empirical distribution function
In statistics, an empirical distribution function (commonly also called an empirical Cumulative Distribution Function, eCDF) is the distribution function associated with the empirical measure of a sam
Somers' D
In statistics, Somers’ D, sometimes incorrectly referred to as Somer’s D, is a measure of ordinal association between two possibly dependent random variables X and Y. Somers’ D takes values between wh
Multinomial test
In statistics, the multinomial test is the test of the null hypothesis that the parameters of a multinomial distribution equal specified values; it is used for categorical data. Beginning with a sampl
Histogram
A histogram is an approximate representation of the distribution of numerical data. The term was first introduced by Karl Pearson. To construct a histogram, the first step is to "bin" (or "bucket") th
Spearman's rank correlation coefficient
In statistics, Spearman's rank correlation coefficient or Spearman's ρ, named after Charles Spearman and often denoted by the Greek letter (rho) or as , is a nonparametric measure of rank correlation
Normal score
The term normal score is used with two different meanings in statistics. One of them relates to creating a single value which can be treated as if it had arisen from a standard normal distribution (ze
McNemar's test
In statistics, McNemar's test is a statistical test used on paired nominal data. It is applied to 2 × 2 contingency tables with a dichotomous trait, with matched pairs of subjects, to determine whethe
Hodges–Lehmann estimator
In statistics, the Hodges–Lehmann estimator is a robust and nonparametric estimator of a population's location parameter. For populations that are symmetric about one median, such as the (Gaussian) no
Functional principal component analysis
Functional principal component analysis (FPCA) is a statistical method for investigating the dominant modes of variation of functional data. Using this method, a random function is represented in the
Kernel (statistics)
The term kernel is used in statistical analysis to refer to a window function. The term "kernel" has several distinct meanings in different branches of statistics.
Transfer entropy
Transfer entropy is a non-parametric statistic measuring the amount of directed (time-asymmetric) transfer of information between two random processes. Transfer entropy from a process X to another pro
Indian buffet process
In the mathematical theory of probability, the Indian buffet process (IBP) is a stochastic process defining a probability distribution over sparse binary matrices with a finite number of rows and an i
Kendall rank correlation coefficient
In statistics, the Kendall rank correlation coefficient, commonly referred to as Kendall's τ coefficient (after the Greek letter τ, tau), is a statistic used to measure the ordinal association between
Rank correlation
In statistics, a rank correlation is any of several statistics that measure an ordinal association—the relationship between rankings of different ordinal variables or different rankings of the same va
Ranklet
In statistics, a ranklet is an orientation-selective non-parametric feature which is based on the computation of Mann–Whitney–Wilcoxon (MWW) rank-sum test statistics. Ranklets achieve similar response
Kernel density estimation
In statistics, kernel density estimation (KDE) is the application of kernel smoothing for probability density estimation, i.e., a non-parametric method to estimate the probability density function of
Tukey–Duckworth test
In statistics, the Tukey–Duckworth test is a two-sample location test – a statistical test of whether one of two samples was significantly greater than the other. It was introduced by John Tukey, who
K-nearest neighbors algorithm
In statistics, the k-nearest neighbors algorithm (k-NN) is a non-parametric supervised learning method first developed by Evelyn Fix and Joseph Hodges in 1951, and later expanded by Thomas Cover. It i
Kuiper's test
Kuiper's test is used in statistics to test that whether a given distribution, or family of distributions, is contradicted by evidence from a sample of data. It is named after Dutch mathematician Nico
Nemenyi test
In statistics, the Nemenyi test is a post-hoc test intended to find the groups of data that differ after a global statistical test (such as the Friedman test) has rejected the null hypothesis that the
Density estimation
In statistics, probability density estimation or simply density estimation is the construction of an estimate, based on observed data, of an unobservable underlying probability density function. The u
Boschloo's test
Boschloo's test is a statistical hypothesis test for analysing 2x2 contingency tables. It examines the association of two Bernoulli distributed random variables and is a uniformly more powerful altern
Medcouple
In statistics, the medcouple is a robust statistic that measures the skewness of a univariate distribution. It is defined as a scaled median difference of the left and right half of a distribution. It
Dependent Dirichlet process
In the mathematical theory of probability, the dependent Dirichlet process (DDP) provides a non-parametric prior over evolving mixture models. A construction of the DDP built on a Poisson point proces
Order statistic
In statistics, the kth order statistic of a statistical sample is equal to its kth-smallest value. Together with rank statistics, order statistics are among the most fundamental tools in non-parametri
Scheirer–Ray–Hare test
The Scheirer–Ray–Hare (SRH) test is a statistical test that can be used to examine whether a measure is affected by two or more factors. Since it does not require a normal distribution of the data, it
Wald–Wolfowitz runs test
The Wald–Wolfowitz runs test (or simply runs test), named after statisticians Abraham Wald and Jacob Wolfowitz is a non-parametric statistical test that checks a randomness hypothesis for a two-valued
Median test
In statistics, Mood's median test is a special case of Pearson's chi-squared test. It is a nonparametric test that tests the null hypothesis that the medians of the populations from which two or more
Kruskal–Wallis one-way analysis of variance
The Kruskal–Wallis test by ranks, Kruskal–Wallis H test (named after William Kruskal and W. Allen Wallis), or one-way ANOVA on ranks is a non-parametric method for testing whether samples originate fr
Chi-squared test
A chi-squared test (also chi-square or χ2 test) is a statistical hypothesis test used in the analysis of contingency tables when the sample sizes are large. In simpler terms, this test is primarily us
Geometric median
In geometry, the geometric median of a discrete set of sample points in a Euclidean space is the point minimizing the sum of distances to the sample points. This generalizes the median, which has the