Alternative approaches to implementing Lagrange multiplier tests for serial correlation in dynamic regression models

An approximate F-form of the Lagrange multiplier (LM) test for serial correlation in dynamic regression models is compared with three bootstrap tests. In one bootstrap procedure, residuals from restricted estimation under the null hypothesis are resampled. The other two bootstrap tests use residuals from unrestricted estimation under an alternative hypothesis. A fixed autocorrelation alternative is assumed in one of the two unrestricted bootstrap tests and the other is based upon a Pitman-type sequence of local alternatives. Monte Carlo experiments are used to estimate rejection probabilities under the null hypothesis and in the presence of serial correlation.     

A new approach to bootstrap inference in functional coefficient models

To infer on functional dependence of regression parameters, a new, factor based bootstrap approach is introduced, that is robust under various forms of heteroskedastic error terms. Modeling the functional coefficient parametrically, the bootstrap approximation of an F-statistic is shown to hold asymptotically. In simulation studies with both parametric and nonparametric functional coefficients, factor based bootstrap inference outperforms the wild bootstrap and pairs bootstrap approach, according to its rejection frequencies under the null hypothesis. Applying the functional coefficient model to a cross sectional investment regression on savings, the saving retention coefficient is found to depend on third variables as the population growth rate and the openness ratio.     

Multivariate significance testing and model calibration under uncertainty

The importance of modeling and simulation in the scientific community has drawn interest towards methods for assessing the accuracy and uncertainty associated with such models. This paper addresses the validation and calibration of computer simulations using the thermal challenge problem developed at Sandia National Laboratories for illustration. The objectives of the challenge problem are to use hypothetical experimental data to validate a given model, and then to use the model to make predictions in an untested domain. With regards to assessing the accuracy of the given model (validation), we illustrate the use of Hotelling’s T² statistic for multivariate significance testing, with emphasis on the formulation and interpretation of such an analysis for validation assessment. In order to use the model for prediction, we next employ the Bayesian calibration method introduced by Kennedy and O’Hagan. Towards this end, we discuss how inherent variability can be reconciled with “lack-of-knowledge” and other uncertainties, and we illustrate a procedure that allows probability distribution characterization uncertainty to be included in the overall uncertainty analysis of the Bayesian calibration process.     

Bootstrapping divergence statistics for testing homogeneity in multinomial populations

We consider the problem of testing the equality of ν$\nu$ (ν≥2$\nu \ge 2$) multinomial populations, taking as test statistic a sample version of an f-dissimilarity between the populations, obtained by the replacement of the unknown parameters in the expression of the f-dissimilarity among the theoretical populations, by their maximum likelihood estimators. The null distribution of this test statistic is usually approximated by its limit, the asymptotic null distribution. Here we study another way to approximate it, the bootstrap. We show that the bootstrap yields a consistent distribution estimator. We also study by simulation the finite sample performance of the bootstrap distribution and compare it with the asymptotic approximation. From the simulations it can be concluded that it is worth calculating the bootstrap estimator, because it is more accurate than the approximation yielded by the asymptotic null distribution which, in addition, cannot always be exactly computed.     

Practical multiagent rendezvous through modified circumcenter algorithms

We present a class of modified circumcenter algorithms that allow a group of agents to achieve “practical rendezvous” when they are only able to take noisy measurements of their neighbors. Assuming a uniform detection probability in a disk of radius σ about each neighbor’s true position, we show how initially connected agents converge to a practical stability ball. More precisely, a deterministic analysis allows us to guarantee convergence to such a ball under r-disk graph connectivity in 1D under the condition that r/σ be sufficiently large. A stochastic analysis leads to a similar convergence result in probability, but for any r/σ>1, and under a sequence of switching graphs that contains a connected graph within bounded time intervals. We include several simulations to discuss the performance of the proposed algorithms.     

Divergence statistics for testing uniform association in cross-classifications

In this paper, we consider the problem of testing uniform association in cross-classifications having ordered categories, taking as test statistic one in the family proposed by Conde and Salicrú [J. Conde, M. Salicrú, Uniform association in contingency tables associated to Csiszár divergence, Statistics and Probability Letters 37 (1998) 149-154]. We consider two approximations to the null distribution of the test statistics in this family: an estimation of the asymptotic null distribution and a bootstrap estimator. We prove that both approximations are asymptotically equivalent. To study their finite sample performance, we carried out two simulation experiments, whose results are presented. From the simulations it can be concluded that the bootstrap estimator behaves much better than the estimated asymptotic null distribution.     

Eliminating bias due to censoring in Kendall’s tau estimators for quasi-independence of truncation and failure

While the currently available estimators for the conditional Kendall’s tau measure of association between truncation and failure are valid for testing the null hypothesis of quasi-independence, they are biased when the null does not hold. This is because they converge to quantities that depend on the censoring distribution. The magnitude of the bias relative to the theoretical Kendall’s tau measure of association between truncation and failure due to censoring has not been studied, and so its importance in real problems is not known. We quantify this bias in order to assess the practical usefulness of the estimators. Furthermore, we propose inverse probability weighted versions of the conditional Kendall’s tau estimators to remove the effects of censoring and provide asymptotic results for the estimators. In simulations, we demonstrate the decrease in bias achieved by these inverse probability weighted estimators. We apply the estimators to the Channing House data set and an AIDS incubation data set.     

A multi-path mechanism for reliable VoIP transmission over wireless networks

With the advances in audio encoding standards and wireless access networks, voice over IP (VoIP) is becoming quite popular. However, real-time voice data over lossy networks (such as WLAN and UMTS), still posses several challenging problems because of the adverse effects caused by complex network dynamics. One approach to provide QoS for VoIP applications over the wireless networks is to use multiple paths to deliver VoIP data destined for a particular receiver. This paper introduced cmpSCTP, a transport layer solution for concurrent multi-path transfer that modifies the standard stream control transmission protocol (SCTP). The cmpSCTP aims at exploiting SCTP’s multi-homing capability by selecting several best paths among multiple available network interfaces to improve data transfer rate to the same multi-homed device. Through the use of path monitoring and packet allotment techniques, cmpSCTP tries to transmit an amount of packets corresponding to the path’s ability. At the same time, cmpSCTP updates the transmission strategy based on the real-time information of all of paths. Using cmpSCTP’s flexible path management capability, we may switch the flow between multiple paths automatically to realize seamless path handover. The theoretical analysis evaluated the model of cmpSCTP and formulated optimal traffic fragmentation of VoIP data. Extensive simulations under different scenarios using OPNET verified that cmpSCTP can effectively enhance VoIP transmission efficiency and highlighted the superiority of cmpSCTP against the other SCTP’s extension implementations under performance indexes such as throughput, handover latency, packet delay, and packet loss.     

A resampling approach for adjustment in prediction models for covariate measurement error

Recent works on covariate measurement errors focus on the possible biases in model coefficient estimates. Usually, measurement error in a covariate tends to attenuate the coefficient estimate for the covariate, i.e., a bias toward the null occurs. Measurement error in another confounding or interacting variable typically results in incomplete adjustment for that variable. Hence, the coefficient for the covariate of interest may be biased either toward or away from the null. This paper presents a new method based on a resampling technique to deal with covariate measurement errors in the context of prediction modeling. Prediction accuracy is our primary parameter of interest. Prediction accuracy of a model is defined as the success rate of prediction when the model predicts new response. We call our method bootstrap regression calibration (BRC). We study logistic regression with interacting covariates as our prediction model. We measure the prediction accuracy of a model by receiver operating characteristic (ROC) method. Results from simulations show that bootstrap regression calibration offers consistent enhancement over the commonly used regression calibration (RC) method in terms of improving prediction accuracy of the model and reducing bias in the estimated coefficients.     

A Theory of Historical Discovery: The Construction of Componential Models

One of the major goals of 18th century chemistry was to determine the components of substances. In this paper we describe STAHL, a system that models significant portions of 18th century reasoning about compositional models. The system includes a number of heuristics for generating componential models from reactions, as well as error recovery mechanisms for dealing with inconsistent results. STAHL processes chemical reactions incrementally, and is therefore capable of reconstructing extended historic episodes, such as the century-long development of the phlogiston theory. We evaluate STAHL’s heuristics in the light of historical data, and conclude that the same reasoning mechanisms account for a variety of historical achievements, including Black’s models of mild alkali and Lavoisier’s oxygen theory. STAHL explains the generation of competing accounts of the same reactions, since the system’s reasoning chain depends on knowledge it has accumulated at earlier stages.     

Worst case dimensioning and modeling of reliable real-time multihop wireless sensor network

Wireless Sensor Network (WSN) should be capable of fulfilling its mission, in a timely manner and without loss of important information. In this paper, we propose a new analytical model for calculating RRT (Reliable Real-Time) degree in multihop WSNs, where RRT degree describes the percentage of real-time data that the network can reliably deliver on time from any source to its destination. Also, packet loss probability is modeled as a function of the probability of link failure when the buffer is full and the probability of node failure when node’s energy is depleted. Most of the network properties are considered as random variables and a queuing theory based model is derived. In this model, the effect of network load on the packets’ delay, RRT degree, and node’s energy depletion rate are considered. Also network calculus is tailored and extended so that a worst case analysis of the delay and queue quantities in sensor networks is possible. Simulation results are used to validate the proposed model. The simulation results agree very well with the model.     

Geometric characterization, hydraulic behavior and upscaling of 3D fissured geologic media

In this article, we present numerical modeling and upscaling procedures for highly fissured and discontinuous geologic media, such as ‘karsts’. In particular, we propose a geomorphological generation model, and we address the ‘upscaling’ problem for flow in a highly fissured porous medium (‘what is the macroscale hydraulic behavior of the fissured porous medium?’). The morphological model is partly Boolean, based on statistical distributions of discrete objects (voids), combined with a (random) continuum representation for the underlying porous matrix. Various methods for constraining these two types of media are discussed (self-consistent thresholding; genetic dissolution). Hydraulic simulations are then conducted with the 3D finite volume code BIGFLOW, for the case of 3D composite media with constant matrix and high ‘fissure/matrix’ permeability contrast. The hydrodynamic equations are based on either Darcy’s linear head loss law, or on a linear/quadratic combination of Darcy and Ward–Forchheimer quadratic law (inertial effects). The numerical experiments are conducted for saturated steady flow under permeametric boundary conditions. They are used to analyze the equivalent macroscale behavior of fissured media, as well as quasi-percolation effects, in comparison with analytical results and bounds (Darcian case, low Reynolds). In addition, at moderate to large Reynolds numbers, the macroscale effects of non-Darcian (inertial) head losses are also analyzed.     

Testing for independence in heavy-tailed time series using the codifference function

In this paper, we consider a Portmanteau-type test of randomness for symmetric α stable random variables with exponent 0<α≤2, using a test statistic that differs from, but has the same general form as Box–Pierce Q-statistic, which is defined using the codifference function. We obtain that unlike a similar test proposed in [Runde, R., 1997. The asymptotic null distribution of the Box–Pierce Q-statistic for random variables with infinite variance—with an application to German stock returns. Journal of Econometrics 78, 205–216], the asymptotic distribution of the proposed statistic is similar to the classical case, that is asymptotically χ² distributed, both in finite and infinite variance cases. Simulation studies are performed to obtain the small sample performance of the proposed statistic. We found that the proposed statistic works fairly well, in the sense that in the infinite variance case, under suitable choice of the design parameter, its empirical levels are closer to the theoretical ones than Runde’s statistic. In the finite variance case, its empirical level is approximately the same as that of Ljung–Box’s statistic [Ljung, G.M. and Box, G.E.P., 1978. On a measure of lack of fit in time series models. Biometrika 65, 297–303]. Furthermore, the statistic also has good power against the AR(1) alternative. We provide an empirical example using some stocks chosen from the LQ45 index listed in the Indonesia Stock Exchange (IDX).     

Homogeneity tests for several Poisson populations

In this paper we compare the size distortions and powers for Pearson’s χ²-statistic, likelihood ratio statistic LR, score statistic SC and two statistics, which we call UT and VT here, proposed by [Potthoff, R.F., Whittinghill, M., 1966. Testing for homogeneity: II. The Poisson distribution. Biometrika 53, 183–190] for testing the equality of the rates of K Poisson processes. Asymptotic tests and parametric bootstrap tests are considered. It is found that the asymptotic UT test is too conservative to be recommended, while the other four asymptotic tests perform similarly and their powers are close to those of their parametric bootstrap counterparts when the observed counts are large enough. When the observed counts are not large, Monte Carlo simulation suggested that the asymptotic test using SC, LR and UT statistics are discouraged; none of the parametric bootstrap tests with the five statistics considered here is uniformly best or worst, and the asymptotic tests using Pearson’s χ² and VT always have similar powers to their bootstrap counterparts. Thus, the asymptotic Pearson’s χ² and VT tests have an advantage over all five parametric bootstrap tests in terms of their computational simplicity and convenience, and over the other four asymptotic tests in terms of their powers and size distortions.     

Bootstrap hypothesis testing for some common statistical problems: A critical evaluation of size and power properties

The construction of bootstrap hypothesis tests can differ from that of bootstrap confidence intervals because of the need to generate the bootstrap distribution of test statistics under a specific null hypothesis. Similarly, bootstrap power calculations rely on resampling being carried out under specific alternatives. We describe and develop null and alternative resampling schemes for common scenarios, constructing bootstrap tests for the correlation coefficient, variance, and regression/ANOVA models. Bootstrap power calculations for these scenarios are described. In some cases, null-resampling bootstrap tests are equivalent to tests based on appropriately constructed bootstrap confidence intervals. In other cases, particularly those for which simple percentile-method bootstrap intervals are in routine use such as the correlation coefficient, null-resampling tests differ from interval-based tests. We critically assess the performance of bootstrap tests, examining size and power properties of the tests numerically using both real and simulated data. Where they differ from tests based on bootstrap confidence intervals, null-resampling tests have reasonable size properties, outperforming tests based on bootstrapping without regard to the null hypothesis. The bootstrap tests also have reasonable power properties.     

Bootstrap hypothesis testing for some common statistical problems: A critical evaluation of size and power properties

The construction of bootstrap hypothesis tests can differ from that of bootstrap confidence intervals because of the need to generate the bootstrap distribution of test statistics under a specific null hypothesis. Similarly, bootstrap power calculations rely on resampling being carried out under specific alternatives. We describe and develop null and alternative resampling schemes for common scenarios, constructing bootstrap tests for the correlation coefficient, variance, and regression/ANOVA models. Bootstrap power calculations for these scenarios are described. In some cases, null-resampling bootstrap tests are equivalent to tests based on appropriately constructed bootstrap confidence intervals. In other cases, particularly those for which simple percentile-method bootstrap intervals are in routine use such as the correlation coefficient, null-resampling tests differ from interval-based tests. We critically assess the performance of bootstrap tests, examining size and power properties of the tests numerically using both real and simulated data. Where they differ from tests based on bootstrap confidence intervals, null-resampling tests have reasonable size properties, outperforming tests based on bootstrapping without regard to the null hypothesis. The bootstrap tests also have reasonable power properties.     

A bootstrap test for the comparison of nonlinear time series

The difference between the regression functions of two stationary conditional heteroskedastic autoregressive time series is tested. The functions can be equal, or shifted, under the null hypothesis. Local linear estimation of the regression function results in observable residuals. Bootstrap residuals lead to a marked empirical process as test statistic and a Kolmogorov-Smirnov version is applied. The simulation study for linear, exponential or trigonometric regression functions with homoskedastic or heteroskedastic errors finds the rejection probability under the null hypothesis to be near the level. Comparing series with different combinations of linear, exponential and trigonometric functions, the rejection probability under the alternative yields mixed results.     

A Comparative analysis of Green’s functions of 1D matching equations for motion synthesis

When filtering an input image, the Green’s functions of matching equations are capable of inducing a broad class of motions, a property that has led to their use in several computer graphics and computer vision applications. In all such applications, the Green’s functions of second-order differential equations have been considered, even though no justification has been given for their preference over simpler, first-order equations. Here we present a study of first-order one-dimensional matching equations, both in the uniform and in the affine motion models. Comparing their Green’s functions with those of the corresponding second-order cases, we find evidence for the latter’s superiority in motion synthesis. We also propose and discuss a general discretization scheme for Green’s functions of one-dimensional matching equations, showing that the affine motion model is particularly sensitive to the sampling frequency. In this case, we advocate the use of area sampling, for allowing realistic motion simulations.     

Experimental analysis of self-organizing team’s behaviors

This paper is focused on the study of self-organizing team’s behaviors which are dependent on the interaction rules and the decision factors of team members. The self-organizing team’s behavior means that team members work unconditionally with one of the three work attitudes (diligence, average, and shirking). A small-world network is suggested as the basic relationships of team members. Different from the traditional models, Reciprocators encourage their friends if they work diligently and punish them if they shirk work. It is supposed that team member’s decision of choosing work attitude depends on four decision factors, humanity, herd instinct, rationality, and follower tendency. Firstly, all of the four decision factors’ weights are supposed as 0.25. Multiple experiments were conducted to analyze the behavior of a team by a multi-agent experiment system. It is found that, in order to increase the fraction of diligent team members, different strategies should be used under different Reciprocators’ fractions. Increasing Reciprocators’ fraction is beneficial to the increase of diligent members; however, the increase rate will slow down after an inflexion (here it means the inflexion of Reciprocators’ fraction). After the previous experiments study, extended experiments were developed to work on the influence of the four factors’ different weights. A self-adaptive algorithm is suggested to achieve the four decision factors’ weights. The results of self-adaptive algorithm have different influences on the team’s behaviors under different fractions of Reciprocators. Finally, influences of members’ different relationships are studied by other experiments. It is also proved that the fraction of diligent members is not dependent on the structure of team members’ relationships. The results demonstrate that the self-organizing team’s behavior can be significantly influenced by its scenario while managing a self-organizing team.