Journal ArticleDOI
On estimation and testing for the folded normal distribution
Reads0
Chats0
TLDR
In this article, the large sample behaviour of the maximum likelihood estimate in this non-regular case is investigated. But the results of the analysis are restricted to the case where σ is known and σ = 0, and the estimate of μ is consistent at a rate of convergence of order n-1/4.Abstract:
For the folded normal distribution, generated froma N(μσ2) by loss of the signs of observations, μ=o corresponds to a non-regular case of estimation and testing. The large sample behaviour of the maximum likelihood estimate in this non-regular case is investigated. If σ is known, the estimate of μ is consistent at a rate of convergence of order n-1/4; if 0 is unknown the rate is or order n-1/8, as the sample size n tends to infinity. As a by-product it is shown that a moment method of estimation proposed by Elandt (1961) is locally asymptotically(as μ/σ→ 0 and n→∞).equivalent to the maximum likelihood method. Tests ofμ=0 are derived from the point of view of local optimality. In direct correspondence to the slow consistency of the estimates, the tests have very slowly increasing power functions.read more
Citations
More filters
Posted Content
On the Folded Normal Distribution
TL;DR: In this paper, the authors derived the characteristic function of the folded normal distribution and its moment function using Taylor series and obtained the maximum likelihood estimates and confidence intervals for the parameters using the asymptotic theory and bootstrap method.
Maximum Likelihood Theory for Incomplete Data from an Exponential Family
TL;DR: In this article, the authors studied distribu- tions which are generated from exponential families by loss of information due to the fact that only some function of the exponential family variable is observable.
Journal ArticleDOI
On the Folded Normal Distribution
TL;DR: In this paper, the authors derived the characteristic function of the folded normal distribution and its moment function using Taylor series and obtained the maximum likelihood estimates and confidence intervals for the parameters using the asymptotic theory and bootstrap method.
Journal ArticleDOI
The folded t distribution
Stelios Psarakis,J. Panaretoes +1 more
TL;DR: In this paper, the relationship between the folded-t distribution and a special case of the folded normal distribution was studied, where the underlying distribution of measurements is replaced by a distribution of absolute measurements.
Book
Statistical Modelling by Exponential Families
TL;DR: This book is a readable, digestible introduction to exponential families, encompassing statistical models based on the most useful distributions in statistical theory, including the normal, gamma, binomial, Poisson, and negative binomial.
References
More filters
Journal ArticleDOI
The Folded Normal Distribution
TL;DR: In this paper, the authors describe methods for estimating the mean and standard deviation of the normal distribution based on estimates of the estimated mean and the standard deviation determined from the folded normal.
Journal ArticleDOI
On Optimal Asymptotic Tests of Composite Statistical Hypotheses
James B. Bartoo,Prem S. Puri +1 more
TL;DR: In this article, a locally asymptotically most powerful test for a composite hypothesis $H:\xi = \xi_0$ has been developed for the case where the observable random variables $\{X_{nk}, k = 1, 2, \cdots, n\}$ are independently but not necessarily identically distributed.
Journal ArticleDOI
The Folded Normal Distribution: Two Methods of Estimating Parameters from Moments
TL;DR: In this article, a general formula for the rth moment of the folded normal distribution is obtained, and formulae for the first four non-central and central moments are calculated explicitly.
Journal ArticleDOI
The Folded Normal Distribution: Accuracy of Estimation By Maximum Likelihood
TL;DR: In this paper, a sequel of two previous papers on the subject of the Folded Normal Distribution appeared in Technometrics, S, pp. 543-550 and 551-562, (1961).