Parametric bootstrap inferences for unbalanced panel data models

This article presents parametric bootstrap (PB) approaches for hypothesis testing and interval estimation for the regression coefficients of panel data regression models with incomplete panels. Some simulation results are presented to compare the performance of the PB approaches with the approximate inferences. Our studies show that the PB approaches perform satisfactorily for various sample sizes and parameter configurations, and the performance of PB approaches is mostly better than the approximate methods with respect to the coverage probabilities and the Type I error rates. The PB inferences have almost exact coverage probabilities and Type I error rates. Furthermore, the PB procedure can be simply carried out by a few simulation steps, and the derivation is easier to understand and to be extended to the multi-way error component regression models with unbalanced panels. Finally, the proposed approaches are illustrated by using a real data example.     

Parametric bootstrap inferences for the growth curve models with intraclass correlation structure

This paper presents parametric bootstrap (PB) approaches for hypothesis testing and interval estimation of the fixed effects and the variance component in the growth curve models with intraclass correlation structure. The PB pivot variables are proposed based on the sufficient statistics of the parameters. Some simulation results are presented to compare the performance of the proposed approaches with the generalized inferences. Our studies show that the PB approaches perform satisfactorily for various cell sizes and parameter configurations, and tends to outperform the generalized inferences with respect to the coverage probabilities and powers. The PB approaches not only have almost exact coverage probabilities and Type I error rates, but also have the shorter expected lengths and the higher powers. Furthermore, the PB procedure can be simply carried out by a few simulation steps. Finally, the proposed approaches are illustrated by using a real data example.     

Confidence Intervals for Linear Function of Variance Components in Two-Fold Nested Random Effects Model

In the article, we consider the unbalanced case of the two-way nested random effects model under partial balance. Using the method of generalized confidence intervals (GCIs) introduced in Weeranhandi (1993 Weeranhandi , S. ( 1993 ). Generalized confidence intervals . J. Amer. Statist. Assoc. 88 : 899 – 905 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar] 1995 Weeranhandi , S. ( 1995 ). Exact Statistical Methods for Data Analysis . New York : Springer-Verlag . [Google Scholar]), a new method is proposed for constructing confidence intervals on linear function of variance components. To compare the resulted intervals with the Modified Large Sample (MLS) intervals by Hernandez and Burdick (1993 Hernandez , R. P. , Burdick , R. K. ( 1993 ). Confidence intervals on the total variance in unbalanced two-fold nested designs . Biom. J. 35 : 515 – 522 .[Crossref] , [Google Scholar]), a simulation study is conducted. The results indicate that the proposed method performs better than the MLS method, especially for very unbalanced designs.     

Interval estimation for a binomial proportion: a bootstrap approach

This paper discusses the classic but still current problem of interval estimation of a binomial proportion. Bootstrap methods are presented for constructing such confidence intervals in a routine, automatic way. Three confidence intervals for a binomial proportion are compared and studied by means of a simulation study, namely: the Wald confidence interval, the Agresti–Coull interval and the bootstrap-t interval. A new confidence interval, the Agresti–Coull interval with bootstrap critical values, is also introduced and its good behaviour related to the average coverage probability is established by means of simulations.     

A parametric bootstrap approach for two-way error component regression models

In this article, the two-way error component regression model is considered. For the nonhomogenous linear hypothesis testing of regression coefficients, a parametric bootstrap (PB) approach is proposed. Simulation results indicate that the PB test, regardless of the sample sizes, maintains the Type I error rates very well and outperforms the existing generalized variable test, which may far exceed the intended significance level when the sample sizes are small or moderate. Real data examples illustrate the proposed approach work quite satisfactorily.     

Confidence Intervals on Sum of Variance Components in Unbalanced Two-Fold Nested Designs with Equal Subsampling

I hybrid significance test, which blends exact and asymptotic theory in a unique way, is presided as an alternative to Fisher's exact test for unordered rxc contingency tables. The hybrid test is almost equivlent to Fisher's exact test, but requires considerably less computational effort The accuracy of the hybrid p-value is not compromised by sparse contingency tables.     

Asymptotics and bootstrap for random-effects panel data transformation models

This article investigates the asymptotic properties of quasi-maximum likelihood (QML) estimators for random-effects panel data transformation models where both the response and (some of) the covariates are subject to transformations for inducing normality, flexible functional form, homoskedasticity, and simple model structure. We develop a QML-type procedure for model estimation and inference. We prove the consistency and asymptotic normality of the QML estimators, and propose a simple bootstrap procedure that leads to a robust estimate of the variance-covariance (VC) matrix. Monte Carlo results reveal that the QML estimators perform well in finite samples, and that the gains by using the robust VC matrix estimate for inference can be enormous.     

Comparison of bootstrap and generalized bootstrap methods for estimating high quantiles

The generalized bootstrap is a parametric bootstrap method in which the underlying distribution function is estimated by fitting a generalized lambda distribution to the observed data. In this study, the generalized bootstrap is compared with the traditional parametric and non-parametric bootstrap methods in estimating the quantiles at different levels, especially for high quantiles. The performances of the three methods are evaluated in terms of cover rate, average interval width and standard deviation of width of the 95% bootstrap confidence intervals. Simulation results showed that the generalized bootstrap has overall better performance than the non-parametric bootstrap in high quantile estimation.     

Studentized bootstrap confidence intervals based on M-estimates

This article reviews and applies saddlepoint approximations to studentized confidence intervals based on robust M-estimates. The latter are known to be very accurate without needing standard theory assumptions. As examples, the classical studentized statistic, the studentized versions of Huber's M-estimate of location, of its initially MAD scaled version and of Huber's proposal 2 are considered. The aim is to know whether the studentized statistics yield robust confidence intervals with coverages close to nominal, with short intervals. The results of an extensive simulation study and the recommendations for practical use given in this article may fill gaps in the current literature and stimulate further discussion and research.     

Generalized inferences on the common mean vector of several multivariate normal populations

The hypothesis testing and confidence region are considered for the common mean vector of several multivariate normal populations when the covariance matrices are unknown and possibly unequal. A generalized confidence region is derived using the concepts of generalized method based on the generalized p$p$-value. The generalized confidence region is illustrated with two numerical examples. The merits of the proposed method are numerically compared with those of existing methods with respect to their expected area or expected d-dimensional volumes and coverage probabilities under different scenarios.     

Generalized confidence intervals for proportions of total variance in mixed linear models

Exact confidence intervals for a proportion of total variance, based on pivotal quantities, only exist for mixed linear models having two variance components. Generalized confidence intervals (GCIs) introduced by Weerahandi [1993. Generalized confidence intervals (Corr: 94V89 p726). J. Am. Statist. Assoc. 88, 899–905] are based on generalized pivotal quantities (GPQs) and can be constructed for a much wider range of models. In this paper, the author investigates the coverage probabilities, as well as the utility of GCIs, for a proportion of total variance in mixed linear models having more than two variance components. Particular attention is given to the formation of GPQs and GCIs in mixed linear models having three variance components in situations where the data exhibit complete balance, partial balance, and partial imbalance. The GCI procedure is quite general and provides a useful method to construct confidence intervals in a variety of applications.     

Importance resampling for the smoothed bootstrap

Alternative methods of estimating properties of unknown distributions include the bootstrap and the smoothed bootstrap. In the standard bootstrap setting, Johns (1988) introduced an importance resam¬pling procedure that results in more accurate approximation to the bootstrap estimate of a distribution function or a quantile. With a suitable “exponential tilting” similar to that used by Johns, we derived a smoothed version of importance resampling in the framework of the smoothed bootstrap. Smoothed importance resampling procedures were developed for the estimation of distribution functions of the Studentized mean, the Studentized variance, and the correlation coefficient. Implementation of these procedures are presented via simulation results which concentrate on the problem of estimation of distribution functions of the Studentized mean and Studentized variance for different sample sizes and various pre-specified smoothing bandwidths for the normal data; additional simulations were conducted for the estimation of quantiles of the distribution of the Studentized mean under an optimal smoothing bandwidth when the original data were simulated from three different parent populations: lognormal, t(3) and t(10). These results suggest that in cases where it is advantageous to use the smoothed bootstrap rather than the standard bootstrap, the amount of resampling necessary might be substantially reduced by the use of importance resampling methods and the efficiency gains depend on the bandwidth used in the kernel density estimation.     

Instrumental variable-based empirical likelihood inferences for varying-coefficient models with error-prone covariates

This paper presents the empirical likelihood inferences for a class of varying-coefficient models with error-prone covariates. We focus on the case that the covariance matrix of the measurement errors is unknown and neither repeated measurements nor validation data are available. We propose an instrumental variable-based empirical likelihood inference method and show that the proposed empirical log-likelihood ratio is asymptotically chi-squared. Then, the confidence intervals for the varying-coefficient functions are constructed. Some simulation studies and a real data application are used to assess the finite sample performance of the proposed empirical likelihood procedure.     

Comparison of One-Sided Tolerance Limits in Unbalanced One-Way Random Models

Cox's discrete logistic model was extended to the study of the life table by Thompson (1977) to handle grouped survival data. Inferences about the effect of grouping are studies byMonte Carlo methods. The results show that the effect of grouping is not substantial. This approach is applied to the grouped data on liver cancer. The computer program developed for grouped censored data with continuous and indicator covariates is of practical importance and is available fromThe Ohio State University     

Prediction intervals for time series models with trend via sieve bootstrap

This paper discusses method for constructing the prediction intervals for time series model with trend using the sieve bootstrap procedure. Gasser–Müller type of kernel estimator is used for trend estimation and prediction. The boundary modification of the kernel is applied to control the edge effect and to construct the predictor of a trend.     

The estimating function bootstrap

The authors propose a bootstrap procedure which estimates the distribution of an estimating function by resampling its terms using bootstrap techniques. Studentized versions of this so‐called estimating function (EF) bootstrap yield methods which are invariant under reparametrizations. This approach often has substantial advantage, both in computation and accuracy, over more traditional bootstrap methods and it applies to a wide class of practical problems where the data are independent but not necessarily identically distributed. The methods allow for simultaneous estimation of vector parameters and their components. The authors use simulations to compare the EF bootstrap with competing methods in several examples including the common means problem and nonlinear regression. They also prove symptotic results showing that the studentized EF bootstrap yields higher order approximations for the whole vector parameter in a wide class of problems.     

Comparing three bootstrap methods for survey data

Various bootstrap methods for variance estimation and confidence intervals in complex survey data, where sampling is done without replacement, have been proposed in the literature. The oldest, and perhaps the most intuitively appealing, is the without-replacement bootstrap (BWO) method proposed by Gross (1980). Unfortunately, the BWO method is only applicable to very simple sampling situations. We first introduce extensions of the BWO method to more complex sampling designs. The performance of the BWO and two other bootstrap methods, the rescaling bootstrap (Rao and Wu 1988) and the mirror-match bootstrap (Sitter 1992), are then compared through a simulation study. Together these three methods encompass the various bootstrap proposals.     

Linear bootstrap methods for vector autoregressive moving-average models

We provide the theoretical justification of bootstrapping stationary invertible echelon vector autoregressive moving-average (VARMA) models using linear methods. The asymptotic validity of the bootstrap is established with strong white noise under parametric and nonparametric assumptions. Our methods are practical and useful for building reliable simulation-based inference and forecasting without implementing nonlinear estimation techniques such as ML which is usually burdensome, time demanding or impractical, particularly in big or highly persistent systems. The relevance of our procedures is more pronounced in the context of dynamic simulation-based techniques such as maximized Monte Carlo (MMC) tests [see Dufour J-M. Monte Carlo tests with nuisance parameters: a general approach to finite-sample inference and nonstandard asymptotics in econometrics. J Econom. 2006;133(2):443–477 and Dufour J-M, Jouini T. Finite-sample simulation-based tests in VAR models with applications to Granger causality testing. J Econom. 2006;135(1–2):229–254 for the VAR case]. Simulation evidence shows that, compared with conventional asymptotics, our bootstrap methods have good finite-sample properties in approximating the actual distribution of the studentized echelon VARMA parameter estimates, and in providing echelon parameter confidence sets with satisfactory coverage.