• Title/Summary/Keyword: Asymptotic variance

Search Result 142, Processing Time 0.019 seconds

Asymptotic Distribution of Sample Autocorrelation Function for the First-order Bilinear Time Series Model

  • Kim, Won-Kyung
    • Journal of the Korean Statistical Society
    • /
    • v.19 no.2
    • /
    • pp.139-144
    • /
    • 1990
  • For the first-order bilinear time series model $X_t = aX_{t-1} + e_i + be_{t-1}X_{t-1}$ where ${e_i}$ is a sequence of independent normal random variables with mean 0 and variance $\sigma^2$, the asymptotic distribution of sample autocarrelation function is obtained and shown to follow a normal distribution. The variance of the asymptotic distribution is of a complicated form and hence a bootstrap estimate of the variance is proposed for large sample inference. This result can be used to distinguish between different bilinear models.

  • PDF

A Note on the Asymptotic Property of S2 in Linear Regression Model with Correlated Errors

  • Lee, Seung-Chun
    • Communications for Statistical Applications and Methods
    • /
    • v.10 no.1
    • /
    • pp.233-237
    • /
    • 2003
  • An asymptotic property of the ordinary least squares estimator of the disturbance variance is considered in the regression model with correlated errors. It is shown that the convergence in probability of S$^2$ is equivalent to the asymptotic unbiasedness. Beyond the assumption on the design matrix or the variance-covariance matrix of disturbances error, the result is quite general and simplify the earlier results.

Asymptotics of the Variance Ratio Test for MA Unit Root Processes

  • Lee, Jin
    • Communications for Statistical Applications and Methods
    • /
    • v.17 no.2
    • /
    • pp.223-229
    • /
    • 2010
  • We consider the asymptotic results of the variance ratio statistic when the underlying processes have moving average(MA) unit roots. This degenerate situation of zero spectral density near the origin cause the limit of the variance ratio to become zero. Its asymptotic behaviors are different from non-degenerating case, where the convergence rate of the variance ratio statistic is formally derived.

The Asymptotic Variance of the Studentized Residual Autocorrelations for a Generalized Random Coefficient Autoregressive Processes

  • Park, Sang-Woo;Cho, Sin-Sup;Hwang, Sun Y.
    • Journal of the Korean Statistical Society
    • /
    • v.26 no.4
    • /
    • pp.531-541
    • /
    • 1997
  • The asymptotic distribution of residual autocorrelation functions from a generalized p-order random coefficient autoregressive process (GRCA(p)) is derived. To this end, we first describe the GRCA(p) models and then consider the normalised residuals after fitting the model. This result can be applied to the residual analysis for the diagonostic purpose.

  • PDF

On Copas′ Local Likelihood Density Estimator

  • Kim, W.C.;Park, B.U.;Kim, Y.G.
    • Journal of the Korean Statistical Society
    • /
    • v.30 no.1
    • /
    • pp.77-87
    • /
    • 2001
  • Some asymptotic results on the local likelihood density estimator of Copas(1995) are derived when the locally parametric model has several parameters. It turns out that it has the same asymptotic mean squared error as that of Hjort and Jones(1996).

  • PDF

On Asymptotic Property of Matheron′s Spatial Variogram Estimators

  • Lee, Yoon-Dong;Lee, Eun-Kyung
    • Journal of the Korean Statistical Society
    • /
    • v.30 no.4
    • /
    • pp.573-583
    • /
    • 2001
  • A condition in which the covariances of Matheron's variogram estimators are expressed in a simple form is reviewed. An asymptotic property of the covariances of the variogram estimators is examined, and a sufficient condition that guaranties the finiteness of the asymptotic variance of the normalized variogram estimators is provided.

  • PDF

Asymptotic Properties of Least Square Estimator of Disturbance Variance in the Linear Regression Model with MA(q)-Disturbances

  • Jong Hyup Lee;Seuck Heum Song
    • Communications for Statistical Applications and Methods
    • /
    • v.4 no.1
    • /
    • pp.111-117
    • /
    • 1997
  • The ordinary least squares estimator $S^2$ for the variance of the disturbances is considered in the linear regression model with sutocorrelated disturbances. It is proved that the OLS-estimator of disturbance variance is asymptotically unbiased and weakly consistent, when the distrubances are generated by an MA(q) process. In particular, the asymptotic unbiasedness and consistency of $S^2$ is satisfied without any restriction on the regressor matrix.

  • PDF

Optimal step stress accelerated life tests for the exponential distribution under periodic inspection and type I censoring

  • Moon, Gyoung-Ae;Park, Yong-Kil
    • Journal of the Korean Data and Information Science Society
    • /
    • v.20 no.6
    • /
    • pp.1169-1175
    • /
    • 2009
  • In this paper, the inferences of data obtained from periodic inspection and type I censoring for the step-stress accelerated life test are studied. The exponential distribution with a failure rate function that a log-linear function of stress and the tampered failure rate model are considered. The maximum likelihood estimators of the model parameters are estimated and also the optimal stress change time which minimize the asymptotic variance of maximum likelihood estimators of parameters is determined. A numerical example will be given to illustrate the proposed inferential procedures and the sensitivity of the asymptotic variance of the estimated mean by the guessed parameters is investigated.

  • PDF

Minimax Choice and Convex Combinations of Generalized Pickands Estimator of the Extreme Value Index

  • Yun, Seokhoon
    • Journal of the Korean Statistical Society
    • /
    • v.31 no.3
    • /
    • pp.315-328
    • /
    • 2002
  • As an extension of the well-known Pickands (1975) estimate. for the extreme value index, Yun (2002) introduced a generalized Pickands estimator. This paper searches for a minimax estimator in the sense of minimizing the maximum asymptotic relative efficiency of the Pickands estimator with respect to the generalized one. To reduce the asymptotic variance of the resulting estimator, convex combinations of the minimax estimator are also considered and their asymptotic normality is established. Finally, the optimal combination is determined and proves to be superior to the generalized Pickands estimator.