1.6 Автокорельовані популяції
Для багатьох реальних популяцій є підстави очікувати, що два спостереження
![](data:image/png;base64,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)
та
![](data:image/png;base64,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)
будуть більш схожими, якщо одиниці
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAkAAAARCAYAAAAPFIbmAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAACNSURBVCjPY2hsbGQghBnIUgQEjEDMhFdRnodsEQOD8e3Y+npJ8q0DWQPFjFgV1dfHShozMNwGKvhnHN3gg9Okjo40Hnc541nI7sFQVJ3lYiRrHNWL1005brLFsh55RTgVgazykJVd6ZFXb4hTEcjhRgxGe6Kj3cLRFcIZDbHG3kCf/WUwjl5AnbijrSIAJrDaRde1p1wAAAAASUVORK5CYII=)
та
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAAUCAYAAABWMrcvAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADDSURBVDjLY2hsbGQgFTPQRNMqBgYmBoZQZpI0RRkzzGdgMLoVW18vSRvnQZzFwMzAsIqJaE0QZzH8ZZD12J3W0cFDtJ/qI419ZT3yioi2CQgYo4xlez3y6g2J1lSd5WIkK+u5At1peDXluMmWyLrlFBMdeh0daTweMgx7jGMbvInWBHYag/FJ5AjFqokBEi+MIAx2GpZQQ9FUXx8racQge8olq9oYaIsx0JYTuGxB08RwC2jLHwZZ913YQoz2WWNgNQEA9zt1lOF9qBoAAAAASUVORK5CYII=)
розташовані в ряді недалеко одна від одної. Таке буває, коли будь-які природні причини обумовлюють повільну зміну значень при просуванні вздовж ряду. В математичній моделі такої ситуації можна вважати, що між
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAYCAYAAAAcYhYyAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAE0SURBVDjL7ZSxTsMwEIb/0rUvUKjzDE2PvgFqLgodAyqWJ6QOqIqEOnQokpMtCzsbzHmE0hcBqQ/QdwBBbBQRkIEWRjrccLbv0//7zkaWZfhrYAf5d5AC2APQBOJmtfYCNOr5j5Azwm1Z8YwOL8d53jJrqaIIgu+rfCM7qaRjgFZK67bJ83zcYuKrrSA6YV9APHCifZPPZmqfOYm3ulitVZuAFcm0VIRGMhicVKpsUXlvm0NGeji/OOr1eXJe7VlrfZ7XrTkh9mAHSxHw9aHHN/WCt+597NSXkFBgAfQe6zZMSMIdRLhwKoGdhcJ6jcs5kVKGTqsjGpJKI6cS2xERFGqmDoJSBSkduSCSSH9W9z4bU+56wBrw1jxNuy6AabXvn2aV4l+9HW0mF3gSPLnc/Sffxyvr9k05ok+r7wAAAABJRU5ErkJggg==)
та
![](data:image/png;base64,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)
існує додатна кореляція, яка залежить тільки від відстані між ними,
![](data:image/png;base64,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)
, та прямує до нуля при збільшенні цієї відстані.
Для з’ясування того, чи можна застосовувати цю модель до конкретної популяції, можна обчислити коефіцієнти кореляції
![](data:image/png;base64,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)
між парами спостережень, що знаходяться на відстані
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAAPCAYAAAA/I0V3AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADTSURBVDjLY2hsbGQgFTMMjCYgYARiZgaGVUwwsf9gsf+MWDWBNNRHGvsCVfxlMI5eABPPcZMtlvXIK8KqqSHW2JvBOGo+UFEJTBHIoCgj2T6PvHpDnM4rL4+VMmKQPQVTVJ3lYiTLYHQqtr5eEqcmkPMYZD12p3V08IBtMWZYiOxUrJpAikBOg/lPVlb2iHF0gw/OgKivj5UEOc0lq9oY6CxjOROPme5yxrNDq0ONjY2j6/BoYrgFtOUPg6z7rrw8Dxs5BoaXDAxGt/D6aZAnI2IxAJrxEErOAiiLAAAAAElFTkSuQmCC)
одиниць одне від одного, та побудувати графік відповідних значень як функції
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAAPCAYAAAA/I0V3AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADTSURBVDjLY2hsbGQgFTMMjCYgYARiZgaGVUwwsf9gsf+MWDWBNNRHGvsCVfxlMI5eABPPcZMtlvXIK8KqqSHW2JvBOGo+UFEJTBHIoCgj2T6PvHpDnM4rL4+VMmKQPQVTVJ3lYiTLYHQqtr5eEqcmkPMYZD12p3V08IBtMWZYiOxUrJpAikBOg/lPVlb2iHF0gw/OgKivj5UEOc0lq9oY6CxjOROPme5yxrNDq0ONjY2j6/BoYrgFtOUPg6z7rrw8Dxs5BoaXDAxGt/D6aZAnI2IxAJrxEErOAiiLAAAAAElFTkSuQmCC)
. Цей графік, чи функція, яку він представляє, називається корелограмою. Навіть якщо модель можна застосовувати до будь-якої скінченої популяції, корелограма для неї не буде гладкою функцією через неправильності, обумовлені скінченим характером популяції. При порівнянні систематичного та стратифікованого випадкового відборів із популяцій, що описуються моделлю, ці неправильності ускладнюють отримання результатів для будь-якої скінченої популяції. Таке порівняння можна провести, якщо розглядати середнє з цілого ряду популяцій, отриманих навмання з деякої нескінченої надпопуляції, до якої можна застосувати цю модель. Такий прийом вже застосовувався в теоремі 1.3.2.
Отже, ми припускаємо, що спостереження
![](data:image/png;base64,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)
вилучені з над популяції, для якої
![](data:image/png;base64,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)
(1.6.1)
де
![](data:image/png;base64,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)
при довільних
![](data:image/png;base64,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)
.
Здобуття одного набору значень
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAYCAYAAAAcYhYyAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAEoSURBVDjL7VSxUsJAEH1gyw/AcPkGwuofOHEZoFQHb1I5k4LiCihSqHOXLo29ndb5BOFHdIYP4B90lIsTiZkTQUsptni53Xf79u0FSZLgr4E9yb8jyYA6gAMgq38mAbUy/pHkgnC/KnpFm+dRmjbsNxNSH4JnBd5KjpE0AGgRat20OE2jRkDBzU4kWrEvIJ5Yad/iOA5bzOp0p8FqHTYJWJA0AzsPFQRnRVfFjLYnGenh1fi4e8Tqsjiz0pj4uizNSZIntjEXzLeHHt+VCz7c++rU9yQCM6D7XJZhQxIeqk7BtQv2Nillzyl1REMKTd/ZSe6IOMmiOGr1BB6rietOSFe7W+/GlDsesAS8JU9Nx0Vgrfb981XVW+3XbyffXOBF8Hiy/59sjnePEE3vaZSwIAAAAABJRU5ErkJggg==)
з цієї надпопуляції призводить до утворення деякої скінченої популяції обсягом
![](data:image/png;base64,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)
.
Середня дисперсія по всім скінченим популяціям при систематичному відборі позначається через
![](data:image/png;base64,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)
.
Для цього класу популяцій неважко показати, що стратифікований випадковий відбір краще простого випадкового відбору, але відносно систематичного відбору загального твердження сформулювати не можна. Всередині цього класу існують надпопуляції, для яких систематичний відбір краще стратифікованого випадкового відбору, але існують і такі, для яких, при певних значеннях
![](data:image/png;base64,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)
, систематичний відбір поступається стратифікованому випадковому відбору.
Якщо припустити, що корелограма є випуклою вниз функцією, то можна довести одну загальну теорему.
Теорема 1.6.1. Якщо, разом з умовами (1.6.1), виконується
![](data:image/png;base64,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)
,
![](data:image/png;base64,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)
,
то при будь якому обсязі вибірки
![](data:image/png;base64,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)
.
Далі, за винятком випадку
![](data:image/png;base64,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)
, виконується
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAH8AAAAZCAYAAAAYEPFUAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAK+SURBVGje7ZmxTsMwEIb9ADwAlTAbD0DNympcxFyJWplATMgLM0q7dYAXYGNk4AnaJ+gbMPAGvAPICU7c9M5O06TU1MNJKE3iu+/Od78DmUwmJNp+WoQQkx8tJj9aTH60PU7+PacPhJBvzJgcX+n7Roy8gvew0Su2YJomvT7pz5I07bUZSFfvDZmL753og2PJrgihX0Klp+badHp3ICh9s6/lQNinWUAvyAj5JEdifjedHqy+s7w3c8ABc+1glTilhH7Y/rVt2+LSFhsXE3eVA44qzoe2k1mVVyo6D6bcCdvamWWw/UVX64TIBWOCPqCdp/z+oahsIW+gtqKr2Q5mqcqt4O33dW1Zghwt1vWcz8dQuUBM0FlhO68rFnIQa1cZlCMyN4vl1U0XUOsp5qO1m7L3Arurq91vZrkvCSFzgZg45hosZlYcBJypVjgGA4OlIXHGHxsnH9l5GOC6Oy9kLhATHMqvg3rBi2P2glUxBC6vMvJlfquKH58o0Y5yroabqFwdKJZUk3RfcfwnLhCTWhUihbhZqWKHiszhlkF5g6ysWRVPbSbfJGDd5IfOpVbyoaNMqWjZrbmOqV5I0framx2khse4ut30fNt22w+dS622j80rOyhsZ2Ht1CVsllrlYPDEji9ems76LgVfCFyw04dX8NntEDMdlPMrl0OJuo40hQpGdkGhfM/Eu1HLGWgESJtHvSC4aB6ecVb7qNfJhwZPlUspBxgAW+HaSVdJcg4p6m18TNo1Lnkx0GfoPRiT7QZqiaHsbyre1Fgd6up2zWd73pmg9XNJos6bzPqdK4AWuGCd0MXkjyq9P5NKXOZtChZRmKgqjlgJH9rPhbbj2+YCCcLG/9jZBStn3vLchL6b75NBXArNsQaXoIKWjKXXqTqptvtozSwoZ3N1W68dRvtnyY8Wkx8tJj/apvYDPtgcRXuYp/sAAAAASUVORK5CYII=)
.
Теорема 1.6.1 була доведена Кокреном у 1946 році.
Наведемо частину доведення при
![](data:image/png;base64,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)
, яка показує, яку роль відіграє умова випуклості вгору. Члени пари, які утворюють систематичну вибірку, завжди відстоять один від одного на
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAATCAYAAABLN4eXAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAC4SURBVDjLY2hsbGQgFTMMIU319bGSxgwMdxkYGP7LuuUUE20TSKMRg+wpj7x6Q+I15XkYysp6rEzr6OAhWlOOm2wxg3HUQqL91NGRxuMhw7DHOLrBB2wjA8MbkP/Q/YjpNAajU7H19ZLgQDGOridoE8xpyJoJaooyZlgIcw4Dg/FdgpqQgxpik+xNXMEOZzREG/swyHjsAQU1LEBAngezPaKTsWoCOQ05hMD+AztT9g26jUMplROLAcI8Z5L9Aa5bAAAAAElFTkSuQmCC)
одиниць. Отже,
![](data:image/png;base64,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)
.
У випадку стратифікованої вибірки для кожної одиниці, що вилучається з відповідної страти, існує
![](data:image/png;base64,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)
можливих місць, що утворюють
![](data:image/png;base64,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)
можливих комбінацій розташування вибірки. Числа комбінацій, для яких відстань між одиницями складає
![](data:image/png;base64,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)
, будуть такими:
Отже, середнє значення
![](data:image/png;base64,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)
, яке береться по всім
![](data:image/png;base64,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)
комбінаціям, може бути подане у вигляді
![](data:image/png;base64,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)
Аналогічно
![](data:image/png;base64,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)
можна виразити у вигляді
![](data:image/png;base64,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)
Отже,
![](data:image/png;base64,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)
Якщо
![](data:image/png;base64,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)
,
то неважко показати, що кожний член всередині дужок додатний. Теорема доведена.
Середня відстань між одиницями дорівнює
![](data:image/png;base64,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)
як для систематичної вибірки, так і для стратифікованої вибірки, але завдяки умові випуклості стратифікована вибірка більш програє у точності, коли відстань між одиницями менше
![](data:image/png;base64,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)
, ніж виграє, коли ця відстань більше
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAATCAYAAABLN4eXAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAC4SURBVDjLY2hsbGQgFTMMIU319bGSxgwMdxkYGP7LuuUUE20TSKMRg+wpj7x6Q+I15XkYysp6rEzr6OAhWlOOm2wxg3HUQqL91NGRxuMhw7DHOLrBB2wjA8MbkP/Q/YjpNAajU7H19ZLgQDGOridoE8xpyJoJaooyZlgIcw4Dg/FdgpqQgxpik+xNXMEOZzREG/swyHjsAQU1LEBAngezPaKTsWoCOQ05hMD+AztT9g26jUMplROLAcI8Z5L9Aa5bAAAAAElFTkSuQmCC)
.