• Title/Summary/Keyword: asymptotic normality

Search Result 140, Processing Time 0.026 seconds

Asymptotic Approximation of Kernel-Type Estimators with Its Application

  • 장유선;김성래;김성균
    • Proceedings of the Korean Society of Computational and Applied Mathematics Conference
    • /
    • 2003.09a
    • /
    • pp.12.1-12
    • /
    • 2003
  • Sufficient conditions are given under which a generalized class of kernel-type estimators allows asymptotic approximation On the modulus of continuity This generalized class includes sample distribution function, kernel-type estimator of density function, and an estimator that may apply to the censored case. In addition, an application is given to asymptotic normality of recursive density estimators of density function at an unknown point.

  • PDF

Asymptotic Normality for Threshold-Asymmetric GARCH Processes of Non-Stationary Cases

  • Park, J.A.;Hwang, S.Y.
    • Communications for Statistical Applications and Methods
    • /
    • v.18 no.4
    • /
    • pp.477-483
    • /
    • 2011
  • This article is concerned with a class of threshold-asymmetric GARCH models both for stationary case and for non-stationary case. We investigate large sample properties of estimators from QML(quasi-maximum likelihood) and QL(quasilikelihood) methods. Asymptotic distributions are derived and it is interesting to note for non-stationary case that both QML and QL give asymptotic normal distributions.

Asymptotics for Accelerated Life Test Models under Type II Censoring

  • Park, Byung-Gu;Yoon, Sang-Chul
    • Journal of the Korean Data and Information Science Society
    • /
    • v.7 no.2
    • /
    • pp.179-188
    • /
    • 1996
  • Accelerated life testing(ALT) of products quickly yields information on life. In this paper, we investigate asymptotic normalities of maximum likelihood(ML) estimators of parameters for ALT model under Type II censored data using results of Bhattacharyya(1985). Further illustrations include the treatment of asymptotic of the exponential and Weibull regression models.

  • PDF

Asymptotic Relative Efficiency of t-test Following Transformations

  • Yeo, In-Kwon
    • Journal of the Korean Statistical Society
    • /
    • v.26 no.4
    • /
    • pp.467-476
    • /
    • 1997
  • The two-sample t-test is not expected to be optimal when the two samples are not drawn from normal populations. According to Box and Cox (1964), the transformation is estimated to enhance the normality of the tranformed data. We investigate the asymptotic relative efficiency of the ordinary t-test versus t-test applied transformation introduced by Yeo and Johnson (1997) under Pitman local alternatives. The theoretical and simulation studies show that two-sample t-test using transformed date gives higher power than ordinary t-test for location-shift models.

  • PDF

Estimation for Autoregressive Models with GARCH(1,1) Error via Optimal Estimating Functions.

  • Kim, Sah-Myeong
    • Journal of the Korean Data and Information Science Society
    • /
    • v.10 no.1
    • /
    • pp.207-214
    • /
    • 1999
  • Optimal estimating functions for a class of autoregressive models with GARCH(1,1) error are discussed. The asymptotic properties of the estimator as the solution of the optimal estimating equation are investigated for the models. We have also some simulation results which suggest that the proposed optimal estimators have smaller sample variances than those of the Conditional least-squares estimators under the heavy-tailed error distributions.

  • PDF

Testing NBUCA Class of Life Distribution Using U-Test

  • Al-Nachawati, H.
    • International Journal of Reliability and Applications
    • /
    • v.8 no.2
    • /
    • pp.125-135
    • /
    • 2007
  • In this paper, testing exponentiality against new better than used in convex average and denote by (NBUCA), or its dual (NWUCA) is investigated through the U-test. The percentiles of these tests are tabulated for samples sizes n = 5(1)40. The power estimates of the test are simulated for some commonly used distributions in reliability. Pitman's asymptotic efficiency of the test is calculated and compared. Data of 40 patients suffering from blood cancer disease (Leukemia) is considered as a practical application of the proposed test in the medical sciences.

  • PDF

A JONCKHEERE TYPE TEST FOR THE PARALLELISM OF REGRESSION LINES

  • Jee, Eunsook
    • The Pure and Applied Mathematics
    • /
    • v.20 no.2
    • /
    • pp.109-116
    • /
    • 2013
  • In this paper, we propose a Jonckheere type test statistic for testing the parallelism of k regression lines against ordered alternatives. The order restriction problems could arise in various settings such as location, scale, and regression problems. But most of theory about the statistical inferences under order restrictions has been developed to deal with location parameters. The proposed test is an application of Jonckheere's procedure to regression problem. Asymptotic normality and asymptotic distribution-free properties of the test statistic are obtained under some regularity conditions.

On the Estimation of the Empirical Distribution Function for Negatively Associated Processes

  • Kim, Tae-Sung;Lee, Seung-Woo;Ko, Mi-Hwa
    • Communications for Statistical Applications and Methods
    • /
    • v.8 no.1
    • /
    • pp.229-235
    • /
    • 2001
  • Let {X$\_$n/, n$\geq$1] be a stationary sequence of negatively associated random variables with distribution function F(x)=P(X$_1$$\leq$x). The empirical distribution function F$\_$n/(x) based on X$_1$, X$_2$,....., X$\_$n/ is proposed as an estimator for F$\_$n/(x). Strong consistency and asymptotic normality of F$\_$n/(x) are studied. We also apply these ideas to estimation of the survival function.

  • PDF

Asymptotic Test for Dimensionality in Sliced Inverse Regression (분할 역회귀모형에서 차원결정을 위한 점근검정법)

  • Park, Chang-Sun;Kwak, Jae-Guen
    • The Korean Journal of Applied Statistics
    • /
    • v.18 no.2
    • /
    • pp.381-393
    • /
    • 2005
  • As a promising technique for dimension reduction in regression analysis, Sliced Inverse Regression (SIR) and an associated chi-square test for dimensionality were introduced by Li (1991). However, Li's test needs assumption of Normality for predictors and found to be heavily dependent on the number of slices. We will provide a unified asymptotic test for determining the dimensionality of the SIR model which is based on the probabilistic principal component analysis and free of normality assumption on predictors. Illustrative results with simulated and real examples will also be provided.