Bootstrap Selector for the Smoothing Parameter of Beran’s Estimator

This work proposes a resampling technique to approximate the smoothing parameter of Beran’s estimator. It is based on resampling by the smoothed bootstrap and minimising the bootstrap approximation of the mean integrated squared error to find the bootstrap bandwidth. The behaviour of this method has been tested by simulation on several models. Bootstrap confidence intervals are also addressed in this research and their performance is analysed in the simulation study.

Monitoring Persistence Change in Heavy-Tailed Observations

In this paper, a ratio test based on bootstrap approximation is proposed to detect the persistence change in heavy-tailed observations. This paper focuses on the symmetry testing problems of I(1)-to-I(0) and I(0)-to-I(1). On the basis of residual CUSUM, the test statistic is constructed in a ratio form. I prove the null distribution of the test statistic. The consistency under alternative hypothesis is also discussed. However, the null distribution of the test statistic contains an unknown tail index. To address this challenge, I present a bootstrap approximation method for determining the rejection region of this test. Simulation studies of artificial data are conducted to assess the finite sample performance, which shows that our method is better than the kernel method in all listed cases. The analysis of real data also demonstrates the excellent performance of this method.

Integrated conditional moment test and beyond: when the number of covariates is divergent

Summary The classic integrated conditional moment test is a promising method for model checking and its basic idea has been applied to develop several variants. However, in diverging dimension scenarios, the integrated conditional moment test may break down and has completely different limiting properties from those in fixed dimension cases, and the related wild bootstrap approximation would also be invalid. To extend this classic test to diverging dimension settings, we propose a projected adaptive-to-model version of the integrated conditional moment test. We study the asymptotic properties of the new test under both the null and alternative hypotheses to examine its significance level maintenance and its sensitivity to the global and local alternatives that are distinct from the null at the rate n-1/2. The corresponding wild bootstrap approximation can still work for the new test in diverging dimension scenarios. We also derive the consistency and asymptotically linear representation of the least squares estimator of the parameter at the fastest rate of divergence in the literature for nonlinear models. The numerical studies show that the new test can greatly enhance the performance of the integrated conditional moment test in high-dimensional cases. We also apply the test to a real data set for illustration.

Consistency of bootstrap approximation to the null distributions of local spatial statistics with application to house price analysis

With the increasing availability of spatially extensive geo-referenced data, much attention has been paid to the use of local statistics to identify local patterns of spatial association, in which the null distributions of local statistics play an essential role in the related statistical inference. As a powerful tool to approximate the distribution of a statistic, the bootstrap method is used in this paper to derive null distributions of the commonly used local spatial statistics including local Getis and Ord’s $G_{i}$ G i , Moran’s $I_{i}$ I i and Geary’s $c_{i}$ c i . Strong consistency of the bootstrap approximation to the null distributions of the statistics is proved under some mild conditions, and the Boston housing price data are analyzed to demonstrate the application of the theoretical results.

Bootstrapping M-estimators in generalized autoregressive conditional heteroscedastic models

Summary We consider the weighted bootstrap approximation to the distribution of a class of M-estimators for the parameters of the generalized autoregressive conditional heteroscedastic model. We prove that the bootstrap distribution, given the data, is a consistent estimate in probability of the distribution of the M-estimator, which is asymptotically normal. We propose an algorithm for the computation of M-estimates which at the same time is useful for computing bootstrap replicates from the given data. Our simulation study indicates superior coverage rates for various weighted bootstrap schemes compared with the rates based on the normal approximation and existing bootstrap methods for the generalized autoregressive conditional heteroscedastic model, such as percentile $t$-subsampling schemes. Since some familiar bootstrap schemes are special cases of the weighted bootstrap, this paper thus provides a unified theory and algorithm for bootstrapping in generalized autoregressive conditional heteroscedastic models.

Network Selection in Wireless Heterogeneous Environment Based on Available Bandwidth Estimation

Background: With the availability of multiple options in wireless network simultaneously, Always Best Connected (ABC) requires dynamic selection of the best network and access technologies. Objective: In this paper, a novel dynamic access network selection algorithm based on the real time is proposed. The available bandwidth (ABW) of each network is required to be estimated to solve the network selection problem. Method: Proposed algorithm estimates available bandwidth by taking averages, peaks, low points and bootstrap approximation for network selection. It monitors real-time internet connection and resolves the selection issue in internet connection. The proposed algorithm is capable of adapting to prevailing network conditions in heterogeneous environment of 2G, 3G and WLAN networks without user intervention. It is implemented in temporal and spatial domains to check its robustness. Estimation error, overhead, estimation time with the varying size of traffic and reliability are used as the performance metrics. Results: Through numerical results, it is shown that the proposed algorithm’s ABW estimation based on bootstrap approximation gives improved performance in terms of estimation error (less than 20%), overhead (varies from 0.03% to 83%) and reliability (approx. 99%) with respect to existing techniques. Conclusion: Our proposed methodology of network selection criterion estimates the available bandwidth by taking averages, peaks, and low points and bootstrap approximation method (standard deviation) for the selection of network in the wireless heterogeneous environment. It monitors real-time internet connection and resolves internet connections selection issue. All the real-time usage and test results demonstrate the productivity and adequacy of available bandwidth estimation with bootstrap approximation as a practical solution for consistent correspondence among heterogeneous wireless networks by precise network selection for multimedia services.