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# 统计代写|概率模型代写Statistical Model代考|STA3064 Third assumption

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## 统计代写|概率模型代写Statistical Model代考|Third assumption

If we also assume that the observations are conditionally independent, then the least-squares estimates have the smallest variance among all unbiased linear estimates. Since the estimates were computed by minimizing the residual variation, this outcome should not be particularly surprising. The assumption of conditional independence is harder to check definitively. Checking this assumption appropriately will usually require the use of some knowledge about the design of the data collection. Generally the analyst will use information about the design to guide the choice of the types of dependence to check. For example, if groups of the observations have similar origin, clustering, then it may be worth checking for intra-group correlation, and if the data have a time stamp then checking for autocorrelation is an important consideration.

## 统计代写|概率模型代写Statistical Model代考|Fourth condition

This point is mentioned because it is relevant here, although it resides more naturally with Section 3.3. It is not really an assumption about the conditional distribution of the response variable, as such. Least-squares estimates can be expressed as sums of conditionally independent random variables, so the estimates are subject to the Central Limit Theorem. The interested reader can learn more from Huber (1981, Theorem 2.3, Chapter 7), Demidenko (2004, $\S 13.1 .1)$, and DasGupta (2008, Theorem $5.3$ and Example 5.1). Consequently, asymptotically, the estimates are normally distributed. This observation can be used to justify an assumption of normality for the parameter estimates, which can in turn be used to construct interval estimates and hypothesis tests. However, the assumption of conditionally normal errors, as in Section 3.3, is more commonly used. We discuss this point further in Section 3.4.8.4.

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