Distribution estimation is very important in order to make statistical inference for parameters or its functions based on this distribution. In this work we propose an estimator of the distribution of some variable with non-smooth auxiliary information, for example, a symmetric distribution of this variable, A smoothing technique is employed to handle the non-differentiable function. Hence, a distribution can be estimated based on smoothed auxiliary information. Asymptotic properties of the distribution estimator are derived and analyzed. The distribution estimators based on our method are found to be significantly efficient than the corresponding estimators without these auxiliary information. Some simulation studies are conducted to illustrate the finite sample performance of the proposed estimators.
Continuous-time Markowitz＇s by parameterizing a critical quantity. It mean-variance efficient strategies are modified is shown that these parameterized Markowitz strategies could reach the original mean target with arbitrarily high probabilities. This, in turn, motivates the introduction of certain stopped strategies where stock holdings are liquidated whenever the parameterized Markowitz strategies reach the present value of the mean target. The risk aspect of the revised Markowitz strategies are examined via expected discounted loss from the initial budget. A new portfolio selection model is suggested based on the results of the paper.
Multivariate failure time data arise frequently in survival analysis.A commonly used tech-nique is the working independence estimator for marginal hazard models.Two natural questions are how to improve the effciency of the working independence estimator and how to identify the situations under which such an estimator has high statistical effciency.In this paper,three weighted estimators are proposed based on three different optimal criteria in terms of the asymptotic covariance of weighted estimators.Simplifiedclose-form solutions are found,which always outperform the working indepen-dence estimator.We also prove that the working independence estimator has high statistical effciency,when asymptotic covariance of derivatives of partial log-likelihood functions is nearly exchangeable or diagonal.Simulations are conducted to compare the performance of the weighted estimator and work-ing independence estimator.A data set from Busselton population health surveys is analyzed using the proposed estimators.
FAN JianQing1,2,ZHOU Yong2,3,CAI JianWen4 & CHEN Min3 1 Department of Operations Research and Financial Engineering,Princeton University,Princeton,NJ08544,USA 2 Department of Statistics,Shanghai University of Finance and Economics,Shanghai 200433,China 3 Institute of Applied Mathematics,Academy of Mathematics and Systems Science,Chinese Academy of Sci-ences,Beijing 100190,China 4 Department of Biostatistics,University of North Carolina at Chapel Hill,Chapel Hill,NC 27599-7420,USA
