Quasi score-driven models

In this research paper various new advanced inferential tools namely modified likelihood ratio (LR), Ward and Lagrange Multiplier test statistics have been proposed for testing general linear hypothesis in stochastic linear regression model. In this process internally studentized residuals have been used. This research study has brought out some new advance tools for analysing inferential aspects of stochastic linear regression models by using internally studentized residuals. Miguel Fonseca et.al [1] developed statistical inference in linear models dealing with the theory of maximum likelihood estimates and likelihood ratio tests under some linear inequality restrictions on the regression coefficients. Tim Coelli [2] used Monte carlo experimentation to investigate the finite sample properties of maximum likelihood (ML) and correct ordinary least squares (COLS) estimators of the half –normal stochastic frontier production function. In 2011, p. Bala siddamuni et.al [3] have developed advanced tools for mathematical and stochastic modelling.

This paper studies the applications of extreme value theory on analysis for closing price data of the Dow-Jones industrial index and Danish fire insurance claims data. The generalized extreme value (GEV) distribution is considered in analyzing the real data, and the hypothesis testing problem for the shape parameter of GEV distribution is investigated based on a new test statistic—the $$L_q$$ -likelihood ratio ( $$L_q$$ R) statistic. The $$L_q$$ R statistic can be treated as a generalized form of the classical likelihood ratio (LR) statistic. We show that the asymptotic behavior of proposed statistic is characterized by the degree of distortion $$q$$ . For small and modest sample sizes, the $$L_q$$ R statistic is still available when $$q$$ is properly chosen. By simulation studies, the proposed statistic not only performs the asymptotic properties, but also outperforms the classical LR statistic as the sample sizes are modest or even small. Meanwhile, the test power based on the new statistic is also simulated by Monte Carlo methods. At last, the models are diagnosed by graphical methods.

Dynamic Factor Models with Clustered Loadings: Forecasting Education Flows using Unemployment Data

In this paper, we examine by Monte Carlo experiments the small sample properties of the W (Wald), LM (Lagrange Multiplier) and LR (Likelihood Ratio) tests for equality between sets of coefficients in two linear regressions under heteroscedasticity. The small sample properties of the size-corrected W, LM and LR tests proposed by Rothenberg (1984) are also examined and it is shown that the performances of the size-corrected W and LM tests are very good. Further, we examine the two-stage test which consists of a test for homoscedasticity followed by the Chow (1960) test if homoscedasticity is indicated or one of the W, LM or LR tests if heteroscedasticity should be assumed. It is shown that the pretest does not reduce much the bias in the size when the sizecorrected citical values are used in the W, LM and LR tests.

A simple iterative procedure is found for the exact null and alternative distributions of likelihood ratio, cumulative sum and related statistics for testing for a change in probability of a sequence of independent binomial random variables. It is concluded that the likelihood ratio test is slightly less powerful than the cumulative sum test near the middle of the sequence, but that the likelihood ratio test is much more powerful near the ends. An example from epidemiology is used to illustrate the results. Under certain conditions the cumulative sum test is identical to a two-sample Kolmogorov-Smirnov test and so the iterative procedure can be used to find the null distribution of Kolmogorov-Smirnov and related statistics.

This paper will discuss the current research in building models of conditional variances using the Autoregressive Conditional Heteroskedastic (ARCH) and Generalized ARCH (GARCH) formulations. The discussion will be motivated by a simple asset pricing theory which is particularly appropriate for examining futures contracts with risk averse agents. A new class of models defined to be integrated in variance is then introduced. This new class of models includes the variance analogue of a unit root in the mean as a special case. The models are argued to be both theoretically important for the asset pricing models and empirically relevant. The conditional density is then generalized from a normal to a Student-t with unknown degrees of freedom. By estimating the degrees of freedom, implications about the conditional kurtosis of these models and time aggregated models can be drawn. A further generalization allows the conditional variance to be a non-linear function of the squared innovations. Throughout empirical...

This article evaluates the accuracy of approximate confidence intervals for parameters and quantiles of the smallest extreme value and normal distributions. The findings also apply to the Weibull and the lognormal distributions. The interval estimates are based on (a) the asymptotic normality of the maximum likelihood estimator, (b) the asymptotic x 2 distribution of the likelihood ratio (LR) statistic, (c) a mean and variance correction to the signed square roots of the LR statistic, and (d) the Bartlett correction to the LR statistic. The extensive Monte Carlo results about true error probabilities and average lengths under various degrees of censoring show advantages of the LR-based intervals. For complete or moderately censored samples, the mean and variance correction to the LR statistic gives nearly exact and symmetric error probabilities. In small samples with heavy censoring, the Bartlett correction tends to give conservative error probabilities, whereas the uncorrected LR interval is often anticonservative. The results also indicate that LR-based methods have longer interval lengths than intervals based on the asymptotic normality of the maximum likelihood estimator.

This paper proposes a bias-adjusted version of Breusch and Pagan (1980) Lagrange multiplier (LM) test statistic of error cross-section independence, in the case of panel models with strictly exogenous regressors and normal errors. The exact mean and variance of the test indicator of the LM test statistic are provided for the purpose of the bias-adjustments. It is shown that the centring of the LM statistic is correct for fixed T and N. Importantly, the proposed bias-adjusted LM test is consistent even when the Pesaran's (2004) CD test is inconsistent. Also an alternative bias-adjusted LM test, which is consistent under local error cross-section dependence of any fixed order p, is proposed. The finite sample behaviour of the proposed tests is investigated and compared to that of the LM and CD tests. It is shown that the bias-adjusted LM tests successfully control the size, maintaining satisfactory power in panel with exogenous regressors and normal errors. However, it is also shown that the bias-adjusted LM test is not as robust as the CD test to non-normal errors and/or in the presence of weakly exogenous regressors. Copyright Royal Economic Society 2007

From first principles, we derive a quadratic nonlinear, first-order dynamical system capable of performing exact Bayes-Markov inferences for a wide class of biologically plausible stimulus-dependent patterns of activity while simultaneously providing an online estimate of model performance. This is accomplished by constructing a dynamical system that has solutions proportional to the probability distribution over the stimulus space, but with a constant of proportionality adjusted to provide a local estimate of the probability of the recent observations of stimulus-dependent activity-given model parameters. Next, we transform this exact equation to generate nonlinear equations for the exact evolution of log likelihood and log-likelihood ratios and show that when the input has low amplitude, linear rate models for both the likelihood and the log-likelihood functions follow naturally from these equations. We use these four explicit representations of the probability distribution to argue that, in contrast to the arguments of previous work, the dynamical system for the exact evolution of the likelihood (as opposed to the log likelihood or log-likelihood ratios) not only can be mapped onto a biologically plausible network but is also more consistent with physiological observations.

Two step-down tests for equality of covariance matrices

Tests for a family of random-effects covariance structures in a multivariate growth curve model

In this article, we focus on the integer valued autoregressive model, INAR (1), with Poisson innovations. We test the null of serial independence, where the INAR parameter is zero, versus the alternative of a positive INAR parameter. To this end, we propose different explicit approximations of the likelihood ratio (LR) statistic. We derive the limiting distributions of our statistics under the null. In a simulation study, we compare size and power of our tests with the score test, proposed by Sun and McCabe [2013. Score statistics for testing serial dependence in count data. Journal of Time Series Analysis 34 (3):315–29]. The size is either asymptotic or derived via response surface regressions of critical values. We find that our statistics are superior to score in terms of power and work just as well in terms of size. Another finding is that the powers of our approximate LR statistics compare well with the power of the numerical LR statistic. Power simulations are also performed under an INAR(2) framework, with similar outcome.

The limit distributions of likelihood ratio and cumulative sum tests for a change in a binomial probability

In this article, the size and power properties of the Common-factor Im, Pesaran and Shin (CIPS), Wald (W), Likelihood Ratio (LR) and Lagrange Multiplier (LM) tests are investigated when the error term follows a spatial error model. In this study, the results from the Monte Carlo simulations, first, show that the CIPS test over-estimates the nominal size. Second, the simulation results show that the empirical size of the W test approaches the nominal size quickly, while the LR and LM tests underestimate the null hypothesis in both small and moderate sample sizes. Finally, the results also show that even though the LM and LR tests under-reject the true-null hypothesis they have higher power than the W test.

In some survival studies part of the population may be no longer subject to the event of interest. The called cure rate models take this fact into account. They have been extensively studied for several authors who have proposed extensions and applications in real lifetime data. Classic large sample tests are usually considered in these applications, especially the likelihood ratio. Recently a new test called \textit{gradient test} has been proposed. The gradient statistic shares the same asymptotic properties with the classic likelihood ratio and does not involve knowledge of the information matrix, which can be an advantage in survival models. Some simulation studies have been carried out to explore the behavior of the gradient test in finite samples and compare it with the classic tests in different models. However little is known about the properties of these large sample tests in finite sample for cure rate models. In this work we performed a simulation study based on the promotion time model with Weibull distribution, to assess the performance of likelihood ratio and gradient tests in finite samples. An application is presented to illustrate the results.