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We present two stochastic models that describe the relationship between biomarker process values at random time points, event times, and a vector of covariates. In both models the biomarker processes are degradation processes that represent the decay of systems over time. In the first model the biomarker process is a Wiener process whose drift is a function of the covariate vector. In the second model the biomarker process is taken to be the difference between a stationary Gaussian process and a time drift whose drift parameter is a function of the covariates. For both models we present statistical methods for estimation of the regression coefficients. The first model is useful for predicting the residual time from study entry to the time a critical boundary is reached while the second model is useful for predicting the latency time from the infection until the time the presence of the infection is detected. We present our methods principally in the context of conducting inference in a population of HIV infected individuals. 相似文献
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Kjell Hausken 《Theory and Decision》2007,62(2):135-160
Axelord’s [(1970), Conflict of Interest, Markham Publishers, Chicago] index of conflict in 2 × 2 games with two pure strategy equilibria has the property that a
reduction in the cost of holding out corresponds to an increase in conflict. This article takes the opposite view, arguing
that if losing becomes less costly, a player is less likely to gamble to win, which means that conflict will be less frequent.
This approach leads to a new power index and a new measure of stubbornness, both anchored in strategic reasoning. The win
probability defined as power constitutes an equilibrium refinement which differs from Harsanyi and Selten’s [(1988), A General Theory of Equilibrium Selection in Games, MIT Press, Cambridge] refinement. In contrast, Axelrod’s approach focuses on preferences regarding divergences from imaginary
outmost rewards that cannot be obtained jointly. The player who is less powerful in an asymmetric one-shot game becomes more
powerful in the repeated game, provided he or she values the future sufficiently more than the opponent. This contrasts with
the view that repetition induces cooperation, but conforms with the expectation that a more patient player receives a larger
share of the pie.
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In this paper we address the problem of estimating a vector of regression parameters in the Weibull censored regression model. Our main objective is to provide natural adaptive estimators that significantly improve upon the classical procedures in the situation where some of the predictors may or may not be associated with the response. In the context of two competing Weibull censored regression models (full model and candidate submodel), we consider an adaptive shrinkage estimation strategy that shrinks the full model maximum likelihood estimate in the direction of the submodel maximum likelihood estimate. We develop the properties of these estimators using the notion of asymptotic distributional risk. The shrinkage estimators are shown to have higher efficiency than the classical estimators for a wide class of models. Further, we consider a LASSO type estimation strategy and compare the relative performance with the shrinkage estimators. Monte Carlo simulations reveal that when the true model is close to the candidate submodel, the shrinkage strategy performs better than the LASSO strategy when, and only when, there are many inactive predictors in the model. Shrinkage and LASSO strategies are applied to a real data set from Veteran's administration (VA) lung cancer study to illustrate the usefulness of the procedures in practice. 相似文献