Method of Moments

# Method of Moments - Detection and Estimation(Spring 2009...

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Detection and Estimation (Spring , 2009) Method of Moments NCTU EE P.1 Method of Moments ~ Method of Moments 9 No optimal properties 9 Useful if the data record is long enough 9 Easy to implement 9 Usually consistent Example: Gaussian Mixture where and 0 < ε < 1 Assume σ 1 2 and σ 2 2 are known and

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Detection & Estimation (Spring, 2009) Method of Moments NCTU EE P.2 ε σ = = = 2 1 2 2 2 1 1 0 2 ) ] [ 1 ( ) ˆ ( N n n x N E E As N →∞ , 0 ) ˆ var( consistent! Remark: Since the estimates of the moments approach the true moments for large data records, the equation to be solved approaches the theoretical equation.
Detection & Estimation (Spring, 2009) Method of Moments NCTU EE P.3 The method of moments for a scalar parameter: Example: DC Level in WGN x[n] = A + w[n], n = 0, 1, …, N-1 Example: Exponential pdf Consider N iid observations from the exponential pdf Want to estimate λ , where λ > 0.

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Method of Moments - Detection and Estimation(Spring 2009...

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