###### ratio

- Generalized likelihood ratio statistics have been proposed in Fan, Zhang and Zhang [Ann. (kent.ac.uk)
- The likelihood ratio statistics are constructed based on the assumption that the distributions of stochastic errors are in a certain parametric family. (kent.ac.uk)
- We extend their work to the case where the error distribution is completely unspecified via newly proposed sieve empirical likelihood ratio (SELR) tests. (kent.ac.uk)
- The proposed approach has two advantages over the generalized likelihood ratio method: it requires one only to specify some conditional estimating equations rather than the entire distribution of the stochastic error, and the procedure adapts automatically to the unknown error distribution including heteroscedasticity. (kent.ac.uk)

###### hypotheses

- 29 (2001) 153-as a generally applicable method for testing norparametic hypotheses about nonparametric functions. (kent.ac.uk)

###### parameters

- In statistics, a likelihood function (often simply the likelihood) is a function of the parameters of a statistical model given data. (wikipedia.org)
- A number of modified likelihood and message length functions have been developed for better handling of nuisance parameters but they are not equally efficient. (umn.edu)
- In this paper, we empirically compare different modified likelihood and message length functions in the context of estimation and testing of parameters from linear regression disturbances that follow either first-order moving average or first-order autoregressive error processes. (umn.edu)
- neo-Fisherian statistics emphasizes likelihood functions of parameters. (wikipedia.org)
- Second, Kempthorne was skeptical of Bayesian statistics, which use not only likelihoods but also probability distributions on parameters. (wikipedia.org)
- In a stationary Gaussian time series model, the likelihood function is (as usual in Gaussian models) a function of the associated mean and covariance parameters. (wikipedia.org)
- Whittle's likelihood is commonly used to estimate signal parameters for signals that are buried in non-white noise. (wikipedia.org)
- In summary, to ensure efficient inference of the regression parameters and the regression function, the heteroscedasticity must be accounted for. (wikipedia.org)
- In all model-based statistical inference, the likelihood function is of central importance, since it expresses the probability of the observed data under a particular statistical model, and thus quantifies the support data lend to particular values of parameters and to choices among different models. (wikipedia.org)
- When fitting models, it is possible to increase the likelihood by adding parameters, but doing so may result in overfitting. (wikipedia.org)
- In statistics, the likelihood principle is that, given a statistical model, all the evidence in a sample relevant to model parameters is contained in the likelihood function. (wikipedia.org)
- The likelihood principle is this: all information from the data that is relevant to inferences about the value of the model parameters is in the equivalence class to which the likelihood function belongs. (wikipedia.org)

###### method of maximum

- This is the basis for the widely used method of maximum likelihood. (wikipedia.org)
- The method of maximum likelihood is used with a wide range of statistical analyses. (wikipedia.org)
- The method of maximum likelihood is based on the likelihood function. (wikipedia.org)
- The method of maximum likelihood selects the set of values of the model parameter that maximize the likelihood function. (wikipedia.org)

###### exact likelihood

- The Exact Likelihood Function for a Space Time Model. (eudml.org)

###### histogram based

- We considered five LFDR estimators for detecting enriched GO terms: a binomial-based estimator (BBE), a maximum likelihood estimator (MLE), a normalized MLE (NMLE), a histogram-based estimator assuming a theoretical null hypothesis (HBE), and a histogram-based estimator assuming an empirical null hypothesis (HBE-EN). (biomedcentral.com)

###### satisfies

- It is argued that as long as the likelihood function satisfies certain criteria its analytical form is not critical in the stated tracking context. (uclan.ac.uk)

###### Gaussian

- This is demonstrated through an experimental comparison between the use of the standard Bhattacharyya distance/Gaussian likelihood combination and the potentially computationally simpler histogram intersection distance/triangular likelihood combination in particle filter tracking sequences. (uclan.ac.uk)
- In statistics, Whittle likelihood is an approximation to the likelihood function of a stationary Gaussian time series. (wikipedia.org)

###### estimators

- The results show that estimators based on the conditional profile likelihood and tests based on the marginal likelihood are best. (umn.edu)

###### computationally

- However, for more complex models, an analytical formula might be elusive or the likelihood function might be computationally very costly to evaluate. (wikipedia.org)

###### marginal

- It is shown that the differences between the approaches are marginal when the likelihood criteria are applied. (uclan.ac.uk)

###### discrete

- The likelihood function is usually defined differently for discrete and continuous probability distributions. (wikipedia.org)
- Let X be a discrete random variable with probability mass function p depending on a parameter θ. (wikipedia.org)
- This provides a likelihood function for any probability model with all distributions, whether discrete, absolutely continuous, a mixture or something else. (wikipedia.org)
- The discussion above of likelihood with discrete probabilities is a special case of this using the counting measure, which makes the probability of any single outcome equal to the probability density for that outcome. (wikipedia.org)

###### probabilities

- That illustrates an important aspect of likelihoods: likelihoods do not have to integrate (or sum) to 1, unlike probabilities. (wikipedia.org)

###### Model

- This paper presents an adaptation of the Expectation-Maximization (EM) algorithm to enable a mobile robot to learn both its action and sensor model functions, starting without an accurate version of either. (utexas.edu)
- To explore the resulting model space, we develop a likelihood-based hierarchical clustering, and we examine the eigenvalues of the linear dynamics. (pnas.org)
- Model definition function. (wikipedia.org)
- Mixed model - likelihood function. (wikipedia.org)

###### yields

- Combining the likelihood principle with the law of likelihood yields the consequence that the parameter value which maximizes the likelihood function is the value which is most strongly supported by the evidence. (wikipedia.org)

###### models

- A very important use of this function is in the framework of generalized linear models and non-parametric regression. (wikipedia.org)
- For simple models, an analytical formula for the likelihood function can typically be derived. (wikipedia.org)

###### Procedure

- The use of frequentist methods involving p-values leads to different inferences for the two cases above, showing that the outcome of frequentist methods depends on the experimental procedure, and thus violates the likelihood principle. (wikipedia.org)

###### partial

- In a stratified analysis, the partial likelihood is the product of the partial likelihood functions for the individual strata. (sas.com)
- NumXL generates the corresponding analysis blocks (with underlying formulas) in the designated location NumXL functions are organized into eleven (11) categories: Autocorrelation function (ACF) and partial autocorrelation function (PACF). (wikipedia.org)

###### context

- The choice of particle filter dissimilarity distance measures and likelihood functions is considered in the context of object tracking in grey scale CCTV video. (uclan.ac.uk)

###### gamma

- Here Γ(k) is the gamma function evaluated at k. (wikipedia.org)

###### measure

- 20 . (The largest value the instrument can measure is 10) a)What is the likelihood function? (physicsforums.com)
- Probability is the measure of the likelihood that an event will occur. (wikipedia.org)
- θ) is a likelihood function of θ: it gives a measure of how "likely" any particular value of θ is, if we know that X has the value x. (wikipedia.org)
- The density function may be a density with respect to counting measure, i.e. a probability mass function. (wikipedia.org)

###### follows

- Birnbaum proved that the likelihood principle follows from two more primitive and seemingly reasonable principles, the conditionality principle and the sufficiency principle. (wikipedia.org)

###### form

- The power transformation is defined as a continuously varying function, with respect to the power parameter λ, in a piece-wise function form that makes it continuous at the point of singularity (λ = 0). (wikipedia.org)

###### methods

- ABC methods bypass the evaluation of the likelihood function. (wikipedia.org)

###### given

- Write down the likelihood function for θ based upon these four given independant tests. (mathhelpforum.com)

###### different

- Test score interpretation may be invalidated by the presence of differential item functioning (DIF) among different groups of respondents based on characteristics such as gender, country or the language version of the test used. (thefreelibrary.com)

###### General

- The Whittle likelihood in general is only an approximation, it is only exact if the spectrum is constant, i.e., in the trivial case of white noise. (wikipedia.org)