Comovements and asymmetric tail dependence in state housing prices in the USA: A nonparametric approach

We reexamine the methods used in estimating comovements among US regional home prices and find that there are insufficient moments to ensure a normal limit necessary for employing the quasi‐maximum likelihood estimator. Hence we propose applying the self‐weighted quasi‐maximum exponential likelihood estimator and a bootstrap method to test and account for the asymmetry of comovements as well as different magnitudes across state pairs. Our results reveal interstate asymmetric tail dependence based on observed house price indices rather than residuals from fitting autoregressive–generalized autoregressive conditional heteroskedasticity (AR‐GARCH) models.     

Modelling heterogeneity and dynamics in the volatility of individual wages

This paper presents a model for the heterogeneity and dynamics of the conditional mean and conditional variance of individual wages. A bias‐corrected likelihood approach, which reduces the estimation bias to a term of order 1/T², is used for estimation and inference. The small‐sample performance of the proposed estimator is investigated in a Monte Carlo study. The simulation results show that the bias of the maximum likelihood estimator is substantially corrected for designs calibrated to the data used in the empirical analysis, drawn from the PSID. The empirical results show that it is important to account for individual unobserved heterogeneity and dynamics in the variance, and that the latter is driven by job mobility. The model also explains the non‐normality observed in log‐wage data. Copyright © 2010 John Wiley & Sons, Ltd.     

Semiparametric maximum likelihood estimation in Cox proportional hazards model with covariate measurement errors

This paper studies semiparametric maximum likelihood estimators in the Cox proportional hazards model with covariate error, assuming that the conditional distribution of the true covariate given the surrogate is known. We show that the estimator of the regression coefficient is asymptotically normal and efficient, its covariance matrix can be estimated consistently by differentiation of the profile likelihood, and the likelihood ratio test is asymptotically chi-squared. We also provide efficient algorithms for the computations of the semiparametric maximum likelihood estimate and the profile likelihood. The performance of this method is successfully demonstrated in simulation studies.     

Finite sample properties of estimators for autoregressive moving average models

We analyze by simulation the properties of three estimators frequently used in the analysis of autoregressive moving average time series models for both nonseasonal and seasonal data. The estimators considered are exact maximum likelihood, exact least squares and conditional least squares. For samples of the size commonly found in economic applications, the estimators are compared in terms of bias, mean squared error, and predictive ability. The reliability of the usually calculated confidence intervals is assessed for the maximum likelihood estimator.     

Asymptotic distribution of the cointegrating vector estimator in error correction models with conditional heteroskedasticity

This paper explores the asymptotic distribution of the cointegrating vector estimator in error correction models with conditionally heteroskedastic errors. Asymptotic properties of the maximum likelihood estimator (MLE) of the cointegrating vector, which estimates the cointegrating vector and the multivariate GARCH process jointly, are provided. The MLE of the cointegrating vector follows mixture normal, and its asymptotic distribution depends on the conditional heteroskedasticity and the kurtosis of standardized innovations. The reduced rank regression (RRR) estimator and the regression-based cointegrating vector estimators do not consider conditional heteroskedasticity, and thus the efficiency gain of the MLE emerges as the magnitude of conditional heteroskedasticity increases. The simulation results indicate that the relative power of the t-statistics based on the MLE improves significantly as the GARCH effect increases.     

Inconsistency of the MLE and inference based on weighted LS for LARCH models

This paper considers a class of finite-order autoregressive linear ARCH models. The model captures the leverage effect, allows the volatility to be arbitrarily close to zero and to reach its minimum for non-zero innovations, and is appropriate for long memory modeling when infinite orders are allowed. However, the (quasi-)maximum likelihood estimator is, in general, inconsistent. A self-weighted least-squares estimator is proposed and is shown to be asymptotically normal. A score test for conditional homoscedasticity and diagnostic portmanteau tests are developed. Their performance is illustrated via simulation experiments. It is also investigated whether stock market returns exhibit some of the characteristic features of the linear ARCH model.     

Strong Consistency of the Maximum Likelihood Estimator in Generalized Linear and Nonlinear Mixed-Effects Models

Generalized linear and nonlinear mixed-effects models are used extensively in biomedical, social, and agricultural sciences. The statistical analysis of these models is based on the asymptotic properties of the maximum likelihood estimator. However, it is usually assumed that the maximum likelihood estimator is consistent, without providing a proof. A rigorous proof of the consistency by verifying conditions from existing results can be very difficult due to the integrated likelihood. In this paper, we present some easily verifiable conditions for the strong consistency of the maximum likelihood estimator in generalized linear and nonlinear mixed-effects models. Based on this result, we prove that the maximum likelihood estimator is consistent for some frequently used models such as mixed-effects logistic regression models and growth curve models.     

On the inefficiency of the restricted maximum likelihood

The restricted maximum likelihood is preferred by many to the full maximum likelihood for estimation with variance component and other random coefficient models, because the variance estimator is unbiased. It is shown that this unbiasedness is accompanied in some balanced designs by an inflation of the mean squared error. An estimator of the cluster‐level variance that is uniformly more efficient than the full maximum likelihood is derived. Estimators of the variance ratio are also studied.     

Semiparametric estimation of logistic regression model with missing covariates and outcome

We consider a semiparametric method to estimate logistic regression models with missing both covariates and an outcome variable, and propose two new estimators. The first, which is based solely on the validation set, is an extension of the validation likelihood estimator of Breslow and Cain (Biometrika 75:11–20, 1988). The second is a joint conditional likelihood estimator based on the validation and non-validation data sets. Both estimators are semiparametric as they do not require any model assumptions regarding the missing data mechanism nor the specification of the conditional distribution of the missing covariates given the observed covariates. The asymptotic distribution theory is developed under the assumption that all covariate variables are categorical. The finite-sample properties of the proposed estimators are investigated through simulation studies showing that the joint conditional likelihood estimator is the most efficient. A cable TV survey data set from Taiwan is used to illustrate the practical use of the proposed methodology.     

Conditional empirical likelihood for quantile regression models

In this paper, we propose a new Bayesian quantile regression estimator using conditional empirical likelihood as the working likelihood function. We show that the proposed estimator is asymptotically efficient and the confidence interval constructed is asymptotically valid. Our estimator has low computation cost since the posterior distribution function has explicit form. The finite sample performance of the proposed estimator is evaluated through Monte Carlo studies.     

Estimation and testing for a Poisson autoregressive model

This article considers statistical inference for a Poisson autoregressive model. A condition for ergodicity and a necessary and sufficient condition for the existence of moments are given. Asymptotics for maximum likelihood estimator and weighted least squares estimators with estimated weights or known weights of the parameters are established. Testing conditional heteroscedasticity and testing the parameters under a simple ordered restriction are noted. A simulation study is also given.     

Logit based parameter estimation in the Rasch model

The similarities between the logistic regression model and the Rasch model (used in psychometric item response theory) are used to derive several methods based on logits that produce parameter estimates for the Rasch model. A result from LeCam and Dzhaparidze is used by which an initial consistent estimate is transformed by one scoring method iteration into an estimate that has the same asymptotic efficiency as the (in this case conditional) maximum likelihood estimate of the item parameters. Indirect evidence about the bias of this CML estimator is produced by studying the (more easily derived) bias of the estimator based on the unweighted logits. Finally, some simple weighted least squares logit-based estimates are presented, and their performance is assessed. On the whole, the computationally simpler logit-based estimates give a fairly good approximation to the CML estimates.     

Robust linear static panel data models using ε-contamination

The paper develops a general Bayesian framework for robust linear static panel data models using$\epsilon$-contamination. A two-step approach is employed to derive the conditional type-II maximum likelihood (ML-II) posterior distribution of the coefficients and individual effects. The ML-II posterior means are weighted averages of the Bayes estimator under a base prior and the data-dependent empirical Bayes estimator. Two-stage and three stage hierarchy estimators are developed and their finite sample performance is investigated through a series of Monte Carlo experiments. These include standard random effects as well as Mundlak-type, Chamberlain-type and Hausman–Taylor-type models. The simulation results underscore the relatively good performance of the three-stage hierarchy estimator. Within a single theoretical framework, our Bayesian approach encompasses a variety of specifications while conventional methods require separate estimators for each case.     

Semiparametric efficient adaptive estimation of asymmetric GARCH models

In this paper we derive a semiparametric efficient adaptive estimator of an asymmetric GARCH model. Applying some general results from Drost et al. [1997. The Annals of Statistics 25, 786–818], we first estimate the unknown density function of the disturbances by kernel methods, then apply a one-step Newton–Raphson method to obtain a more efficient estimator than the quasi-maximum likelihood estimator. The proposed semiparametric estimator is adaptive for parameters appearing in the conditional standard deviation model with respect to the unknown distribution of the disturbances.     

Estimation of multivariate models for time series of possibly different lengths

We consider the problem of estimating parametric multivariate density models when unequal amounts of data are available on each variable. We focus in particular on the case that the unknown parameter vector may be partitioned into elements relating only to a marginal distribution and elements relating to the copula. In such a case we propose using a multi‐stage maximum likelihood estimator (MSMLE) based on all available data rather than the usual one‐stage maximum likelihood estimator (1SMLE) based only on the overlapping data. We provide conditions under which the MSMLE is not less asymptotically efficient than the 1SMLE, and we examine the small sample efficiency of the estimators via simulations. The analysis in this paper is motivated by a model of the joint distribution of daily Japanese yen–US dollar and euro–US dollar exchange rates. We find significant evidence of time variation in the conditional copula of these exchange rates, and evidence of greater dependence during extreme events than under the normal distribution. Copyright © 2006 John Wiley & Sons, Ltd.     

Modeling and forecasting short‐term interest rates: The benefits of smooth regimes,macroeconomic variables,and bagging

In this paper we propose a smooth transition tree model for both the conditional mean and variance of the short‐term interest rate process. The estimation of such models is addressed and the asymptotic properties of the quasi‐maximum likelihood estimator are derived. Model specification is also discussed. When the model is applied to the US short‐term interest rate we find: (1) leading indicators for inflation and real activity are the most relevant predictors in characterizing the multiple regimes' structure; (2) the optimal model has three limiting regimes. Moreover, we provide empirical evidence of the power of the model in forecasting the first two conditional moments when it is used in connection with bootstrap aggregation (bagging). Copyright © 2010 John Wiley & Sons, Ltd.     

Finite sample properties of maximum likelihood estimator in spatial models

We investigate the finite sample properties of the maximum likelihood estimator for the spatial autoregressive model. A stochastic expansion of the score function is used to develop the second-order bias and mean squared error of the maximum likelihood estimator. We show that the results can be expressed in terms of the expectations of cross products of quadratic forms, or ratios of quadratic forms in a normal vector which can be evaluated using the top order invariant polynomial. Our numerical calculations demonstrate that the second-order behaviors of the maximum likelihood estimator depend on the degree of sparseness of the weights matrix.     

Capture–recapture estimation based upon the geometric distribution allowing for heterogeneity

Capture–Recapture methods aim to estimate the size of an elusive target population. Each member of the target population carries a count of identifications by some identifying mechanism—the number of times it has been identified during the observational period. Only positive counts are observed and inference needs to be based on the observed count distribution. A widely used assumption for the count distribution is a Poisson mixture. If the mixing distribution can be described by an exponential density, the geometric distribution arises as the marginal. This note discusses population size estimation on the basis of the zero-truncated geometric (a geometric again itself). In addition, population heterogeneity is considered for the geometric. Chao’s estimator is developed for the mixture of geometric distributions and provides a lower bound estimator which is valid under arbitrary mixing on the parameter of the geometric. However, Chao’s estimator is also known for its relatively large variance (if compared to the maximum likelihood estimator). Another estimator based on a censored geometric likelihood is suggested which uses the entire sample information but is less affected by model misspecifications. Simulation studies illustrate that the proposed censored estimator comprises a good compromise between the maximum likelihood estimator and Chao’s estimator, e.g. between efficiency and bias.     

Shrinkage estimation of semiparametric multiplicative error models

Within models for nonnegative time series, it is common to encounter deterministic components (trends, seasonalities) which can be specified in a flexible form. This work proposes the use of shrinkage type estimation for the parameters of such components. The amount of smoothing to be imposed on the estimates can be chosen using different methodologies: Cross-Validation for dependent data or the recently proposed Focused Information Criterion. We illustrate such a methodology using a semiparametric autoregressive conditional duration model that decomposes the conditional expectations of durations into their dynamic (parametric) and diurnal (flexible) components. We use a shrinkage estimator that jointly estimates the parameters of the two components and controls the smoothness of the estimated flexible component. The results show that, from the forecasting perspective, an appropriate shrinkage strategy can significantly improve on the baseline maximum likelihood estimation.     

Estimation of dynamic models with nonparametric simulated maximum likelihood

We propose an easy-to-implement simulated maximum likelihood estimator for dynamic models where no closed-form representation of the likelihood function is available. Our method can handle any simulable model without latent dynamics. Using simulated observations, we nonparametrically estimate the unknown density by kernel methods, and then construct a likelihood function that can be maximized. We prove that this nonparametric simulated maximum likelihood (NPSML) estimator is consistent and asymptotically efficient. The higher-order impact of simulations and kernel smoothing on the resulting estimator is also analyzed; in particular, it is shown that the NPSML does not suffer from the usual curse of dimensionality associated with kernel estimators. A simulation study shows good performance of the method when employed in the estimation of jump-diffusion models.