Тема: «Интегральная форма МНК»

Впредь вместо будем писать

Предположим, что наши реализации случайных функций зависят от параметров , , в этом случае нашу задачу на МНК можно переписать:

Умножим обе части равенства на

(*)

Определение интеграла:

t0=a

t1

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t2

L t1UKDXHTtVBSKC5JzEtJzMnPS7VVqkwtVrK34+UCAAAA//8DAFBLAwQUAAYACAAAACEANi2BocYA AADbAAAADwAAAGRycy9kb3ducmV2LnhtbESPQWvCQBSE74L/YXmF3nTTgNWmriKBYCl6SOqlt9fs MwnNvo3Zrab+elco9DjMzDfMcj2YVpypd41lBU/TCARxaXXDlYLDRzZZgHAeWWNrmRT8koP1ajxa YqLthXM6F74SAcIuQQW1910ipStrMuimtiMO3tH2Bn2QfSV1j5cAN62Mo+hZGmw4LNTYUVpT+V38 GAXvabbH/Cs2i2ubbnfHTXc6fM6UenwYNq8gPA3+P/zXftMKXuZw/xJ+gFzdAAAA//8DAFBLAQIt ABQABgAIAAAAIQDw94q7/QAAAOIBAAATAAAAAAAAAAAAAAAAAAAAAABbQ29udGVudF9UeXBlc10u eG1sUEsBAi0AFAAGAAgAAAAhADHdX2HSAAAAjwEAAAsAAAAAAAAAAAAAAAAALgEAAF9yZWxzLy5y ZWxzUEsBAi0AFAAGAAgAAAAhADMvBZ5BAAAAOQAAABAAAAAAAAAAAAAAAAAAKQIAAGRycy9zaGFw ZXhtbC54bWxQSwECLQAUAAYACAAAACEANi2BocYAAADbAAAADwAAAAAAAAAAAAAAAACYAgAAZHJz L2Rvd25yZXYueG1sUEsFBgAAAAAEAAQA9QAAAIsDAAAAAA== " filled="f" stroked="f" strokeweight=".5pt">

……….

L t1UKDXHTtVBSKC5JzEtJzMnPS7VVqkwtVrK34+UCAAAA//8DAFBLAwQUAAYACAAAACEAR7IV08IA AADbAAAADwAAAGRycy9kb3ducmV2LnhtbERPy2rCQBTdC/7DcIXudKLQojGjSECU0i5M3bi7Zm4e mLkTM6NJ+/WdRaHLw3kn28E04kmdqy0rmM8iEMS51TWXCs5f++kShPPIGhvLpOCbHGw341GCsbY9 n+iZ+VKEEHYxKqi8b2MpXV6RQTezLXHgCtsZ9AF2pdQd9iHcNHIRRW/SYM2hocKW0oryW/YwCt7T /Seerguz/GnSw0exa+/ny6tSL5NhtwbhafD/4j/3UStYhbHhS/gBcvMLAAD//wMAUEsBAi0AFAAG AAgAAAAhAPD3irv9AAAA4gEAABMAAAAAAAAAAAAAAAAAAAAAAFtDb250ZW50X1R5cGVzXS54bWxQ SwECLQAUAAYACAAAACEAMd1fYdIAAACPAQAACwAAAAAAAAAAAAAAAAAuAQAAX3JlbHMvLnJlbHNQ SwECLQAUAAYACAAAACEAMy8FnkEAAAA5AAAAEAAAAAAAAAAAAAAAAAApAgAAZHJzL3NoYXBleG1s LnhtbFBLAQItABQABgAIAAAAIQBHshXTwgAAANsAAAAPAAAAAAAAAAAAAAAAAJgCAABkcnMvZG93 bnJldi54bWxQSwUGAAAAAAQABAD1AAAAhwMAAAAA " filled="f" stroked="f" strokeweight=".5pt">

tk-1

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tk

L t1UKDXHTtVBSKC5JzEtJzMnPS7VVqkwtVrK34+UCAAAA//8DAFBLAwQUAAYACAAAACEAaZQKA8cA AADcAAAADwAAAGRycy9kb3ducmV2LnhtbESPzWvCQBDF7wX/h2WE3upGoUVSNyIBaRF78OPS2zQ7 +aDZ2ZhdNfav7xwEbzO8N+/9ZrEcXKsu1IfGs4HpJAFFXHjbcGXgeFi/zEGFiGyx9UwGbhRgmY2e Fphaf+UdXfaxUhLCIUUDdYxdqnUoanIYJr4jFq30vcMoa19p2+NVwl2rZ0nyph02LA01dpTXVPzu z87AJl9/4e5n5uZ/bf6xLVfd6fj9aszzeFi9g4o0xIf5fv1pBT8RfHlGJtDZPwAAAP//AwBQSwEC LQAUAAYACAAAACEA8PeKu/0AAADiAQAAEwAAAAAAAAAAAAAAAAAAAAAAW0NvbnRlbnRfVHlwZXNd LnhtbFBLAQItABQABgAIAAAAIQAx3V9h0gAAAI8BAAALAAAAAAAAAAAAAAAAAC4BAABfcmVscy8u cmVsc1BLAQItABQABgAIAAAAIQAzLwWeQQAAADkAAAAQAAAAAAAAAAAAAAAAACkCAABkcnMvc2hh cGV4bWwueG1sUEsBAi0AFAAGAAgAAAAhAGmUCgPHAAAA3AAAAA8AAAAAAAAAAAAAAAAAmAIAAGRy cy9kb3ducmV2LnhtbFBLBQYAAAAABAAEAPUAAACMAwAAAAA= " filled="f" stroked="f" strokeweight=".5pt">

……….

L t1UKDXHTtVBSKC5JzEtJzMnPS7VVqkwtVrK34+UCAAAA//8DAFBLAwQUAAYACAAAACEA7E2c3sYA AADcAAAADwAAAGRycy9kb3ducmV2LnhtbESPT2vCQBDF74V+h2WE3upGoUVSNyIBUaQetF56m2Yn fzA7m2ZXTf30nYPgbYb35r3fzBeDa9WF+tB4NjAZJ6CIC28brgwcv1avM1AhIltsPZOBPwqwyJ6f 5phaf+U9XQ6xUhLCIUUDdYxdqnUoanIYxr4jFq30vcMoa19p2+NVwl2rp0nyrh02LA01dpTXVJwO Z2dgm692uP+Zutmtzdef5bL7PX6/GfMyGpYfoCIN8WG+X2+s4E8EX56RCXT2DwAA//8DAFBLAQIt ABQABgAIAAAAIQDw94q7/QAAAOIBAAATAAAAAAAAAAAAAAAAAAAAAABbQ29udGVudF9UeXBlc10u eG1sUEsBAi0AFAAGAAgAAAAhADHdX2HSAAAAjwEAAAsAAAAAAAAAAAAAAAAALgEAAF9yZWxzLy5y ZWxzUEsBAi0AFAAGAAgAAAAhADMvBZ5BAAAAOQAAABAAAAAAAAAAAAAAAAAAKQIAAGRycy9zaGFw ZXhtbC54bWxQSwECLQAUAAYACAAAACEA7E2c3sYAAADcAAAADwAAAAAAAAAAAAAAAACYAgAAZHJz L2Rvd25yZXYueG1sUEsFBgAAAAAEAAQA9QAAAIsDAAAAAA== " filled="f" stroked="f" strokeweight=".5pt">

tn-1

L t1UKDXHTtVBSKC5JzEtJzMnPS7VVqkwtVrK34+UCAAAA//8DAFBLAwQUAAYACAAAACEAgwE5RcMA AADcAAAADwAAAGRycy9kb3ducmV2LnhtbERPTYvCMBC9C/sfwgjeNK2gSNcoUhBl0YNuL3ubbca2 2Ey6TVarv94Igrd5vM+ZLztTiwu1rrKsIB5FIIhzqysuFGTf6+EMhPPIGmvLpOBGDpaLj94cE22v fKDL0RcihLBLUEHpfZNI6fKSDLqRbYgDd7KtQR9gW0jd4jWEm1qOo2gqDVYcGkpsKC0pPx//jYKv dL3Hw+/YzO51utmdVs1f9jNRatDvVp8gPHX+LX65tzrMj2N4PhMukIsHAAAA//8DAFBLAQItABQA BgAIAAAAIQDw94q7/QAAAOIBAAATAAAAAAAAAAAAAAAAAAAAAABbQ29udGVudF9UeXBlc10ueG1s UEsBAi0AFAAGAAgAAAAhADHdX2HSAAAAjwEAAAsAAAAAAAAAAAAAAAAALgEAAF9yZWxzLy5yZWxz UEsBAi0AFAAGAAgAAAAhADMvBZ5BAAAAOQAAABAAAAAAAAAAAAAAAAAAKQIAAGRycy9zaGFwZXht bC54bWxQSwECLQAUAAYACAAAACEAgwE5RcMAAADcAAAADwAAAAAAAAAAAAAAAACYAgAAZHJzL2Rv d25yZXYueG1sUEsFBgAAAAAEAAQA9QAAAIgDAAAAAA== " filled="f" stroked="f" strokeweight=".5pt">

tn=b

Точки – берутся произвольно, главное из промежутка

–интегральная сумма

t1

t2

……….

tk-1

tk

……….

tn-1

Точно также сумма правой части в оптимизационной задачи (*) будет стремиться при к интегралу:

Наша задача на МНК в интегральной форме будет иметь вид:

(**)