The Asymptotic Properties Of Generalized Edge Frequency Polygons Density Estimator For Strong Mixing Samples

Nonparametric estimation is an important estimation method because most of the overall dis-tribution of the type is unknown in reality, the non-parametric density estimation methods are of-ten used in the field of economic, cultural, medical, etc.There are many non-parameters of density estimation methods, the main histogram estimation, Rosenblatt estimate, frequency difference esti-mation, kernel density estimation, nearest neighbor density estimation, etc. in which the frequency interpolation density estimation and non-negative kernel density estimation There are aspects of the same integral mean square error convergence rate, but in numerical calculation, a relatively small amount of computation frequency interpolation estimate, so this is more relative to the ker-nel density estimation computational advantages. Therefore, the study estimated that the frequency interpolation has very important significance.Scott (1985) proposed frequency polygons density estimator, then Jones (1998), Dong and Zheng (2001) were estimated on the frequency interpolation optimized. Jones (1998) proposed edge frequency polygons density estimator, given under the independent samples points mean square error. Dong and Zheng (2001) follows the edge of the frequency interpolation estimate of thinking, the two edges of the frequency interval averaging method is extended to the edge of 2k intervals averaged frequency, we give a generalized edge frequency interpolation estimation, At the same time independent sample the generalized integral edge frequency interpolation estimated mean square error, And they prove generalized edge frequency polygons estimator's minimum mean square error is less than the edge frequency polygons density estimator's minimum mean square error.However, So far, there has not been a study of the asymptotic properties of the generalized edge frequency polygons estimator under the dependent samples. This article will examine the asymptotic properties of generalized edge frequency polygons estimator under strong mixing sam-ples. Firstly generalized edge frequency interpolation estimate in strong mixing sequence mean square error, And the mean squared error given by the optimal window width and a minimum mean square error. On this basis, and given k=2,3 optimal weights. Second and prove gener-alized edge frequency is estimated at mixing strong asymptotically unbiased sequences and has strong consistency. Finally, selecting the stable AR (1) time series model for generalized edge fre-quency interpolation estimation numerical simulation, simulation results show that the estimated effect of generalized edge frequency polygons estimator estimated well.