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Arjun K. Gupta - One of the best experts on this subject based on the ideXlab platform.

  • Adjusted Empirical Likelihood for Time Series Models
    Sankhya B, 2017
    Co-Authors: Ramadha D. Piyadi Gamage, Wei Ning, Arjun K. Gupta
    Abstract:

    Empirical Likelihood method has been applied to dependent observations by Monti (Biometrika, 84, 395–405 1997) through the Whittle’s estimation method. Similar asymptotic distribution of the empirical Likelihood Ratio Statistic for stationary time series has been derived to construct the confidence regions for the parameters. However, Monti’s approach is valid only when the error terms follow a Gaussian distribution. Nordman and Lahiri (Ann. Statist., 34, 3019–50 2006) derived estimating functions and empirical Likelihood Ratio Statistic using frequency domain empirical Likelihood approach for non-Gaussian error term distributions. Nonetheless, the required numerical problem of computing profile empirical Likelihood function which involves constrained maximization has no solution sometimes, which leads to the drawbacks of using the original version of the empirical Likelihood Ratio. In this paper, we propose an adjusted empirical Likelihood Ratio Statistic to modify the one proposed by Nordman and Lahiri so that it guarantees the existence of the solution of the required maximization problem, while maintaining the similar asymptotic properties as Nordman and Lahiri obtained. Simulations have been conducted to illustrate the coverage probabilities obtained by the adjusted version for different time series models which are competitive to the ones based on Nordman and Lahiri’s version, especially for small sample sizes.

  • Adjusted Empirical Likelihood for Time Series Models
    arXiv: Methodology, 2016
    Co-Authors: Ramadha D. Piyadi Gamage, Wei Ning, Arjun K. Gupta
    Abstract:

    Empirical Likelihood method has been applied to dependent observations by Monti (1997) through the Whittle's estimation method. Similar asymptotic distribution of the empirical Likelihood Ratio Statistic for stationary time series has been derived to construct the confidence regions for the parameters. However, required numerical problem of computing profile empirical Likelihood function which involves constrained maximization has no solution sometimes, which leads to the drawbacks of using the original version of the empirical Likelihood Ratio. In this paper, we propose an adjusted empirical Likelihood Ratio Statistic to modify the one proposed by Monti so that it guarantees the existence of the solution of the required maximization problem, while maintaining the similar asymptotic properties as Monti obtained. Simulations have been conducted to illustrate the coverage probabilities obtained by the adjusted version for different time series models which are better than the ones obtained by Monti's version, especially for small sample sizes.

  • Distribution and percentage points of the Likelihood Ratio Statistic for testing circular symmetry
    Computational Statistics & Data Analysis, 2004
    Co-Authors: Daya K. Nagar, Jie Chen, Arjun K. Gupta
    Abstract:

    Abstract In this paper, the distribution of the Likelihood Ratio Statistic for testing the hypothesis that the covariance matrix of a p -variate normal distribution is circular symmetric has been derived. The distribution is obtained in series form using the inverse Mellin transform and the residue theorem. Percentage points for p =4,5,6 and 7 have been computed using distributional results derived in this article.

  • On the asymptotic distribution of Likelihood Ratio Statistic for testing multisample spherically in the complex case
    Statistica, 1992
    Co-Authors: Arjun K. Gupta, D.k. Nagar, Kalpana Jain
    Abstract:

    In this paper, asymptotic expansions of the distribution of the Likelihood Ratio Statistic for testing multisample spherically in the complex case have been derived in the null and nonnull cases when the alternative are close to the null hypothesis. These expansions are obtained in the form of series of beta distributions.

Augustine C. M. Wong - One of the best experts on this subject based on the ideXlab platform.

  • On standardizing the signed root log Likelihood Ratio Statistic
    Statistics & Probability Letters, 2012
    Co-Authors: L. Jiang, Augustine C. M. Wong
    Abstract:

    A simple connection between the Bartlett adjustment factor of the log Likelihood Ratio Statistic and the normalizing constant of the p∗ formula–an approximate conditional density for the maximum Likelihood estimate given an exact or an approximate ancillary Statistic–was established in Barndorff-Nielsen and Cox (1984). In this paper, the explicit form of the normalizing constant of the p∗ formula for the scalar parameter model is derived. By change of variables, the mean and variance of the signed root log Likelihood Ratio Statistic are obtained explicitly, and, hence, tail probabilities can be calculated from the standardized signed root log Likelihood Ratio Statistic. Examples are used to illustrate the implementation and accuracy of the proposed method.

  • Approximating the F distribution via a general version of the modified signed log-Likelihood Ratio Statistic
    Computational Statistics & Data Analysis, 2008
    Co-Authors: Augustine C. M. Wong
    Abstract:

    A simple normal approximation for the cumulative distribution function of the F distribution is obtained via a general version of the modified signed log-Likelihood Ratio Statistic. This approximation exhibits remarkable accuracy even when the degrees of freedom are small. Using the same methodology, but with a simpler set up, simple and accurate normal approximations to the cumulative distribution functions of the Student t and @g^2 distributions can also be obtained.

Jens Ledet Jensen - One of the best experts on this subject based on the ideXlab platform.

  • Tests and Confidence Intervals for an Extended Variance Component Using the Modified Likelihood Ratio Statistic
    Scandinavian Journal of Statistics, 2007
    Co-Authors: Ole F. Christensen, Jens Ledet Jensen, Morten Frydenberg, Jørgen Granfeldt Pedersen
    Abstract:

    The large deviation modified Likelihood Ratio Statistic is studied for testing a variance component equal to a specified value. Formulas are presented in the general balanced case, whereas in the unbalanced case only the one-way random effects model is studied. Simulation studies are presented, showing that the normal approximation to the large deviation modified Likelihood Ratio Statistic gives confidence intervals for variance components with coverage probabilities very close to the nominal confidence coefficient. Copyright 2007 Board of the Foundation of the Scandinavian Journal of Statistics..

  • A Historical Sketch and Some New Results on the Improved Log Likelihood Ratio Statistic
    Scandinavian Journal of Statistics, 1993
    Co-Authors: Jens Ledet Jensen
    Abstract:

    In the first part we discuss the known results concerning the reduction of the error of the chi-squared approximation when using the Bartlett adjusted log Likelihood Ratio Statistic. In the second part we state some new results for the case where the first four log Likelihood derivatives have both continuous and lattice variables. The latter results are of interest for example in connection with censored life times and in logistic regression. Finally, in the last section we discuss how to perform the algebraic manipulations using REDUCE.

  • The modified signed Likelihood Statistic and saddlepoint approximations
    Biometrika, 1992
    Co-Authors: Jens Ledet Jensen
    Abstract:

    SUMMARY For a number of tests in exponential families we show that the use of a normal approximation to the modified signed Likelihood Ratio Statistic r* is equivalent to the use of a saddlepoint approximation. This is also true in a large deviation region where the signed Likelihood Ratio Statistic r is of order In.

Kehai Yuan - One of the best experts on this subject based on the ideXlab platform.

  • What Causes the Mean Bias of the Likelihood Ratio Statistic with Many Variables
    Multivariate behavioral research, 2019
    Co-Authors: Kehai Yuan, Chao Fan, Yanyun Zhao
    Abstract:

    AbstractSurvey data often contain many variables. Structural equation modeling (SEM) is commonly used in analyzing such data. However, conventional SEM methods are not crafted to handle data with a...

  • empirical correction to the Likelihood Ratio Statistic for structural equation modeling with many variables
    Psychometrika, 2015
    Co-Authors: Kehai Yuan, Yubin Tian, Hirokazu Yanagihara
    Abstract:

    Survey data typically contain many variables. Structural equation modeling (SEM) is commonly used in analyzing such data. The most widely used Statistic for evaluating the adequacy of a SEM model is T ML, a slight modification to the Likelihood Ratio Statistic. Under normality assumption, T ML approximately follows a chi-square distribution when the number of observations (N) is large and the number of items or variables (p) is small. However, in practice, p can be rather large while N is always limited due to not having enough participants. Even with a relatively large N, empirical results show that T ML rejects the correct model too often when p is not too small. Various corrections to T ML have been proposed, but they are mostly heuristic. Following the principle of the Bartlett correction, this paper proposes an empirical approach to correct T ML so that the mean of the resulting Statistic approximately equals the degrees of freedom of the nominal chi-square distribution. Results show that empirically corrected Statistics follow the nominal chi-square distribution much more closely than previously proposed corrections to T ML, and they control type I errors reasonably well whenever N≥max(50,2p). The formulations of the empirically corrected Statistics are further used to predict type I errors of T ML as reported in the literature, and they perform well.

  • Normal theory Likelihood Ratio Statistic for mean and covariance structure analysis under alternative hypotheses
    Journal of Multivariate Analysis, 2007
    Co-Authors: Kehai Yuan, Kentaro Hayashi, Peter M. Bentler
    Abstract:

    The normal distribution based Likelihood Ratio (LR) Statistic is widely used in structural equation modeling. Under a sequence of local alternative hypotheses, this Statistic has been shown to asymptotically follow a noncentral chi-square distribution. In practice, the population mean vector and covariance matrix as well as the model and sample size are always fixed. It is hard to justify the validity of the noncentral chi-square distribution for the resulting LR Statistic even when data are normally distributed and sample size is large. By extending results in the literature, this paper develops normal distributions to describe the behavior of the LR Statistic for mean and covariance structure analysis. A sequence of local alternative hypotheses is not necessary for the proposed distributions to be asymptotically valid. When the effect size is medium and above or when the model is not trivially misspecified, empirical results indicate that a refined normal distribution describes the behavior of the LR Statistic better than the commonly used noncentral chi-square distribution, as measured by the Kolmogorov-Smirnov distance. Quantile-quantile plots are also provided to better understand the different distributions.

  • Asymptotic robustness of the normal theory Likelihood Ratio Statistic for two-level covariance structure models
    Journal of Multivariate Analysis, 2005
    Co-Authors: Kehai Yuan, Peter M. Bentler
    Abstract:

    Data in social and behavioral sciences are often hierarchically organized. Special Statistical procedures have been developed to analyze such data while taking into account the resulting dependence of observations. Most of these developments require a multivariate normality distribution assumption. It is important to know whether normal theory-based inference can still be valid when applied to nonnormal hierarchical data sets. Using an analytical approach for balanced data and numerical illustRations for unbalanced data, this paper shows that the Likelihood Ratio Statistic based on the normality assumption is asymptotically robust for many nonnormal distributions. The result extends the scope of asymptotic robustness theory that has been established in different contexts.

Yanyun Zhao - One of the best experts on this subject based on the ideXlab platform.