Sampling Distribution Of Test Statistic Research Articles

A Mahalanobis Distance‐Based Automatic Threshold Selection Method for Peaks Over Threshold Model

AbstractAn unresolved problem in statistical analysis of hydrological extremes (e.g., storms, floods) using POT model is identification of optimal threshold. There are various issues affecting performance of different methods available for threshold selection (TS). To overcome those issues, this study contributes a novel Mahalanobis distance‐based automatic TS method. It involves use of proposed transformation to map Generalized Pareto distributed random variable (depicting peaks over tentative thresholds) from the original space to standard exponential (Exp(1)) distributed random variable in a nondimensional space. Optimal threshold is identified as that which minimizes Mahalanobis distance between L‐moments of the transformed random variable and those of the population (i.e., Exp(1) distribution) in the nondimensional space. Its effectiveness is demonstrated over four existing automatic TS methods through Monte Carlo simulation experiments and case studies over rainfall and streamflow data sets chosen from India, United Kingdom, and Australia. The four methods include three based on goodness of fit (GoF) test statistics (of Anderson‐Darling and two nonparametric tests), and a recent one based on L‐moment ratio diagram whose potential is unexplored in hydrology. This study further provides insight into properties and effectiveness of the four TS methods, which is scanty in literature. Results indicate that there is inconsistency in performance of GoF test‐based methods across data sets exhibiting fat and thin tail behavior, owing to their theoretical assumptions and uncertainty associated with sampling distribution of test statistics. Issues affecting performance of L‐moment ratio diagram‐based TS method are also identified. The proposed method overcomes those issues and appears promising for hydrologic applications.

Tests on a Subset of Regression Parameters for Factorial Experimental Data with Uncertain Higher Order Interactions

The data generated by many factorial experiments are analyzed by linear regression models. Often the higher order interaction terms of such models are negligible (e.g., R. Mead, The Design of Experiments, Cambridge University Press, Cambridge, 1988, p. 368) although there is uncertainty around it. This kind of nonsample prior information (NSPI) can be presented by null hypotheses (cf. T.A. Bancroft, Ann. Math. Stat. 15 (1944), 190–204), and its uncertainty removed through appropriate statistical test. Depending on the level of the NSPI the unrestricted, restricted, and pretest (PTT) tests are defined. The sampling distributions of test statistics and power functions of the three tests are derived. The graphical and analytical comparisons of powers reveal that the PTT dominates over the other tests.

Data Analysis in Multimedia Quality Assessment: Revisiting the Statistical Tests

Assessment of multimedia quality relies heavily on subjective assessment, and is typically done by human subjects in the form of preferences or continuous ratings. Such data are crucial for analysis of different multimedia-processing algorithms as well as validation of objective (computational) methods for the said purpose. To that end, statistical testing provides a theoretical framework toward drawing meaningful inferences, and making well-grounded conclusions and recommendations. While parametric tests (such as t test, ANOVA, and error estimates like confidence intervals) are popular and widely used in the community, there appears to be a certain degree of confusion in the application of such tests. Specifically, the assumptions of normality and homogeneity of variance are often not well understood, leading to incorrect application and/or interpretation of the statistical test results. Therefore, the main goal of this paper is to present new guidelines toward proper use of statistical tests and, hence, fix some of the issues in multimedia quality assessment. The said guidelines are derived based on theoretical analysis of sampling distribution of test statistics, and consider practical aspects of data analysis in the said domain. Experimental results on both simulated and real data are presented to support the arguments made. Software that implements the said recommendations is also made publicly available, in order to help researchers and practitioners perform correct statistical comparison of models.

Improving robust model selection tests for dynamic models

Summary We propose an improved model selection test for dynamic models using a new asymptotic approximation to the sampling distribution of a new test statistic. The model selection test is applicable to dynamic models with very general selection criteria and estimation methods. Since our test statistic does not assume the exact form of a true model, the test is essentially non-parametric once competing models are estimated. For the unknown serial correlation in data, we use a Heteroscedasticity/Autocorrelation-Consistent (HAC) variance estimator, and the sampling distribution of the test statistic is approximated by the fixed-b asymptotic approximation. The asymptotic approximation depends on kernel functions and bandwidth parameters used in HAC estimators. We compare the finite sample performance of the new test with the bootstrap methods as well as with the standard normal approximations, and show that the fixed-b asymptotics and the bootstrap methods are markedly superior to the standard normal approximation for a moderate sample size for time series data. An empirical application for foreign exchange rate forecasting models is presented, and the result shows the normal approximation to the distribution of the test statistic considered appears to overstate the data's ability to distinguish between two competing models.

Bootstrap Tests for Multivariate Event Studies

Statistical tests for multivariate event studies—exact or asymptotic—are derived based on multivariate normality. As it has been previously documented that the performances of these tests are not satisfactory, because stock returns are far from normally distributed (especially for daily returns), this paper proposes the use of bootstrap methods, which are free from any specific distributional assumption, to provide better approximations to the sampling distributions of test statistics in multivariate event studies. The Monte Carlo experiments based on real daily returns data show that the bootstrap tests outperform the traditional tests by having close rejection rates to the nominal significance levels. The traditional tests, in contrast, tend to reject the null hypotheses too often.

Monte Carlo Analysis of Mean Reversion in Commodity Futures Prices

AbstractThis study examines whether mean reversion is present in corn, soybean, wheat, live hog, and live cattle futures prices. Consistent with earlier studies, asymptotic regression results provide substantial evidence of mean reversion in commodity futures price movements. In sharp contrast, the Monte Carlo regression analysis does not provide support for the existence of mean reversion in commodity futures prices. A clear implication is that the asymptotic regression results are misleading. The reason is that the small sample distributions of test statistics are not well approximated by assumed asymptotic distributions.

An Empirical Examination of the Fisher Effect in Australia*

This paper analyzes the Fisher effect in Australia. Initial testing indicates that both interest rates and inflation contain unit roots. Furthermore, there are indications that the variables have non‐standard error processes. To overcome problems associated with this and derive the correct small sample distributions of test statistics we make use of Monte Carlo simulations. These tests indicate that while a long‐run Fisher effect seems to exist, there is no evidence of a short‐run Fisher effect. This suggests that, while short‐run changes in interest rates reflect changes in monetary policy, longer run levels indicate inflationary expectations. Thus, the longer run level of interest rates should not be used to characterize the stance of monetary policy.

Detection of outlying data in bioavailability/bioequivalence studies

This paper considers the problem of detecting outlying data in bioavailability/bioequivalence studies. We define outlying subjects as those whose responses in bioavailability to all formulations differ from the rest of the subjects. We also define an outlying observation as the response in bioavailability of a subject to a particular formulation which is grossly different from the average bioavailability of that formulation calculated from all subjects. We propose two test procedures. The first, based on two-sample Hotelling T2, is to detect possible outlying subjects. The second, based on residuals from formulation means, is to identify possible outlying observations within subjects. Both procedures take into account the covariance structure of the responses to formulations, dependence of test statistics, and multiplicity of test procedures. We apply the Monte Carlo or bootstrap simulation to evaluate the sampling distributions of test statistics. An example from a 3-way crossover bioequivalence study illustrates the two procedures.

Use of classroom experiments and the computer to illustrate statistical concepts

Abstract Because of the modest mathematical background of most students, there are major difficulties in teaching basic statistical concepts in undergraduate statistical courses in geography. This paper describes statistical experiments in which students can participate, which may be supplemented by computer results. The objective is to show how greater rigour may be brought to undergraduate course‐work with little or no increase in mathematical formality. The sampling distributions of test statistics in point pattern analysis are used as illustration.