SEQUENTIAL ESTIMATION OF THE SQUARE OF THE RAYLEIGH PARAMETER

Tahir Tahir

doi:10.3844/jmssp.2014.275.280

Abstract

The problem addressed is that of sequentially estim ating the square of the parameter of the Rayleigh distribution, subject to a weighted squared loss pl us cost of sampling. We propose a sequential procedure and provide a second-order asymptotic expansion for the incurred regret. It is seen that the asymptotic regret is negative for a range of values of the parameter.

Highlights

INTRODUCTIONLet X1,,...,Xn denote independent observations to be taken sequentially up to a predetermined stage n from the Rayleigh distribution with p.d.f:
Let X1,...,Xn denote independent observations to be taken sequentially up to a predetermined stage n from the Rayleigh distribution with p.d.f: ∑ ∑ ln (θ ) = n ln xi i =1 − 2nlnθ −1 2θ 2 n ln xi2 i =1For θ>o
We propose a sequential procedure and provide a second-order asymptotic expansion for the incurred regret

Summary

INTRODUCTION

Let X1,,...,Xn denote independent observations to be taken sequentially up to a predetermined stage n from the Rayleigh distribution with p.d.f:. One might be interested in estimating the population variance σ 2 = 1⁄2(4-π)θ2 or the population second moment μ2 = 2θ2. Since both of these parameters are linear functions of θ2, it suffices to estimate θ2. Since na depends on the unknown value of θ, there is no fixed-sample-size procedure that attains the minimum risk Ra* in practice. We propose to use the sequential procedure (T,YT ) which stops the sampling process after observing Y1,...,YT and estimates θ2 by WT = YT , where Equation 3:. By Martinsek (1988), since the skewness of Y1 is equal to 2 This shows that YT is biased for large values of a. Mousa et al (2005; Prakash, 2013) focused on Bayesian prediction and Bayesian estimation for Rayleigh models

ASYMPTOTIC EXPANSION FOR THE REGRET OF THE SEQUENTIAL PROCEDURE

NEGATIVE ASYMPTOTIC REGRET

CONCLUSION