Quasi Maximum Likelihood Estimation for Large-Dimensional Matrix Factor Models

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

Quasi Maximum Likelihood Estimation of Value at Risk and Expected Shortfall

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.

This thesis introduces some topics about initial downlink synchronization, algorithm derivations, and program simulations of IEEE 802.16m system. When a mobile station entering to the network, it needs to perform initial synchronization, including of symbol timing offset, carrier frequency offset and preamble index. We utilize the trait which the power of preamble is larger than it of the common data symbol to compute the moving power sum, and then estimate the left boundary of preamble by finding out the peak value of moving power sum. A symbol period from this estimated boundary is regarded as the estimated preamble, which has a phase noise with the exact preamble. We derive the quasi maximum likelihood estimation from the likelihood function of the estimated preamble to obtain fractional carrier frequency offset (FCFO) and the formula of channel estimation. After compensating the estimated fractional carrier frequency offset to the formula of channel estimation, we substitute several reasonable integral carrier frequency offsets (ICFOs) and primary advanced preambles (PA-Preambles) into this formula and obtain channel impulse responses (CIRs). After that, we compute different fine timing offset index 64-points power sum of these CIRs and find out the peak value whose ICFO, PA-Preamble index, and fine timing offset index are regarded as the result of the joint estimation. In terms of simulations, above all, we present a reasonable received signal model of IEEE 802.16m, and then simulate our algorithm in floating point under AWGN (additive white Gaussian noise) channel to verify its performance. Moreover, we test this algorithm under different multipath fading channels, Pedestrian B and SUI-5, at different speed which cause Doppler shifts, and signal to noise ratio (SNR) to observe the effect on this algorithm.

GMM estimation of spatial autoregressive models with moving average disturbances

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.

This paper examines the estimation of the Stochastic Conditional Duration model by the empirical characteristic function and the generalized method of moments when maximum likelihood is unavailable. The joint characteristic function for the durations along with general expressions for the moments are derived, leading naturally to estimation via the empirical characteristic function and generalized method of moments. In a Monte Carlo study as well as an empirical application, these alternative methods are compared with quasi maximum likelihood. These experiments reveal that the empirical characteristic function approach outperforms the quasi maximum likelihood and generalized method of moments in terms of both bias and root mean square error. Copyright The Author(s). Journal compilation Royal Economic Society 2008

SummaryBlundell, Pistaferri, and Preston (American Economic Review, 2008, 98(5), 1887–1921) report an estimate of household consumption insurance with respect to permanent income shocks of 36%. In replicating findings for their model and data, we find that this estimate is distorted by a code error and is not robust to weighting scheme for generalized method of moments (GMM) or consideration of quasi maximum likelihood estimation (QMLE), which produces a significantly higher estimate of consumption insurance at 55%. For sub‐groups by age and education, the differences between estimates across methods are even more pronounced, and QMLE provides new insights into heterogeneity across households compared to the original study. Monte Carlo experiments using non‐normal shocks suggest that consumption insurance estimates for the model are more accurate for QMLE than GMM, including when correcting for bias and especially given a smaller sample such as is only available when looking at sub‐groups.

We consider a model for a multivariate time series where the conditional covariance matrix is a function of a finite-dimensional parameter and the innovation distribution is nonparametric. The semiparametric lower bound for the estimation of the euclidean parameter is characterized, and it is shown that adaptive estimation without reparametrization is not possible. Based on a consistent first-stage estimator (such as quasi maximum likelihood), we propose a semiparametric estimator that estimates the efficient influence function using kernel estimators. We state conditions under which the estimator attains the semiparametric lower bound. For particular models such as the constant conditional correlation model, adaptive estimation of the dynamic part of the model is shown to be possible. To avoid the curse of dimensionality one can, e.g., restrict the multivariate density to the class of spherical distributions, for which we also derive the semiparametric efficiency bound and an estimator that attains this bound. A simulation experiment demonstrates the efficiency gain of the proposed estimator compared with quasi maximum likelihood estimation.Rombouts work was supported by the Centre for Research on e-Finance, HEC Montreal. Hafner gratefully acknowledges financial support by the Fonds Sp ciaux de Recherche (FSR 05) of the Universit catholique de Louvain. The authors thank three anonymous referees for valuable comments and suggestions and Luc Bauwens, Geert Dhaene, Feico Drost, Wolfgang H rdle, Douglas Hodgson, Jens Peter Kreiss, Oliver Linton, and Bas Werker for helpful discussions. We also thank participants of the CORE econometrics seminar, the York annual meeting in econometrics, the annual econometric study group meeting 2002 in Bristol, the 2003 workshop The Art of Semiparametrics in Berlin, and the statistics seminar of the Stockholm School of Economics for valuable comments.

We propose a method for the modelling of the propagation of text data in web site space among some groups by using a multivariate Hawkes process with a sparse structure. For estimation, we introduced a hybrid method using a quasi-maximum likelihood estimator (QMLE) and a $L^1$-penalized QMLE. As a real example, we investigated posts on a Japanese web service about uncomfortable gender experiences, which we classified into 12 groups by age and sex, and we calculated the magnitude of the correlation between each group. In addition, we visualized the propagation structure of posts in each group by summarizing the results in a directed Hawkes graph and a heat map of time integrals of kernel functions.

High precision technique for PPS estimation in impulsive noise environment

This paper performs a Monte Carlo study on efficient method of moments (EMM), generalized method of moments (GMM), quasi-maximum likelihood estimation (QMLE) and maximum likelihood estimation (MLE) for a continuous-time square-root model under two challenging scenarios – high persistence in mean and strong conditional volatility – that are commonly found in estimating the interest rate process. MLE turns out to be the most efficient of the four methods, but its finite sample inference and convergence rate suffer severely from approximating the likelihood function, especially in the scenario of highly persistent mean. QMLE comes second in terms of estimation efficiency, but it is the most reliable in generating inferences. GMM with lag-augmented moments has, overall, the lowest estimation efficiency, possibly due to the ad hoc choice of moment conditions. EMM shows an accelerated convergence rate in the high-volatility scenario, while its over-rejection bias in the mean persistence scenario is unacceptably large. Finally, under a stylized alternative model of the US interest rates, the overidentification test of EMM obtains the ultimate power for detecting misspecification, while the GMM J-test is increasingly biased downwards in finite samples.

Unified [formula omitted]-estimation of fixed-effects spatial dynamic models with short panels

<title>Abstract</title> We establish Central Limit Theorems (CLTs) for Quasi–Maximum Likelihood Estimators (QMLE) in $\text{ARMA}(p,q)$ models under weak dependence, formalized via $\alpha$-mixing. The estimators are $\sqrt{n}$–consistent and asymptotically normal, with covariance in the familiar HAC–sandwich form. To assess finite–sample behavior, we run Monte Carlo experiments for $\text{ARMA}(1,1)$ under Gaussian and non-Gaussian innovations (Student-$t$ with $\nu=3,5$, Gamma with $\alpha=2$, and Poisson with $\lambda=2$). Histograms and Q--Q plots of standardized statistics align closely with $\mathcal N(0,1)$, empirical coverages approach 95\%, and joint scatters of $(\sqrt{n}(\hat\phi-\phi_0), \sqrt{n}(\hat\theta-\theta_0))$ exhibit the expected elliptical shape. The results confirm that QMLE with HAC inference provides reliable estimation and valid uncertainty quantification beyond the classical i.i.d.\ Gaussian setting, offering a practical framework for weakly dependent, non-Gaussian time series.

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.