球面数据核近邻估计的强相合性

Abstract

Abstract:

In this article, we introduce a kernel neighbor estimator of density function of spherical data. By investigating the relationship between kernel estimator and kernel neighbor estimator, we establish the strong consistency and the uniformly strong consistency for this kernel neighbor estimator.

Key words: Ｓｐｈｅｒｉｃａｌｄａｔａ, Ｄｅｎｓｉｔｙｆｕｎｃｔｉｏｎｋｅｒｎｅｌｎｅｉｇｈｂｏｒｅｓｔｉｍａｔｏｒ, Ｐｏｉｎｔｗｉｓｅｓｔｒｏｎｇｃｏｎｓｉｓｔｅｎｃｙ, Ｕｎｉｆｏｒｍｌｙｓｔｒｏｎｇｃｏｎｓｉｓｔｅｎｃｙ

CLC Number:

６２Ｇ０５

Wang Xiaoming. Strong Consistency for Kernel Neighbor Estimator of Density Function of spherical Data[J].Acta mathematica scientia,Series A, 2000, 20(3): 386-393.

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References

１　ＢａｉＺＤ，ＲａｄｈａｋｒｉｓｈｎａＲａｏＣ，ＺｈａｏＬＣ．Ｋｅｒｎｅｌｅｓｔｉｍａｔｏｒｓｏｆｄｅｎｓｉｔｙｆｕｎｃｔｉｏｎｏｆｄｉｒｅｃｔｉｏｎａｌｄａｔａ．ＪＭｕｌｔｉｖａｒｉａｔｅＡｎａｌ，１９８８，２７：２４－３９
２　ＨａｌｌＰ，ＷａｔｓｏｎＧＳ，ＣａｂｒｅｒａＪ．Ｋｅｒｎｅｌｄｅｎｓｉｔｙｅｓｔｉｍａｔｉｏｎｗｉｔｈｓｐｈｅｒｉｃａｌｄａｔａ．Ｂｉｏｍｅｔｒｉｋａ，１９８７，７４：７５１－７６２
３　ＭａｒｄｉａＫＶ．Ｓｔａｔｉｓｔｉｃｓｏｆｄｉｒｅｃｔｉｏｎａｌｄａｔｅ．ＮｅｗＹｏｒｋ：ＡｃａｄｅｍｉｃＰｒｅｓｓ，１９７２
４　ＰｕｋｋｉｌａＬ，ＲａｏＣＲ．Ｐａｔｔｅｒｎｒｅｃｏｇｎｉｔｉｏｎｂａｓｅｄｏｎｓｃａｌｅｉｍａｒｉａｎｔｄｉｓｃｒｉｍｉｎａｎｔｆｕｎｃｔｉｏｎｓ．ＴｅｃｈｎｉｃａｌＲｅｐｏｒｔＣｅｎｔｅｒｆｏｒＭｕｌｔｉｃａｒｉａｔｅＡｎａｌｙｓｉｓ，ＵｎｉｖｅｒｓｉｔｙｏｆＰｉｔｔｓｂｕｒｇｈ，１９８６．８６－９０
５　ＶａｐｎｉｋＶＮ，ＣｈｅｒｖｏｎｅｎｋｉｓＡＹａ．Ｏｎｔｈｅｕｎｉｆｏｒｍｃｏｎｖｅｒｇｅｎｃｅｏｆｒｅｌａｔｉｖｅｆｒｅｑｕｅｎｃｉｅｓｏｆｅｖｅｎｔｓｔｏｔｈｅｉｒｐｒｏｂａｂｉｌｉｔｉｅｓ．ＴｈｅｏｒｙＰｒｏｂａｂＡｐｐｌ，１９７１，１６：２４６－２８０
６　ＷａｔｓｏｎＧＳ．Ｓｔａｔｉｓｔｉｃｓｏｎｓｐｈｅｒｅｓ，ＶｎｉｖｅｒｓｉｔｙｏｆＡｒｋａｎｓａｓ，ＬｅｃｔｕｒｅＮｏｔｅｓｉｎＭａｔｈｅｍｔｉｃａｌＳｃｉｅｎｃｅｓ６，ＮｅｗＹｏｒｋ：Ｗｉｌｅｙ，１９８３
７　ＷｅｎｏｃｕｒＲＳ，ＤｕｄｌｙＲＭ．Ｓｏｍｅｓｐｅｃｉａｌｖａｐｎｉｋｃｈｅｒｖｏｎｅｎｋｉｓｃｌａｓｓｅｓ，ｄｉｓｃｒｅｔｅＭａｔｈ，１９８１，３３：３１３－３１８
８　ＺｈａｏＬＣ．Ａｎｉｎｅｑｕａｌｉｔｙｃｏｎｃｅｒｎｉｎｇｔｈｅｄｅｖｉａｔｉｏｎｂｅｔｗｅｅｎｔｈｅｏｒｅｔｉｃａｌａｎｄｅｍｐｉｒｉｃａｌｄｉｓｔｒｉｂｕｔｉｏｎｓ．Ｔｅｃｈｎｉｃａｌｒｅｐｏｒｔ，Ｃｅｎｔｅｒｆｏｒｍｕｌｔｉｃａｒｉａｔｅａｎａｌｙｓｉｓ，ＵｎｉｖｅｒｓｉｔｙｏｆＰｉｔｔｓｂｕｒｇｈ．１９８５，８５－３０

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Strong Consistency for Kernel Neighbor Estimator of Density Function of spherical Data

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