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let x1 xnnbspbe iid binary random variables with pxinbsp 1 theta where theta isin 0 1 is unknown and n is an even
consider an estimation problem with p ptheta theta isin theta a parametric family a theta and the squared error loss
suppose that the action space is bk where isin bk let x be a sample from p isin p delta0x be a nonrandomized rule
nonexistence of an unbiased estimator let x be a random variable having the binomial distribution bip n with an unknown
let x1 xnnbspbe iid random variables having the normal distribution ntheta 1 where theta 0 or 1 consider the
let t be a complete or boundedly complete and sufficient statistic suppose that there is a minimal sufficient statistic
let t and s be two statistics such that s psit for a measurable psi show thata if t is complete then s is completeb
let x1 xnnbspbe iid from the ntheta theta2 distribution where theta gt 0 is a parameter find a minimal sufficient
consider the estimation of an unknown parameter theta ge 0 under the squared error loss show that if t and u are two
let x1 xnnbspbe iid random variables from patheta where a theta isin r2nbspis a parameter find a two-dimensional
let x and y be two random variables such that y has the binomial distribution bipi n and given y y x has the binomial
let x1 xnnbspbe iid random variables having a distribution p isin p where p is the family of distributions on r having
a coin has probability p of coming up heads and 1 - p of coming up tails where p isin 0 1 the first stage of an
let x1 xn be iid random variables having the cauchy distribution cmicro sigma with unknown micro isin r and sigma gt 0
let x1 xnnbspbe iid random variables having the double exponential distribution demicro theta with unknown micro isin
let x1 xnnbspbe iid random variables having the weibull distribution walpha theta with unknown alpha gt 0 and theta gt
let x1 xnnbspbe iid random variables having the beta distribution bbeta beta with an unknown beta gt 0 find a
a box has an unknown odd number of balls labeled consecutively as -theta -theta - 1 -2 -1 0 1 2 theta - 1 theta where
let x1 xnnbspbe iid random variables having the lebesgue pdf theta-1e-x-thetathetaithetainfinx where theta gt 0 is an
let x be a random variable with a distribution pthetanbspin ptheta theta isin theta fthetanbspbe the pdf of
show that the family of weibull distributions walpha theta with two unknown parameters alpha and theta is not an
is the family of log-normal distributions lnmicro sigma2 with two unknown parameters micro and sigma2nbspan exponential
show that the family of double exponential distributions demicro theta with two unknown parameters micro and theta is
let x be a random variable with a pdf fthetanbspin an exponential family pthetanbsp theta isin theta and let a be a
let pmicrosigma micro isin rk sigma isin mk be a location-scale family on rk suppose that p0ik has a lebesgue pdf that