ﺑﺮآورد ﺗﺎﺑﻊ ﮐﻮوارﯾﺎﻧﺲ ﻓﻀﺎﯾﯽ ﺑﺎ اﺳﺘﻔﺎده از روش درﺳﺘﻨﻤﺎﯾﯽ ﻣﺮﮐﺐ ﺑﻠﻮﮐﯽ ﺗﻔﺎﺿﻠﯽ

Estimating of Spatial Covariance Function Using Block Differenced Composite Likelihood

ﭼﮑﯿﺪه: در اﯾﻦ ﻣﻘﺎﻟﻪ ﭘﺎراﻣﺘﺮﻫﺎي ﺗﺎﺑﻊ ﮐﻮوارﯾﺎﻧﺲ ﻫﺎي ﻓﻀﺎﯾﯽ ﺑﺎ اﺳﺘﻔﺎده از روش درﺳﺘﻨﻤﺎﯾﯽ ﻣﺮﮐﺐ ﺑﻠﻮﮐﯽ ﺑﺮآورد ﻣﯽ ﺷﻮد. در اﯾﻦ روش درﺳﺘﻨﻤﺎﯾﯽ ﻣﺮﮐﺐ ﺑﺎ اﺳﺘﻔﺎده از ﺗﺎﺑﻊ ﻫﺎي ﭼﮕﺎﻟﯽ ﺗﻮأم ﺑﻠﻮك ﻫﺎي زوﺟﯽ داده ﻫﺎي ﺗﻔﺎﺿﻞ ﯾﺎﻓﺘﻪ ﺳﺎﺧﺘﻪ ﻣﯽ ﺷﻮد. ﺑﺮاي اﯾﻦ ﻣﻨﻈﻮر ﭘﺲ از اﻧﺠﺎم ﺗﻔﺎﺿﻞ ﮔﯿﺮي ﻣﺠﻤﻮﻋﻪ داده ﻫﺎي ﺑﺰرگ را ﺑﻪ ﻣﺠﻤﻮﻋﻪ داده ﻫﺎي ﮐﻮﭼﮏ ﺗﺮ اﻓﺮاز ﮐﺮده ﺗﺎﺑﻊ درﺳﺘﻨﻤﺎﯾﯽ ﻫﺮ ﯾﮏ از ﻣﺠﻤﻮﻋﻪ داده ﻫﺎي ﮐﻮﭼﮏ ﺗﺮ ﺑﻪ ﻃﻮر ﺟﺪاﮔﺎﻧﻪ ﻣﺤﺎﺳﺒﻪ و در ﻧﻬﺎﯾﺖ از ﻃﺮﯾﻖ ﺟﻤﻊ ﺑﻪ ﺳﺎدﮔﯽ ﺑﺎ ﻫﻢ ﺗﺮﮐﯿﺐ ﻣﯽ ﺷﻮﻧﺪ. از ﻣﺰاﯾﺎي روش درﺳﺘﻨﻤﺎﯾﯽ ﺑﻠﻮﮐﯽ اﯾﻦ اﺳﺖ ﮐﻪ ﻧﯿﺎزي ﺑﻪ ﻣﻌﮑﻮس ﮐﺮدن و ﻣﺤﺎﺳﺒﻪ دﺗﺮﻣﯿﻨﺎن ﻣﺎﺗﺮﯾﺲ ﻫﺎي ﺑﺎ اﺑﻌﺎد ﺑﺎﻻ ﻧﺪارد. ﺳﭙﺲ ﺑﺎ اﺳﺘﻔﺎده از ﻣﻄﺎﻟﻌﻪ ﺷﺒﯿﻪ ﺳﺎزي روش اراﺋﻪ ﺷﺪه در اﯾﻦ ﻣﻘﺎﻟﻪ ﺑﺎ روش درﺳﺘﻨﻤﺎﯾﯽ ﻣﺮﮐﺐ ﺑﻠﻮﮐﯽ زوﺟﯽ از ﻧﻈﺮ ﮐﺎراﯾﯽ و ﻣﺤﺎﺳﺒﺎﺗﯽ ﻣﻘﺎﯾﺴﻪ ﻣﯽ ﺷﻮد. ﻣﻄﺎﻟﻌﺎت ﺷﺒﯿﻪ ﺳﺎزي ﻧﺸﺎن ﻣﯽ دﻫﺪ ﮐﻪ ﺑﺮآوردﮔﺮﻫﺎي ﺣﺎﺻﻞ از روش اراﺋﻪ ﺷﺪه ﺑﻪ ﺧﻮﺑﯽ ﺑﺮآوردﮔﺮﻫﺎي درﺳﺘﻨﻤﺎﯾﯽ اﺳﺖ. در ﻧﻬﺎﯾﺖ ﯾﮏ داده واﻗﻌﯽ ﻣﻮرد ﺗﺤﻠﯿﻞ ﻗﺮار ﺧﻮاﻫﺪ ﮔﺮﻓﺖ.

In this paper parameters of spatial covariance functions have been estimated using block composite likelihood method. In this method, the block composite likelihood is constructed from the joint densities of paired spatial blocks. For this purpose, after differencing data, large data sets are splited into many smaller data sets. Then each separated blocks evaluated separately and finally combined through a simple summation. The advantage of this method is that there is no need to inverse and to find determination of high dimensional matrices. The simulation shows that the block composite likelihood estimates as well as the pair composite likelihood. Finally a real data is analysed.