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"Colm McManamon (Cólm Mac Meanman) is a former Gaelic footballer from Tiernaur, Mulranny, County Mayo, Ireland who played for Burrishoole and Mayo. He represented Ireland twice in International Rules. He is related to Dublin footballer Kevin McManamon. See also * 1996 All-Ireland Senior Football Championship Final * Burrishoole GAA * Geelong Football Club * Irish experiment * Mayo GAA References Burrishoole Gaelic footballers Mayo inter-county Gaelic footballers "
"In econometrics, the information matrix test is used to determine whether a regression model is misspecified. The test was developed by Halbert White, who observed that in a correctly specified model and under standard regularity assumptions, the Fisher information matrix can be expressed in either of two ways: as the outer product of the gradient, or as a function of the Hessian matrix of the log-likelihood function. Consider a linear model \mathbf{y} = \mathbf{X} \mathbf{\beta} + \mathbf{u}, where the errors \mathbf{u} are assumed to be distributed \mathrm{N}(0, \sigma^2 \mathbf{I}). If the parameters \beta and \sigma^2 are stacked in the vector \mathbf{\theta}^{\mathsf{T}} = \begin{bmatrix} \beta & \sigma^2 \end{bmatrix}, the resulting log-likelihood function is :\ell (\mathbf{\theta}) = - \frac{n}{2} \log \sigma^2 - \frac{1}{2 \sigma^2} \left( \mathbf{y} - \mathbf{X} \mathbf{\beta} \right)^{\mathsf{T}} \left( \mathbf{y} - \mathbf{X} \mathbf{\beta} \right) The information matrix can then be expressed as : \mathbf{I} (\mathbf{\theta}) = \operatorname{E} \left[ \left( \frac{\partial \ell (\mathbf{\theta}) }{ \partial \mathbf{\theta} } \right) \left( \frac{\partial \ell (\mathbf{\theta}) }{ \partial \mathbf{\theta} } \right)^{\mathsf{T}} \right] that is the expected value of the outer product of the gradient or score. Second, it can be written as the negative of the Hessian matrix of the log-likelihood function : \mathbf{I} (\mathbf{\theta}) = - \operatorname{E} \left[ \frac{\partial^2 \ell (\mathbf{\theta}) }{ \partial \mathbf{\theta} \, \partial \mathbf{\theta}^{\mathsf{T}}} \right] If the model is correctly specified, both expressions should be equal. Combining the equivalent forms yields : \mathbf{\Delta}(\mathbf{\theta}) = \sum_{i=1}^n \left[ \frac{\partial^2 \ell(\mathbf{\theta}) }{ \partial \mathbf{\theta} \, \partial \mathbf{\theta}^{\mathsf{T}} } + \frac{\partial \ell(\mathbf{\theta}) }{ \partial \mathbf{\theta} } \frac{\partial \ell (\mathbf{\theta}) }{ \partial \mathbf{\theta} } \right] where \mathbf{\Delta} (\mathbf{\theta}) is an (r \times r) random matrix, where r is the number of parameters. White showed that the elements of n^{-1/2} \mathbf{\Delta} ( \mathbf{\hat{\theta}} ), where \mathbf{\hat{\theta}} is the MLE, are asymptotically normally distributed with zero means when the model is correctly specified. In small samples, however, the test generally performs poorly. References Further reading Statistical tests Regression diagnostics "
"A casa de turismo rural in Terras de Bouro, Braga, Portugal A casa de pagès (Catalan) or casa rural (Spanish) is a form of basic self-catering tourist accommodation in Spain equivalent to gîtes in France .Rough Guides Snapshot Spain: The Balearic Islands 0241189004 Rough Guides - 2015 "Casas rurales (rural houses), or casas de pagès in Catalunya, are where many Spanish holidaymakers stay. It's a wideranging concept, from boutique cave dwellings to restored manor houses, many with pools and gardens" The 'country houses' may be rented by the building or by the room.Michelle Lowe, Kirstie Shirra Walking the GR7 in Andalucia: From Tarifa to Puebla de Don Fadrique 2013 1849659117 "Casa rural – country houses let out as whole self-catering houses or by the room. Many of them are tastefully renovated traditional buildings.They are often family-run businesses and can have real character. Those let on a whole-house basis are ... Most casas rurales belong to owner associations. For example on the Canary Islands Acantur co-ordinate cottages on all but Lanzarote.Lucy Corne Canary Islands 2004 - 1841621080 Page 47 " One increasingly popular way to spend a night is staying in a casa rural (rural house). These are often ...Most casas rurales belong to one of the various associations, mentioned in each island chapter. Acantur co-ordinate cottages on all but Lanzarote and have an excellent webpage: www.ecoturismocanarias.com.Brawn David Anthony, Brawn Rosamund Coreen - Sierra de Aracena a Walk! Guidebook 1899554963 2004 - Page 17 "If you are staying in a casa rural or on one of the campsites, and are thinking of self-catering, be aware that there are few large supermarkets, although all but the smallest villages have a little shop for basic goods. " In Portugal the same class of accommodation is called not 'country houses' but casa de turismo rural (Portuguese). References Hotels in Spain Vacation rental "