Nonparametric methods are used to make inferences about infinite dimensional parameters in statistical models.
In situations when a very precise knowledge about a distribution function, a curve or a surface is available, parametric methods are used to identify them when noisy data set is available. When the knowledge is much less precise, non-parametric methods are used. In such situations, the modelling assumptions are that a curve or a surface belongs to certain class of functions.
When using the limited information from the noisy data, attempt is made by the statistician to identify the function from the class that "best" fits the data. Typically, expansions of the function in a suitable basis are used and coefficients of the expansion up to certain order are evaluated using the data. Depending on the bases used, one ends up with kernel methods, wavelet methods, spline-based methods, Edgeworth expansions etc. The semi-parametric approach in inference is also widely used in cases where the main component of interest is parametric but there is a non-parametric "nuisance" component involved in the model specification.
Nonparametric Statistics Research Group Strengths include:
- Wavelet methods in non-parametric inference
- Edgeworth and Saddlepoint approximations for densities and tail-area probabilities
- (Higher order) Edgeworth expansions
- Nonparametric and semi-parametric inference in regression, density estimation and in inference about copulae
- Non-parametric binary regression
- Nonparametric methods in counting process intensity function estimation
- Functional data analysis
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