Relevant Test Statistics Research Articles

Tail index estimation in the presence of covariates: Stock returns’ tail risk dynamics

This paper provides novel theoretical results for the estimation of the conditional tail index of Pareto and Pareto-type distributions in a time series context. We show that both the estimators and relevant test statistics are normally distributed in the limit, when independent and identically distributed or dependent data are considered. Simulation results provide support for the theoretical findings and highlight the good finite sample properties of the approach in a time series context. The proposed methodology is then used to analyse stock returns’ tail risk dynamics. Two empirical applications are provided. The first consists in testing whether the time-varying tail exponents across firms follow Kelly and Jiang’s (2014) assumption of common firm level tail dynamics. The results obtained from our sample seem not to favour this hypothesis. The second application, consists of the evaluation of the impact of two market risk indicators, VIX and Expected Shortfall (ES) and two firm specific covariates, capitalization and market-to-book on stocks tail risk dynamics. Although all variables seem important drivers of firms’ tail risk dynamics, it is found that ES and firms’ capitalization seem to have overall wider impact.

Uniformly most powerful unbiased tests for the dispersion parameter of the Conway–Maxwell–Poisson distribution

Uniformly most powerful unbiased tests for one-sided hypotheses about the dispersion parameter of the Conway–Maxwell–Poisson distribution are derived by utilizing the exponential family structure, and it is shown how to obtain the critical values of the relevant test statistics via simulation. The tests, which do not require parameter estimators, are applied to several real data sets from the literature to statistically confirm under- or overdispersion, giving evidence against the common Poisson model for count data.

Improved EDF-Based Tests for Weibull Distribution Using Ranked Set Sampling

It is well known that ranked set sampling (RSS) is superior to conventional simple random sampling (SRS) in that it frequently results in more effective inference techniques. One of the most popular and broadly applicable models for lifetime data is the Weibull distribution. This article proposes different modified goodness-of-fit tests based on the empirical distribution function (EDF) for the Weibull distribution. The recommended RSS tests are compared to their SRS counterparts. For each scheme, the critical values of the relevant test statistics are computed. A comparison of the power of the suggested goodness-of-fit tests based on a number of alternatives is investigated. RSS tests are more effective than their SRS equivalents, according to simulated data.

New methods for multiple testing in permutation inference for the general linear model.

Permutation methods are commonly used to test the significance of regressors of interest in general linear models (GLMs) for functional (image) data sets, in particular for neuroimaging applications as they rely on mild assumptions. Permutation inference for GLMs typically consists of three parts: choosing a relevant test statistic, computing pointwise permutation tests, and applying a multiple testing correction. We propose new multiple testing methods as an alternative to the commonly used maximum value of test statistics across the image. The new methods improve power and robustness against inhomogeneity of the test statistic across its domain. The methods rely on sorting the permuted functional test statistics based on pointwise rank measures; still, they can be implemented even for large data. The performance of the methods is demonstrated through a designed simulation experiment and an example of brain imaging data. We developed the R package GET, which can be used for the computation of the proposed procedures.

Some New Tests of Conformity with Benford’s Law

This paper presents new perspectives and methodological instruments for verifying the validity of Benford’s law for a large given dataset. To this aim, we first propose new general tests for checking the statistical conformity of a given dataset with a generic target distribution; we also provide the explicit representation of the asymptotic distributions of the relevant test statistics. Then, we discuss the applicability of such novel devices to the case of Benford’s law. We implement extensive Monte Carlo simulations to investigate the size and the power of the introduced tests. Finally, we discuss the challenging theme of interpreting, in a statistically reliable way, the conformity between two distributions in the presence of a large number of observations.

Characteristics and Outcome of Paediatric Traumatic Brain Injuries

Background: As with most ailments common to adult and paediatric age groups, studies that describe and characterize paediatric traumatic brain injuries (TBIs) lag those of their adult counterparts. This is more so in the developing countries where national data are not well developed. The development of local clinical guidelines has been shown to positively impact outcomes of paediatric TBI. Data on the characteristics and outcomes of TBI among paediatric age groups will provide a framework for the development of an all-encompassing management guideline. Methods: In this study, a retrospective review of demography, mechanism of injury, pattern of presentation, nature of treatment, duration of hospital admission, and outcome of children aged 0–17 years managed for traumatic TBI at the University of Nigeria Teaching Hospital, Enugu-Nigeria was performed. Data were analyzed using SPSS version 21. Relevant test statistics were used to test for associations. A P = 0.05 was considered statistically significant. Results: A total of 163 patients' medical records were retrieved and analyzed. Of these, 117 (71.8%) were males and 46 (28.2%) were females. Their ages ranged from 6 weeks to 17 years with a mean age of 7.66 ± 5.1 years and peaked at 3–5 years. No difference in mean age between gender (P = 0.427). Pedestrian motor vehicular accident was the most common cause of injury. Fall from fruit trees and assault were peculiar to children from suburban/rural areas. TBI severity on admission was mild (44.2%), moderate (38.7%), and severe (17.2%). Other systemic injuries were present in 33.7%, of which long bone fractures were the most common (23/55). Abnormal brain computed tomography findings were seen in 83.2% with skull fracture being the most common finding. Operative procedures were carried out on 19.6% of patients. Conservative measures were the mainstay of management. The mean duration of hospital admission was 14.01 ± 11.8 days was significantly associated with admission Glasgow Coma Scale (GCS) Score (P < 0.0001) and Glasgow Outcome Score (GOS) at discharge (P = 0.03). The overall outcome was good (GOS 4 and 5) in 92.0% and has a significant association with GCS on admission (P < 0.0001). Long-term (Extended GOS) was 8 in 98.2% of those followed up. Conclusion: Paediatric TBI is mainly mild to moderate in severity with a male predilection. The main cause is road traffic accidents with most victims being pedestrians. Management is mainly non-operative and the outcome at discharge is good even in a middle-income country and significantly determined by GCS on admission.

A Hierarchical Map and Application to Traverse and Unify Analyses Subsumed by Canonical Correlation

This article presents a hierarchical map of analyses subsumed by canonical correlation and a shiny application to facilitate the connections between said analyses. Building on the work of other researchers who used canonical correlation analyses to unify analyses in the general linear model, we demonstrate that the hierarchy is not as flat as some have portrayed. While a simpler hierarchy may seem to be more accessible, it implies a lack of relationship between analyses that may cause confusion when learning the vast majority of univariate and multivariate analyses in the general linear model. Because it is not always intuitive how all the relevant analyses for a given data type can be conducted, we developed the Shiny application canCORRgam to demonstrate the hierarchical path of analyses subsumed by canonical correlation for 15 different models. The canCORRgam application provides emerging researchers evidence of the transitive properties implied in the map. Our work also promotes meta-analytic thinking and practice as we provide the tools, formula, and software to relate test statistics to effect sizes in addition to transforming relevant test statistics and effect sizes to equivalent test statistics and effect sizes.

Inference for Income Mobility Measures in the Presence of Spatial Dependence

Income mobility measures provide convenient and concise ways to reveal the dynamic nature of regional income distributions. Statistical inference about these measures is important especially when it comes to a comparison of two regional income systems. Although the analytical sampling distributions of relevant estimators and test statistics have been asymptotically derived, their properties in small sample settings and in the presence of contemporaneous spatial dependence within a regional income system are underexplored. We approach these issues via a series of Monte Carlo experiments that require the proposal of a novel data generating process capable of generating spatially dependent time series given a transition probability matrix and a specified level of spatial dependence. Results suggest that when sample size is small, the mobility estimator is biased while spatial dependence inflates its asymptotic variance, raising the Type I error rate for a one-sample test. For the two-sample test of the difference in mobility between two regional economic systems, the size tends to become increasingly upward biased with stronger spatial dependence in either income system, which indicates that conclusions about differences in mobility between two different regional systems need to be drawn with caution as the presence of spatial dependence can lead to false positives. In light of this, we suggest adjustments for the critical values of relevant test statistics.

A Testing Strategy With Adaptive Dose Selection and Two Endpoints

ABSTRACTThe article deals with the design of a complex clinical trial with multiple doses of an experimental treatment tested against a control treatment, interim analyses and several endpoints characterizing treatment success. The closed test principle, methods from group sequential testing, and combination test methodology are combined to control the familywise error rate (FWER) when testing for treatment benefit. We also discuss strategies for utilizing the correlations between some of the relevant test statistics.

Using the Bootstrap to Test for Symmetry Under Unknown Dependence

This article considers tests for symmetry of the one-dimensional marginal distribution of fractionally integrated processes. The tests are implemented by using an autoregressive sieve bootstrap approximation to the null sampling distribution of the relevant test statistics. The sieve bootstrap allows inference on symmetry to be carried out without knowledge of either the memory parameter of the data or of the appropriate norming factor for the test statistic and its asymptotic distribution. The small-sample properties of the proposed method are examined by means of Monte Carlo experiments, and applications to real-world data are also presented.

Correlation Tests Detecting Order Restrictions in Binary Response

The work is on detection of order restrictions in 2 × k cohort study. The existing tests in the literature are mostly based on subjective choice of column scores. Moreover, when the marginal distributions of the column totals differ, it is observed that the normal approximation to the null distribution (having no difference in the disease risks among the exposure categories) of the relevant test statistic for small samples is violated in most of the cases. As a remedy, utilizing such variation in column distributions, single contrast tests are proposed for this purpose. Performance of the proposed tests are assessed numerically and are compared with that of an existing competitor.

Commentary: Robust quantification of orientation selectivity and direction selectivity.

Commentary: Robust quantification of orientation selectivity and direction selectivity.

Factors affecting the evacuation decisions of coastal households during Cyclone Aila in Bangladesh

ABSTRACTDespite sincere efforts by concerned agencies and recent improvements in hazard warnings, thousands of at-risk people did not evacuate during Aila, a category-I tropical cyclone that struck southwestern coastal Bangladesh in 2009. This study investigated the responses of the people affected by Aila to cyclone warnings and associated evacuation orders, and unveiled behavioural aspects that explain why they did or did not comply with the evacuation orders. Utilising the primary data collected from 420 households living in the severely affected coastal sub-district Koyra, located in Khulna District, this study found that although more than 97% of the households had received cyclone warnings and evacuation orders before Aila's landfall, only around 26% had evacuated. We also examined this study's empirical findings for factors that had dissuaded people from complying with the evacuation orders. Relevant test statistics along with results from principal component analysis suggested that the significant and systematic absenteeism of households from disaster preparedness training appears to be one of the key determinants that affected their evacuation decisions, along with factors related to warning messages, the attributes of cyclone shelters, risk perception, and socioeconomic aspects. A number of recommendations are also presented in this study for people at risk to improve their evacuation rates in future emergencies, not only to save their own lives but also to save their livestock.

Distribution Based Level Change Detection in a Random Level Forecasting Model

It is well known that an unexpected level change in time series can cause persistent forecasting errors, depending on the change size and the underlying time series process. This relationship is demonstrated particularly with macroeconomic and financial time series. Forecasting literature suggests using the relevant test statistics to detect the level change, but they are just measures that are not coupled with the correct statistical distributions. Hence, this study aims to find the correct statistical distribution of the level change statistic and to adapt the forecasting equation accordingly. The performance of the proposed method is validated by simulated time series and an empirical example.

Effect of Mortar Joint Thickness on the Compressive Strength of Autoclaved Flyash - Lime Brick Masonry

After autoclaved flyash-lime brick masonry was compressed, in the masonry makes pull stress,bend stress, cut stress and complex stress state. The effect of mortar joint thickness on the compressive strength of masonry is the extend of improving under the complex stress state in the masonry. In the domestic and foreign brick construction teaching materials, they are all value the influence and make some describe and comments, but it was limited to the general qualitative analysis. Still not a series study was conduct on the impact, now in order to explore the influence on it, combining with domestic and foreign relevant theory, test statistics and author’s study.

Estimation of the spatiotemporal structure of event-related desynchronization and synchronization in magnetoencephalography

We present a comprehensive methodology for identifying cerebral areas involved in event-related changes of electromagnetic activity of the human brain, and also for tracing the temporal evolution of this activity. Information from pre- and peristimulus time intervals – in terms of event-related synchronization (ERS) and desynchronization (ERD) of the magnetoencephalographic (MEG) signal – was directly incorporated in the relevant test statistics. For the individual steps of the analysis, we used particular estimations of the time–frequency distribution of the energy along with particular error control methods, that is, short-time Fourier transform and false-discovery rate at the sensor level and multitapers and familywise error rate at the source level. This procedure was applied to two types of group-level tests, a within-condition test and a between-conditions test. The performance of the proposed methodology is assessed by (1) analyzing the event-related brain activity from two experimental conditions of an auditory MEG experiment—passive listening to a sequence of frequency-modulated sweeps and their active categorization with respect to the direction of frequency modulation, and (2) comparing the findings with those obtained with a widely used cluster-based analysis.

Optimal sample size determinations from an industry perspective based on the expected value of information

Traditional sample size calculations for randomized clinical trials depend on somewhat arbitrarily chosen factors, such as type I and II errors. As an alternative, taking a societal perspective, and using the expected value of information based on Bayesian decision theory, a number of authors have recently shown how to determine the sample size that maximizes the expected net gain, i.e., the difference between the cost of the trial and the value of the information gained from the results. Other authors have proposed Bayesian methods to determine sample sizes from an industry perspective. The purpose of this article is to propose a Bayesian approach to sample size calculations from an industry perspective that attempts to determine the sample size that maximizes expected profit. A model is proposed for expected total profit that includes consideration of per-patient profit, disease incidence, time horizon, trial duration, market share, discount rate, and the relationship between the results and the probability of regulatory approval. The expected value of information provided by trial data is related to the increase in expected profit from increasing the probability of regulatory approval. The methods are applied to an example, including an examination of robustness. The model is extended to consider market share as a function of observed treatment effect. The use of methods based on the expected value of information can provide, from an industry perspective, robust sample size solutions that maximize the difference between the expected cost of the trial and the expected value of information gained from the results. The method is only as good as the model for expected total profit. Although the model probably has all the right elements, it assumes that market share, per-patient profit, and incidence are insensitive to trial results. The method relies on the central limit theorem which assumes that the sample sizes involved ensure that the relevant test statistics are normally distributed. Industry officials should consider the use of expected value of information methods for determining sample sizes for proposed trials. The method also can be used to select, from a number of proposed trials, those which maximize return from a fixed research budget.

Testing for linearity in Markov switching models: a bootstrap approach

Testing for linearity in the context of Markov switching models is complicated because standard regularity conditions for likelihood based inference are violated. In particular, under the null hypothesis of linearity, some parameters are not identified and scores are identically zero. Thus, the asymptotic distribution of the relevant test statistic does not possess the standard χ 2-distribution. A bootstrap resampling scheme to approximate the distribution of the relevant test statistic under the null of linearity is proposed. The procedure is relatively easy to program and computation requirements are reasonable. The performance of the bootstrap-based test is investigated by means of Monte Carlo simulations. Results show that this test works well and outperforms the Hansen test and the Carrasco et al. test.

Some Almost-Sure Convergence Properties Useful in Sequential Analysis

Kim and Nelson propose sequential procedures for selecting the simulated system with the largest steady-state mean from a set of alternatives that yield stationary output processes. Each procedure uses a triangular continuation region so that sampling stops when the relevant test statistic first reaches the region's boundary. In applying the generalized continuous mapping theorem to prove the asymptotic validity of these procedures as the indifference-zone parameter tends to zero, we are given (i) a sequence of functions on the unit interval (which are right-continuous with left-hand limits) converging to a realization of a certain Brownian motion process with drift; and (ii) a sequence of triangular continuation regions corresponding to the functions in sequence (i) and converging to the triangular continuation region for the Brownian motion process. From each function in sequence (i) and its corresponding continuation region in sequence (ii), we obtain the associated boundary-hitting point; and we prove that the resulting sequence of such points converges almost surely to the boundary-hitting point for the Brownian motion process. We also discuss the application of this result to a statistical process-control scheme for autocorrelated data and to other selection procedures for steady-state simulation experiments. Recommended by Adam Martinsek

Testing for market efficiency in gambling markets when the errors are non-normal and heteroskedastic an application of the wild bootstrap

By employing the wild bootstrap we calculate the ‘correct’ size of the relevant test statistics for the test of the null hypothesis of efficiency in betting markets. Our findings are that the overall conclusion of the rejection of the null hypothesis is still valid.