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We propose a quasi–maximum likelihood estimator for the location parameters of a linear regression model with bounded and symmetrically distributed errors. The error outcomes are restated as the convex combination of the bounds, and we use the method of maximum entropy to derive the quasi–log likelihood function. Under the stated model assumptions, we show that the proposed estimator is unbiased, consistent, and asymptotically normal. We then conduct a series of Monte Carlo exercises designed to illustrate the sampling properties of the quasi–maximum likelihood estimator relative to the least squares estimator. Although the least squares estimator has smaller quadratic risk under normal and skewed error processes, the proposed QML estimator dominates least squares for the bounded and symmetric error distribution considered in this paper.

This article examines the history, development, and application of the sandwich estimate of variance. In describing this estimator, we pay attention to applications that have appeared in the literature and examine the nature of the problems for which this estimator is used. We describe various adjustments to the estimate for use with small samples, and illustrate the estimator’s construction for a variety of models. Finally, we discuss interpretation of results.

To present the bootstrap procedure to correct biases in maximum likelihood estimator of mean time to failure (MTTF) and percentiles in a Weibull regression model.

A reliability model is described by a Weibull regression model with parameters being estimated by maximum likelihood method and they will be used estimate other quantities of interest as MTTF or percentiles. When a small sample is employed it is known that the estimates of these quantities are biased. A simulation study varying sample size, censored mechanisms, allocation mechanisms and levels of censored data are designed to quantify these biases.

The bootstrap procedure corrects the biased maximum likelihood estimates of MTTF and percentiles.

A minor sample may be required if the bootstrap procedure is required to produce estimator of the quantities as MTTF and percentiles.

The employment of bootstrap procedure to quantify the biases since analytical expression of the biases are very difficult to calculate. And the minor samples are needed to obtain unbiased estimates for bootstrap corrected estimator.

We formulate generalized maximum entropy estimators for the general linear model and the censored regression model when there is first order spatial autoregression in the dependent variable. Monte Carlo experiments are provided to compare the performance of spatial entropy estimators relative to classical estimators. Finally, the estimators are applied to an illustrative model allocating agricultural disaster payments.

Standard stratified sampling (SSS) is a popular non-random sampling scheme. Maximum likelihood estimator (MLE) is inconsistent if some sampled strata depend on the response variable Y (‘endogenous samples’) or if some Y-dependent strata are not sampled at all (‘truncated sample’ – a missing data problem). Various versions of MLE have appeared in the literature, and this paper reviews practical likelihood-based estimators for endogenous or truncated samples in SSS. Also a new estimator ‘Estimated-EX MLE’ is introduced using an extra random sample on X (not on Y) to estimate the distribution EX of X. As information on Y may be hard to get, this estimator's data demand is weaker than an extra random sample on Y in some other estimators. The estimator can greatly improve the efficiency of ‘Fixed-X MLE’ which conditions on X, even if the extra sample size is small. In fact, Estimated-EX MLE does not estimate the full FX as it needs only a sample average using the extra sample. Estimated-EX MLE can be almost as efficient as the ‘Known-FX MLE’. A small-scale simulation study is provided to illustrate these points.

Exact confidence interval estimation for the new extreme value model is often impractical. This paper seeks to evaluate the accuracy of approximate confidence intervals for the two‐parameter new extreme value model.

The confidence intervals of the parameters of the new model based on likelihood ratio, Wald and Rao statistics are evaluated and compared through the simulation study. The criteria used in evaluating the confidence intervals are the attainment of the nominal error probability and the symmetry of lower and upper error probabilities.

This study substantiates the merits of the likelihood ratio, the Wald and the Rao statistics. The results indicate that the likelihood ratio‐based intervals perform much better than the Wald and Rao intervals.

Exact interval estimates for the new model are difficult to obtain. Consequently, large sample intervals based on the asymptotic maximum likelihood estimators have gained widespread use. Intervals based on inverting likelihood ratio, Rao and Wald statistics are rarely used in commercial packages. This paper shows that the likelihood ratio intervals are superior to intervals based on the Wald and the Rao statistics.

This paper is concerned with estimation of the parameters of a high-frequency VAR model using mixed-frequency data, both for the stock and for the flow case. Extended Yule–Walker estimators and (Gaussian) maximum likelihood type estimators based on the EM algorithm are considered. Properties of these estimators are derived, partly analytically and by simulations. Finally, the loss of information due to mixed-frequency data when compared to the high-frequency situation as well as the gain of information when using mixed-frequency data relative to low-frequency data is discussed.

One way to control for the heterogeneity in panel data is to allow for time-invariant, individual specific parameters. This fixed effect approach introduces many parameters into the model which causes the “incidental parameter problem”: the maximum likelihood estimator is in general inconsistent. Woutersen (2001) shows how to approximately separate the parameters of interest from the fixed effects using a reparametrization. He then shows how a Bayesian method gives a general solution to the incidental parameter for correctly specified models. This paper extends Woutersen (2001) to misspecified models. Following White (1982), we assume that the expectation of the score of the integrated likelihood is zero at the true values of the parameters. We then derive the conditions under which a Bayesian estimator converges at rate N where N is the number of individuals. Under these conditions, we show that the variance-covariance matrix of the Bayesian estimator has the form of White (1982). We illustrate our approach by the dynamic linear model with fixed effects and a duration model with fixed effects.