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Which is true if T is consistent estimator of 0?
If the sequence of estimates can be mathematically shown to converge in probability to the true value θ0, it is called a consistent estimator; otherwise the estimator is said to be inconsistent. Consistency is related to bias; see bias versus consistency.
When is a sequence of estimates called a consistent estimator?
In this way one would obtain a sequence of estimates indexed by n, and consistency is a property of what occurs as the sample size “grows to infinity”. If the sequence of estimates can be mathematically shown to converge in probability to the true value θ 0, it is called a consistent estimator; otherwise the estimator is said to be inconsistent.
How is consistency a property of an estimator?
In practice one constructs an estimator as a function of an available sample of size n, and then imagines being able to keep collecting data and expanding the sample ad infinitum. In this way one would obtain a sequence of estimates indexed by n, and consistency is a property of what occurs as the sample size “grows to infinity”.
Which is the limiting distribution of the sequence?
The limiting distribution of the sequence is a degenerate random variable which equals θ0 with probability 1. In statistics, a consistent estimator or asymptotically consistent estimator is an estimator —a rule for computing estimates of a parameter θ0 —having the property that as the number of data points used increases indefinitely,
How to estimate μ based on the first n observations?
To estimate μ based on the first n observations, one can use the sample mean: Tn = ( X1 + + Xn )/ n. This defines a sequence of estimators, indexed by the sample size n . From the properties of the normal distribution, we know the sampling distribution of this statistic: Tn is itself normally distributed, with mean μ and variance σ2 / n.