Proportional Small Sample Bias in Pricing Kernel Estimations

2014 ◽  
Author(s):  
Dietmar Leisen
Keyword(s):  
Small Sample ◽  
Pricing Kernel ◽  
Sample Bias ◽  
Kernel Estimations

Small Sample Bias in the Gamma Frailty Model for Univariate Survival

2005 ◽  
Vol 11 (2) ◽  
pp. 265-284 ◽  
Author(s):  
Peter Barker ◽  
Robin Henderson
Keyword(s):  
Frailty Model ◽  
Small Sample ◽  
Sample Bias ◽  
Gamma Frailty

scholarly journals Dynamic Regression and Filtered Data Series: A Laplace Approximation to the Effects of Filtering in Small Samples

1996 ◽  
Vol 12 (3) ◽  
pp. 432-457 ◽  
Author(s):  
Eric Ghysels ◽  
Offer Lieberman
Keyword(s):  
Regression Model ◽  
Quadratic Forms ◽  
Mean Squared Error ◽  
Small Sample ◽  
Data Series ◽  
Finite Sample ◽  
Sample Bias ◽  
Squared Error ◽  
Lagged Dependent Variable ◽  
Dynamic Regression Model

It is common for an applied researcher to use filtered data, like seasonally adjusted series, for instance, to estimate the parameters of a dynamic regression model. In this paper, we study the effect of (linear) filters on the distribution of parameters of a dynamic regression model with a lagged dependent variable and a set of exogenous regressors. So far, only asymptotic results are available. Our main interest is to investigate the effect of filtering on the small sample bias and mean squared error. In general, these results entail a numerical integration of derivatives of the joint moment generating function of two quadratic forms in normal variables. The computation of these integrals is quite involved. However, we take advantage of the Laplace approximations to the bias and mean squared error, which substantially reduce the computational burden, as they yield relatively simple analytic expressions. We obtain analytic formulae for approximating the effect of filtering on the finite sample bias and mean squared error. We evaluate the adequacy of the approximations by comparison with Monte Carlo simulations, using the Census X-11 filter as a specific example

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