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Model selection is the task of selecting a model from among various candidates on the basis of performance criterion to choose the best one. [1] In the context of machine learning and more generally statistical analysis , this may be the selection of a statistical model from a set of candidate models, given data.
Estimators such as Horvitz–Thompson estimator yield unbiased estimators (if the selection probabilities are indeed known, or approximately known), for total and the mean of the population. Deville and Särndal (1992) coined the term " calibration estimator " for estimators using weights such that they satisfy some condition, such as having ...
The probability of selection under this scheme is = where X is the sum of the N x variates and the x i are the n members of the sample. Then the ratio of the sum of the y variates and the sum of the x variates chosen in this fashion is an unbiased estimate of the ratio estimator.
The likelihood ratio test is not valid in this setting because the estimating equations are not necessarily likelihood equations. Model selection can be performed with the GEE equivalent of the Akaike Information Criterion (AIC), the quasi-likelihood under the independence model criterion (QIC). [8]
Furthermore, the wider application domain of ABC exacerbates the challenges of parameter estimation and model selection. ABC has rapidly gained popularity over the last years and in particular for the analysis of complex problems arising in biological sciences , e.g. in population genetics , ecology , epidemiology , systems biology , and in ...
A statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of sample data (and similar data from a larger population). A statistical model represents, often in considerably idealized form, the data-generating process . [ 1 ]
In statistics, the method of estimating equations is a way of specifying how the parameters of a statistical model should be estimated.This can be thought of as a generalisation of many classical methods—the method of moments, least squares, and maximum likelihood—as well as some recent methods like M-estimators.
An empirical likelihood ratio function is defined and used to obtain confidence intervals parameter of interest θ similar to parametric likelihood ratio confidence intervals. [7] [8] Let L(F) be the empirical likelihood of function , then the ELR would be: = / (). Consider sets of the form