Robust bootstrap forecast densities for GARCH returns and volatilities

Bootstrap procedures are useful to obtain forecast densities for both returns and volatilities in the context of generalized autoregressive conditional heteroscedasticity models. In this paper, we analyse the effect of additive outliers on the finite sample properties of these bootstrap densities and show that, when obtained using maximum likelihood estimates of the parameters and standard filters for the volatilities, they are badly affected with dramatic consequences on the estimation of Value-at-Risk. We propose constructing bootstrap densities for returns and volatilities using a robust parameter estimator based on variance targeting implemented together with an adequate modification of the volatility filter. We show that the performance of the proposed procedure is adequate when compared with available robust alternatives. The results are illustrated with both simulated and real data.     

Estimation of odds ratios under order restrictions

A new method for estimating a set of odds ratios under an order restriction based on estimating equations is proposed. The method is applied to those of the conditional maximum likelihood estimators and the Mantel-Haenszel estimators. The estimators derived from the conditional likelihood estimating equations are shown to maximize the conditional likelihoods. It is also seen that the restricted estimators converge almost surely to the respective odds ratios when the respective sample sizes become large regularly. The restricted estimators are compared with the unrestricted maximum likelihood estimators by a Monte Carlo simulation. The simulation studies show that the restricted estimates improve the mean squared errors remarkably, while the Mantel-Haenszel type estimates are competitive with the conditional maximum likelihood estimates, being slightly worse.     

A more general methodology for fitting global cross-ratio models for discrete longitudinal responses

In this paper, we focus on repeated measurement problems, comprising an interesting research area in statistics. We study longitudinal data which arise when outcomes are observed repeatedly on each experimental subject at several points. We focus on a marginal approach for this type of data with lack of independence among the observations proposed by Dale [Global cross-ratio models for bivariate, discrete, ordered responses. Biometrics. 1986;42(4):909–917] for bivariate, discrete, ordered responses. We propose an alternative estimation based on divergence measures to the full likelihood method proposed in that paper. Finally, a wide simulation study and a data example that illustrates the new methodology is provided.     

Estimation and Inference for Linear Panel Data Models Under Misspecification When Both n and T are Large

This article considers fixed effects (FE) estimation for linear panel data models under possible model misspecification when both the number of individuals, n, and the number of time periods, T, are large. We first clarify the probability limit of the FE estimator and argue that this probability limit can be regarded as a pseudo-true parameter. We then establish the asymptotic distributional properties of the FE estimator around the pseudo-true parameter when n and T jointly go to infinity. Notably, we show that the FE estimator suffers from the incidental parameters bias of which the top order is O(T^{? 1}), and even after the incidental parameters bias is completely removed, the rate of convergence of the FE estimator depends on the degree of model misspecification and is either (nT)^{? 1/2} or n^{? 1/2}. Second, we establish asymptotically valid inference on the (pseudo-true) parameter. Specifically, we derive the asymptotic properties of the clustered covariance matrix (CCM) estimator and the cross-section bootstrap, and show that they are robust to model misspecification. This establishes a rigorous theoretical ground for the use of the CCM estimator and the cross-section bootstrap when model misspecification and the incidental parameters bias (in the coefficient estimate) are present. We conduct Monte Carlo simulations to evaluate the finite sample performance of the estimators and inference methods, together with a simple application to the unemployment dynamics in the U.S.     

A Class of Sampling Two Units with Probability Proportional to Size

A class of sampling two units without replacement with inclusion probability proportional to size is proposed in this article. Many different well known probability proportional to size sampling designs are special cases from this class. The first and second inclusion probabilities of this class satisfy important properties and provide a non-negative variance estimator of the Horvitz and Thompson estimator for the population total. Suitable choice for the first and second inclusion probabilities from this class can be used to reduce the variance estimator of the Horvitz and Thompson estimator. Comparisons between different proportional to size sampling designs through real data and artificial examples are given. Examples show that the minimum variance of the Horvitz and Thompson estimator obtained from the proposed design is not attainable for the most cases at any of the well known designs.     

Maximum likelihood estimation of the bimodal failure rate for censored and tied observations

DIMITROV, RACHEV and YAKOVLEV ( 1985 ) have obtained the isotonic maximum likelihood estimator for the bimodal failure rate function. The authors considered only the complete failure time data. The generalization of this estimator for the case of censored and tied observations is now proposed.     

Using power transformations when approximating quantiles

Estimators are obtained tor quantiles of survival distributions. This is accomplished by approximating Lritr distribution of the transtorrneri data, where the transformation used is that of Box and Cox (1964). The normal approximation as in Box and Cox and, in addition, the extreme value approximation are considered. More generally, to use the methods given, the approximating distribution must come from a location-scale family. For some commonly used survival random variables T the performance of the above approximations are evaluated in terms of the ratio of the true quantiles of T to the estimated one, in the long run. This performance is also evaluated for lower quantiles using simulated lognormai, Weibull and gamma data. Several examples are given to illustrate the methodology herein, including one with actual data.     

Umvu estimation for the cumulative hazard function in a pareto distribution of the first kind

The uniformly minimum variance unbiased estimator of the cumulative hazard function in the Pareto distribution of the first kind is derived. The variance of the estimator is also obtained in an analytic form, and for some cases its values are compared numerically with mean square errors of the maximum likelihood estimator.     

Robust williams trent test

To investigate the biological activities of a new compound or drug, experimenters usually compare a series of increasing doses to a control. Among other objectives, one may try to investigate any possible dose-response trend and to determine the minimum effective dose among all the experimental doses. Williams (1971, 1972) proposed a procedure to test the dose-response trend and also to identify the minimum effective dose based on the normally distributed data. In this paper, we propose a similar test procedure based on the robust estimate'of the average response to perform similar analysis. The proposed method is more resistant to the outliers and more powerful than the Williams procedure when the data distribution deviates from normality. We illustrate the use of this procedure with data arising from a recent study.     

Projectors and linear estimation in general linear models

The paper gives a self-contained account of minimum disper­sion linear unbiased estimation of the expectation vector in a linear model with the dispersion matrix belonging to some, rather arbitrary, set of nonnegative definite matrices. The approach to linear estimation in general linear models recommended here is a direct generalization of some ideas and results presented by Rao (1973, 19 74) for the case of a general Gauss-Markov model

A new insight into the nature of some estimation problems originaly arising in the context of a general Gauss-Markov model as well as the correspondence of results known in the literature to those obtained in the present paper for general linear models are also given. As preliminary results the theory of projectors defined by Rao (1973) is extended.