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Approximating Conditional Density Functions Using Dimension Reduction
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作者 Jian-qing Fan Liang Peng +1 位作者 Qi-wei Yao Wen-yang Zhang 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2009年第3期445-456,共12页
We propose to approximate the conditional density function of a random variable Y given a dependent random d-vector X by that of Y given θ^τX, where the unit vector θ is selected such that the average Kullback-Leib... We propose to approximate the conditional density function of a random variable Y given a dependent random d-vector X by that of Y given θ^τX, where the unit vector θ is selected such that the average Kullback-Leibler discrepancy distance between the two conditional density functions obtains the minimum. Our approach is nonparametric as far as the estimation of the conditional density functions is concerned. We have shown that this nonparametric estimator is asymptotically adaptive to the unknown index θ in the sense that the first order asymptotic mean squared error of the estimator is the same as that when θ was known. The proposed method is illustrated using both simulated and real-data examples. 展开更多
关键词 conditional density function dimension reduction Kullback-Leibler discrepancy local linear regression nonparametric regression Shannon's entropy
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APPROXIMATION RATES OF ERROR DISTRIBUTION OF DOUBLE KERNEL ESTIMATES OF CONDITIONAL DENSITY
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作者 XueLiugen CaiGuoliang 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2000年第4期425-432,共8页
In this paper, the normal approximation rate and the random weighting approximation rate of error distribution of the kernel estimator of conditional density function f(y|x) are studied. The results may be used to... In this paper, the normal approximation rate and the random weighting approximation rate of error distribution of the kernel estimator of conditional density function f(y|x) are studied. The results may be used to construct the confidence interval of f(y|x) . 展开更多
关键词 conditional density function double kernel estimator random weighting method approximation rate.
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Nonparametric inferences for kurtosis and conditional kurtosis
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作者 谢潇衡 何幼桦 《Journal of Shanghai University(English Edition)》 CAS 2009年第3期225-232,共8页
Under the assumption of strictly stationary process, this paper proposes a nonparametric model to test the kurtosis and conditional kurtosis for risk time series. We apply this method to the daily returns of S&P500 i... Under the assumption of strictly stationary process, this paper proposes a nonparametric model to test the kurtosis and conditional kurtosis for risk time series. We apply this method to the daily returns of S&P500 index and the Shanghai Composite Index, and simulate GARCH data for verifying the efficiency of the presented model. Our results indicate that the risk series distribution is heavily tailed, but the historical information can make its future distribution light-tailed. However the far future distribution's tails are little affected by the historical data. 展开更多
关键词 conditional probability density function (PDF) kernel estimate KURTOSIS conditional kurtosis heavy tail
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Asymptotic properties of a nonparametric conditional density estimator in the local linear estimation for functional data via a functional single-index model
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作者 Fadila Benaissa Abdelmalek Gagui Abdelhak Chouaf 《Statistical Theory and Related Fields》 2022年第3期208-219,共12页
This paper deals with the conditional density estimator of a real response variable given a functional random variable(i.e.,takes values in an infinite-dimensional space).Specifically,we focus on the functional index ... This paper deals with the conditional density estimator of a real response variable given a functional random variable(i.e.,takes values in an infinite-dimensional space).Specifically,we focus on the functional index model,and this approach represents a good compromise between nonparametric and parametric models.Then we give under general conditions and when the variables are independent,the quadratic error and asymptotic normality of estimator by local linear method,based on the single-index structure.Finally,wecomplete these theoretical advances by some simulation studies showing both the practical result of the local linear method and the good behaviour for finite sample sizes of the estimator and of the Monte Carlo methods to create functional pseudo-confidence area. 展开更多
关键词 Mean squared error single functional index conditional density function nonparametric estimation local linear estimation asymptotic normality functional data
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