Efficient composite likelihood for a scalar parameter of interest

Quasi-maximum likelihood estimation in GARCH processes when some coefficients are equal to zero

Utilization of high energy photons (>10 MV) with an optimal weight using a mixed energy technique is a practical way to generate a homogenous dose distribution while maintaining adequate target coverage in intact breast radiotherapy. This study represents a model for estimation of this optimal weight for day to day clinical usage. For this purpose, treatment planning computed tomography scans of thirty-three consecutive early stage breast cancer patients following breast conservation surgery were analyzed. After delineation of the breast clinical target volume (CTV) and placing opposed wedge paired isocenteric tangential portals, dosimeteric calculations were conducted and dose volume histograms (DVHs) were generated, first with pure 6 MV photons and then these calculations were repeated ten times with incorporating 18 MV photons (ten percent increase in weight per step) in each individual patient. For each calculation two indexes including maximum dose in the breast CTV (Dmax) and the volume of CTV which covered with 95% Isodose line (VCTV, 95%IDL) were measured according to the DVH data and then normalized values were plotted in a graph. The optimal weight of 18 MV photons was defined as the intersection point of Dmax and VCTV, 95%IDL graphs. For creating a model to predict this optimal weight multiple linear regression analysis was used based on some of the breast and tangential field parameters. The best fitting model for prediction of 18 MV photons optimal weight in breast radiotherapy using mixed energy technique, incorporated chest wall separation plus central lung distance (Adjusted R2=0.776). In conclusion, this study represents a model for the estimation of optimal beam weighting in breast radiotherapy using mixed photon energy technique for routine day to day clinical usage.

We study the properties of the quasi-maximum likelihood estimator (QMLE) and related test statistics in dynamic models that jointly parameterize conditional means and conditional covariances, when a normal log-likelihood os maximized but the assumption of normality is violated. Because the score of the normal log-likelihood has the martingale difference property when the forst two conditional moments are correctly specified, the QMLE is generally Consistent and has a limiting normal destribution. We provide easily computable formulas for asymptotic standard errors that are valid under nonnormality. Further, we show how robust LM tests for the adequacy of the jointly parameterized mean and variance can be computed from simple auxiliary regressions. An appealing feature of these robyst inference procedures is that only first derivatives of the conditional mean and variance functions are needed. A monte Carlo study indicates that the asymptotic results carry over to finite samples. Estimation of several AR and AR-GARCH time series models reveals that in most sotuations the robust test statistics compare favorably to the two standard (nonrobust) formulations of the Wald and IM tests. Also, for the GARCH models and the sample sizes analyzed here, the bias in the QMLE appears to be relatively small. An empirical application to stock return volatility illustrates the potential imprtance of computing robust statistics in practice.

A Primer on Bootstrap Testing of Hypotheses in Time Series Models: With an Application to Double Autoregressive Models

In this study, we introduce a novel approach, called the quasi maximum likelihood estimation (Q-MLE), for estimating large-dimensional matrix factor models. In contrast to the principal component analysis based approach, Q-MLE considers the heteroscedasticity of the idiosyncratic error term, the heteroscedasticity of which is simultaneously estimated with other parameters. Interestingly, under the homoscedasticity assumption of the idiosyncratic error, the Q-MLE estimator encompassed the projected estimator (PE) as a special case. We provide the convergence rates and asymptotic distributions of the Q-MLE estimators under mild conditions. Extensive numerical experiments demonstrate that the Q-MLE method performs better, especially when heteroscedasticity exists. Furthermore, two real examples in finance and macroeconomics reveal factor patterns across rows and columns, which coincide with financial, economic, or geographical interpretations.

SUMMARY This paper presents a simple method of calculating one-sided p-values which yield accurate inferences for a simple null hypothesis or, equivalently, accurate one-sided con fidence limits regarding a scalar parameter in the presence of nuisance parameters. The method, which extends the work of DiCiccio et al. (2001) and Lee & Young (2005) in the context of adjusted likelihood estimation, is based on a test statistic analogous to the signed root of the loglikelihood, but derived from the objective function of an M-estimator from a certain class. Monte Carlo simulation is used to avoid the need for onerous analytical calculations typical of competing procedures based on Edgeworth or saddle point approximations. The specific class of M-estimators under consideration is character ised by the requirement that the associated test statistic has constant variance to second order. This class contains, among others, the maximum likelihood estimator as well as variants of commonly used M-estimators of location, such as Huber's (1964) Proposal 2.

Two competitive analytical approaches, namely, the generalized method of moments (GMM) and quasi-maximum likelihood (QML) are widely used in statistics and econometrics literature for inferences in stochastic volatility models (SVMs). Alternative numerical approaches such as monte carlo markov chain (MCMC), simulated maximum likelihood (SML) and Bayesian approaches are also available. All these later approaches are, however, based on simulations. In this paper, we revisit the analytical estimation approaches and briefly demonstrate that the existing GMM approach is unnecessarily complicated. Also, the asymptotic properties of the likelihood approximation based QML approach are unknown and the finite sample based QML estimators can be inefficient. We then develop a precise set of moment estimating equations and demonstrate that the proposed method of moments (MM) estimators are easy to compute and they perform well in estimating the parameters of the SVMs in both small and large time series set up. A ‘working’ generalized quasi-likelihood (WGQL) estimation approach is also considered. Estimation methods are illustrated by reanalyzing a part of the Swiss-Franc and U.S. dollar exchange rates data.

Quasi maximum likelihood estimation and inference in multivariate volatility models remains a challenging computational task if, for example, the dimension of the parameter space is high. One of the reasons is that typically numerical procedures are used to compute the score and the Hessian, and often they are numerically unstable. We provide analytical formulae for the score and the Hessian for a variety of multivariate GARCH models including the Vec and BEKK specifications as well as the recent dynamic conditional correlation model. By means of a Monte Carlo investigation of the BEKK–GARCH model we illustrate that employing analytical derivatives for inference is clearly preferable to numerical methods.

Inference for a scalar interest parameter in the presence of nuisance parameters is obtained in two steps: an initial ancillary reduction to a variable having the dimension of the full parameter and a subsequent maxginalization to a scalar pivotal quantity for the component parameter of interest. Recent asymptotic likelihood theory has provided highly accurate third order approximations for the second maxginalization to a pivotal quantity, but no general procedure for the initial ancillary conditioning. We develop a second order location type ancillary generalizing (1995) and a first order affine type ancillary generalizing (1980). The second order ancillary leads to third order p-values and the first order ancillary leads to second order p-values. For an n dimensional variable with p dimensional parameter, we also show that the only information needed concerning the ancillary is an array V = (v 1 ... v p ) of p linearly independent vectors tangent to the ancillary surface at the observed data. For the two types of ancillarity simple expressions for the array V are given; these are obtained from a full dimensional pivotal quantity. A brief summary describes the use of V to obtain second and third order p-values and some examples are discussed.KeywordsStatistical InferenceExponential ModelTangent DirectionNuisance ParameterComponent ParameterThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The vector multiplicative error model (vMEM) is a popular model known for its capability of analyzing and forecasting multidimensional non-negative-valued time series. In this paper, we present a closed-form estimator for the vMEM. The estimator has the advantage that it can be easily implemented by solving moment equations and does not require the use of any distribution or optimal weight matrix. We prove consistency and derive the asymptotic properties of the estimator. A simulation study confirms our theoretical results and compares the performance of the closed-form estimator (CLFE) and the quasi-maximum likelihood estimator (QMLE). Empirical application of the absolute return and the high–low range from GE stock illustrates the predictive capacity comparison of the CLFE and the QMLE.

The quasi-likelihood function proposed by Wedderburn [Quasi-likelihood functions, generalized linear models, and the Gauss–Newton method. Biometrika. 1974;61:439–447] broadened the application scope of generalized linear models (GLM) by specifying the mean and variance function instead of the entire distribution. However, in many situations, complete specification of variance function in the quasi-likelihood approach may not be realistic. Following Fahrmeir's [Maximum likelihood estimation in misspecified generalized linear models. Statistics. 1990;21:487–502] treating with misspecified GLM, we define a quasi-likelihood nonlinear models (QLNM) with misspecified variance function by replacing the unknown variance function with a known function. In this paper, we propose some mild regularity conditions, under which the existence and the asymptotic normality of the maximum quasi-likelihood estimator (MQLE) are obtained in QLNM with misspecified variance function. We suggest computing MQLE of unknown parameter in QLNM with misspecified variance function by the Gauss–Newton iteration procedure and show it to work well in a simulation study.

Testing for Common GARCH Factors

Genetic and environmental covariances between pairs of complex traits are important quantitative measurements that characterize their shared genetic and environmental architectures. Accurate estimation of genetic and environmental covariances in genome-wide association studies (GWASs) can help us identify common genetic and environmental factors associated with both traits and facilitate the investigation of their causal relationship. Genetic and environmental covariances are often modeled through multivariate linear mixed models. Existing algorithms for covariance estimation include the traditional restricted maximum likelihood (REML) method and the recent method of moments (MoM). Compared to REML, MoM approaches are computationally efficient and require only GWAS summary statistics. However, MoM approaches can be statistically inefficient, often yielding inaccurate covariance estimates. In addition, existing MoM approaches have so far focused on estimating genetic covariance and have largely ignored environmental covariance estimation. Here we introduce a new computational method, GECKO, for estimating both genetic and environmental covariances, that improves the estimation accuracy of MoM while keeping computation in check. GECKO is based on composite likelihood, relies on only summary statistics for scalable computation, provides accurate genetic and environmental covariance estimates across a range of scenarios, and can accommodate SNP annotation stratified covariance estimation. We illustrate the benefits of GECKO through simulations and applications on analyzing 22 traits from five large-scale GWASs. In the real data applications, GECKO identified 50 significant genetic covariances among analyzed trait pairs, resulting in a twofold power gain compared to the previous MoM method LDSC. In addition, GECKO identified 20 significant environmental covariances. The ability of GECKO to estimate environmental covariance in addition to genetic covariance helps us reveal strong positive correlation between the genetic and environmental covariance estimates across trait pairs, suggesting that common pathways may underlie the shared genetic and environmental architectures between traits.

Spatial dynamic panel data (SDPD) models have received great attention in economics in recent 10 years. Existing approaches for the estimation and test of SDPD models are quasi-maximum likelihood (QML) approach and generalized method of moments (GMM). In this article, we introduce the empirical likelihood (EL) method to the statistical inference for SDPD models. The EL ratio statistics are constructed for the parameters of spatial dynamic panel data models. It is shown that the limiting distributions of the empirical likelihood ratio statistics are chi-squared distributions, which are used to construct confidence regions for the parameters of the models. Simulation results show that the EL based confidence regions outperform the normal approximation based confidence regions.

This paper presents a new data fusion method by adopting random weighting estimation for optimal weighted fusion of multisensor observation data. This method adjusts in real time the weights of individual sensors according to variations in estimated sensor variances to obtain optimal weight distribution. Theories of random weighting estimation are established for optimal data fusion through optimal weighting distribution. Algorithms of random weighting estimation are developed to calculate sensor variances for determination of optimal random weighting factors. The fusion result in least mean square error is achieved directly from multisensor observation data, without requirement of any prior knowledge on unknown parameters. The mean square error estimated by the proposed method is not only smaller than from each individual sensor, but also smaller than by the mean of multisensor observation data.