Testing symmetry and homogeneity in the almost ideal demand system with co-integrated data using fully modified estimation and the bootstrap

Conventional seemingly unrelated estimation of the almost ideal demand system is shown to lead to small sample bias and distortions in the size of a Wald test for symmetry and homogeneity when the data are co-integrated. A fully modified estimator is developed in an attempt to remedy these problems. It is shown that this estimator reduces the small sample bias but fails to eliminate the size distortion.. Bootstrapping is shown to be ineffective as a method of removing small sample bias in both the conventional and fully modified estimators. Bootstrapping is effective, however, as a method of removing. size distortion and performs equally well in this respect with both estimators.

Bootstrap prediction intervals for autoregressive time series

The calculation of interval forecasts for highly persistent autoregressive (AR) time series based on the bootstrap is considered. Three methods are considered for countering the small-sample bias of least-squares estimation for processes which have roots close to the unit circle: a bootstrap bias-corrected OLS estimator; the use of the Roy–Fuller estimator in place of OLS; and the use of the Andrews–Chen estimator in place of OLS. All three methods of bias correction yield superior results to the bootstrap in the absence of bias correction. Of the three correction methods, the bootstrap prediction intervals based on the Roy–Fuller estimator are generally superior to the other two. The small-sample performance of bootstrap prediction intervals based on the Roy–Fuller estimator are investigated when the order of the AR model is unknown, and has to be determined using an information criterion.

Bootstrap percolation on homogeneous trees has 2 phase transitions

We study the threshold theta bootstrap percolation model on the homogeneous tree with degree b + 1, 2 <= theta <= b, and initial density p. It is known that there exists a nontrivial critical value for p, which we call p(f), such that a) for p > p(f), the final bootstrapped configuration is fully occupied for almost every initial configuration, and b) if p < p(f) , then for almost every initial configuration, the final bootstrapped configuration has density of occupied vertices less than 1. In this paper, we establish the existence of a distinct critical value for p, p(c), such that 0 < p(c) < p(f), with the following properties: 1) if p <= p(c), then for almost every initial configuration there is no infinite cluster of occupied vertices in the final bootstrapped configuration; 2) if p > p(c), then for almost every initial configuration there are infinite clusters of occupied vertices in the final bootstrapped configuration. Moreover, we show that 3) for p < p(c), the distribution of the occupied cluster size in the final bootstrapped configuration has an exponential tail; 4) at p = p(c), the expected occupied cluster size in the final bootstrapped configuration is infinite; 5) the probability of percolation of occupied vertices in the final bootstrapped configuration is continuous on [0, p(f)] and analytic on (p(c), p(f) ), admitting an analytic continuation from the right at p (c) and, only in the case theta = b, also from the left at p(f).

The impact of U.S. unions on productivity : a bootstrap meta-analysis

Resampling methods are used to calculate confidence limits in a metaanalysis of the association between unions and productivity for the population of U.S. studies. The available evidence points to a positive and statistically significant association between unions and productivity in the U.S. manufacturing and education sectors, of around 10% and 7%, respectively

Estimating process capability index Cpm using a bootstrap sequential sampling procedure

Construction of a confidence interval for process capability index CPM is often based on a normal approximation with fixed sample size. In this article, we describe a different approach in constructing a fixed-width confidence interval for process capability index CPM with a preassigned accuracy by using a combination of bootstrap and sequential sampling schemes. The optimal sample size required to achieve a preassigned confidence level is obtained using both two-stage and modified two-stage sequential procedures. The procedure developed is also validated using an extensive simulation study.

Optimizing the quality of bootstrap-based prediction intervals

The bootstrap method is one of the most widely used methods in literature for construction of confidence and prediction intervals. This paper proposes a new method for improving the quality of bootstrap-based prediction intervals. The core of the proposed method is a prediction interval-based cost function, which is used for training neural networks. A simulated annealing method is applied for minimization of the cost function and neural network parameter adjustment. The developed neural networks are then used for estimation of the target variance. Through experiments and simulations it is shown that the proposed method can be used to construct better quality bootstrap-based prediction intervals. The optimized prediction intervals have narrower widths with a greater coverage probability compared to traditional bootstrap-based prediction intervals.

Estimating capability index in multivariate processes using bootstrap sequential sampling procedures

Capability indices in both univariate and multivariate processes are extensively employed in quality control to assess the quality status of production batches before their release for operational use. It is traditionally a measure of the ratio of the allowable process spread and the actual spread. In this paper, we will adopt a bootstrap and sequential sampling procedures to determine the optimal sample size for estimating a multivariate capability index introduced by Pearns et. al. [12]. Bootstrap techniques have the distinct advantage of placing very minimum requirement on the distributions of the underlying quality characteristics, thereby rendering them more relevant under a wide variety of situations. Finally, we provide several numerical examples where the sequential sampling procedures are evaluated and compared.

Constructing optimal prediction intervals by using neural networks and bootstrap method

This brief proposes an efficient technique for the construction of optimized prediction intervals (PIs) by using the bootstrap technique. The method employs an innovative PI-based cost function in the training of neural networks (NNs) used for estimation of the target variance in the bootstrap method. An optimization algorithm is developed for minimization of the cost function and adjustment of NN parameters. The performance of the optimized bootstrap method is examined for seven synthetic and real-world case studies. It is shown that application of the proposed method improves the quality of constructed PIs by more than 28% over the existing technique, leading to narrower PIs with a coverage probability greater than the nominal confidence level.

Panel bootstrap tests of slope homogeneity

This paper proposes two bootstrap-based tests that can be used to infer whether the individual slopes in a panel regression model are homogenous. The first test is suitable when wanting to infer the null of homogeneity versus the general alternative, while the second is suitable when wanting to infer the units of the panel that can be pooled. Both approaches are shown to be asymptotically valid, a property that is verified in small samples using Monte Carlo simulation.