Two mixed normal densities from cointegration analysis

Article Abstract:

Mixed normal distributions are broadly used in econometric and statistical theory. They have two characteristics, that of being Normal conditionally and as a mixing variate. As a mixing variate, its density functions as a weight feature in integrating the conditional Normals into the unconditional density. Another kind of mixing variate are the functionals of Brownian motions, whose characteristics are important for interpretation of Monte Carlo studies. The setting and the derivation of the exact closed form formulae of mixed Normals which concur with the limit of the optimal bivariate cointegration estimators are discussed.

Usage, Maximum likelihood estimates (Statistics), Asymptotic distribution (Probability theory), Maximum likelihood (Statistics)

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Estimation of regression coefficients of interest when other regression coefficients are of no interest

Article Abstract:

A mathematical derivation is supplied to support the estimation of regression coefficients of interests when other regression coefficients are of no interest. The explanation involves the estimation of linear combinations of the elements of beta in the linear regression model y = Xbeta + Zgamma + u, where y(n x 1) is the vector of observations, Z(n x m) and x(n x k) are matrices of nonrandom regressors, u(n x 1) is a random vector of unobservable disturbances, and gamma(m x 1) and beta(k x 1) are unknown onrandom parameters.

Econometrics & Model Building, Econometrics, Business models

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Second order approximation in the partially linear regression model

Article Abstract:

The various properties of quantities in the partially linear regression model were investigated. A standardized semiparametric least squares estimator was developed using a stochastic expansion with remainder op(n-2 micron), where micron is less than 1/2. Bandwidth choice was determined using second order expansions to approximate standard error estimates for second order effects. The formula was tested using a standard Monte Carlo experiment.

Parameter estimation

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