Statistical Computing
Raheleh Zamini
Abstract
In various statistical model, such as density estimation and estimation of regression curves or hazardrates, monotonicity constraints can arise naturally. A frequently encountered problem in nonparametricstatistics is to estimate a monotone density function f on a compact interval. A known estimator ...
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In various statistical model, such as density estimation and estimation of regression curves or hazardrates, monotonicity constraints can arise naturally. A frequently encountered problem in nonparametricstatistics is to estimate a monotone density function f on a compact interval. A known estimator fordensity function of f under the restriction that f is decreasing, is Grenander estimator, where is the leftderivative of the least concave majorant of the empirical distribution function of the data. Many authorsworked on this estimator and obtained very useful properties from this estimator. Grenander estimatoris a step function and as a consequence it is not smooth. In this paper, we discuss the estimation of adecreasing density function by the kernel smoothing method. Many works have been done due to theimportance and applicability of Berry-Esseen bounds for the density estimator. In this paper, we studya Berry- Esseen type bound for a smoothed version of Grenander estimator.
mozhgan taavoni
Abstract
This paper considers an extension of the linear mixed model, called semiparametric mixed effects model, for longitudinal data, when multicollinearity is present. To overcome this problem, a new mixed ridge estimator is proposed while the nonparametric function in the semiparametric model is approximated ...
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This paper considers an extension of the linear mixed model, called semiparametric mixed effects model, for longitudinal data, when multicollinearity is present. To overcome this problem, a new mixed ridge estimator is proposed while the nonparametric function in the semiparametric model is approximated by the kernel method. The proposed approache integrates ridge method into the semiparametric mixed effects modeling framework in order to account for both the correlation induced by repeatedly measuring an outcome on each individual over time, as well as the potentially high degree of correlation among possible predictor variables. The asymptotic normality of the exhibited estimator is established. To improve efficiency, the estimation of the covariance function is accomplished using an iterative algorithm. Performance of the proposed estimator is compared through a simulation study and analysis of CD4 data.
