检验式设定错误对时间序列单位根检验小样本性质的影响

首先对单位根检验的两类常见的数据生成系统进行比较，然后利用蒙特卡洛实验研究了时间序列单位根检验式的设定问题。研究发现在利用DF检验和DF-GLS检验进行时间序列的单位根检验时，检验式设定错误直接影响着检验结果，尤其在推断时间序列是趋势平稳过程还是有时间趋势项的随机游走过程或有二阶时间趋势多项式的随机游走过程时，检验式的错误设定很容易将趋势平稳过程误判为非平稳过程。     

Methods for testing subblock patterns

A number of statistical tests have been recommended over the last twenty years for assessing the randomness of long binary strings used in cryptographic algorithms. Several of these tests include methods of examining subblock patterns. These tests are the uniformity test, the universal test and the repetition test. The effectiveness of these tests are compared based on the subblock length, the limitations on data requirements, and on their power in detecting deviations from randomness. Due to the complexity of the test statistics, the power functions are estimated by simulation methods. The results show that for small subblocks the uniformity test is more powerful than the universal test, and that there is some doubt about the parameters of the hypothesised distribution for the universal test statistic. For larger subblocks the results show that the repetition test is the most effective test, since it requires far less data than either of the other two tests and is an efficient test in detecting deviations from randomness in binary strings.     

Extended Analysis of At Least Partially Ordered Multi‐factor ANOVA

For multifactor experimental designs in which the levels of at least one of the factors are ordered we show how to construct components that provide a deep nonparametric scrutiny of the data. The components assess generalised correlations and the resulting tests include and extend the Page and umbrella tests. Application of the tests described is straightforward. Orthonormal polynomials on the ANOVA responses and the factors are required and the formulae needed are given subsequently. These depend on the moments of the responses and of each factor and are easily calculated. Products of at least two of these orthonormal polynomials are then used as inputs into standard ANOVA routines. For example, using the first order orthonormal polynomial on factor A and the second order orthonormal polynomial on the ANOVA response will assess if, with increasing levels of factor A there is an umbrella response with either an increase and then a decrease or a decrease and then an increase.     

Power of depth-based nonparametric tests for multivariate locations

Li and Liu [New nonparametric tests of multivariate locations and scales. Statist Sci. 2004;19(4):686–696] introduced two tests for a difference in locations of two multivariate distributions based on the concept of data depth. Using the simplicial depth [Liu RY. On a notion of data depth based on random simplices. Ann Stat. 1990;18(1):405–414], they studied the performance of these tests for symmetric distributions, namely, the normal and the Cauchy, in a simulation study. However, to the best of our knowledge, the performance of these tests for skewed distributions has not been studied in the current literature. This paper is a contribution in that direction and examines the performance of these depth-based tests in an extensive simulation study involving ten distributions belonging to five well-known families of multivariate skewed distributions. The study includes a comparison of the performance of these tests for four popular affine-invariant depth functions. Conclusions and recommendations are offered.     

Tests for multinormality with applications to time series

Making use of a characterization of multivariate normality by Hermitian polynomials, we propose a multivariate normality test. The approach is then applied to time series analysis by constructing a test for Gaussianity of a stationary univariate series. Simulation study shows that the proposed test has reasonable power and outperforms other tests available in the literature when the innovation series of the time series is symmetric, but non-Gaussian.     

Data-driven smooth tests of the proportional hazards assumption

A new test of the proportional hazards assumption in the Cox model is proposed. The idea is based on Neyman’s smooth tests. The Cox model with proportional hazards (i.e. time-constant covariate effects) is embedded in a model with a smoothly time-varying covariate effect that is expressed as a combination of some basis functions (e.g., Legendre polynomials, cosines). Then the smooth test is the score test for significance of these artificial covariates. Furthermore, we apply a modification of Schwarz’s selection rule to choosing the dimension of the smooth model (the number of the basis functions). The score test is then used in the selected model. In a simulation study, we compare the proposed tests with standard tests based on the score process.     

PERMUTATION TESTS AND OTHER TEST STATISTICS FOR ILL-BEHAVED DATA: EXPERIENCE OF THE NINDS t-PA STROKE TRIAL

Permutation tests are often used to analyze data since they may not require one to make assumptions regarding the form of the distribution to have a random and independent sample selection. We initially considered a permutation test to assess the treatment effect on computed tomography lesion volume in the National Institute of Neurological Disorders and Stroke (NINDS) t-PA Stroke Trial, which has highly skewed data. However, we encountered difficulties in summarizing the permutation test results on the lesion volume. In this paper, we discuss some aspects of permutation tests and illustrate our findings. This experience with the NINDS t-PA Stroke Trial data emphasizes that permutation tests are useful for clinical trials and can be used to validate assumptions of an observed test statistic. The permutation test places fewer restrictions on the underlying distribution but is not always distribution-free or an exact test, especially for ill-behaved data. Quasi-likelihood estimation using the generalized estimating equation (GEE) approach on transformed data seems to be a good choice for analyzing CT lesion data, based on both its corresponding permutation test and its clinical interpretation.     

Goodness of fit tests with interval censored data

Cramér–von Mises type goodness of fit tests for interval censored data case 2 are proposed based on a resampling method called the leveraged bootstrap, and their asymptotic consistency is shown. The proposed tests are computationally efficient, and in fact can be applied to other types of censored data, including right censored data, doubly censored data and (mixture of) case k interval censored data. Some simulation results and an example from AIDS research are presented.     

Large sample tests for equality of medians under unequal right-censoring

Two tests are proposed for testing equality of the medians of two distributions on the basis of right cansored data. The tests do not require any assumption on the scales or the shapes of the distributions and can be used without assuming equal censorship in the two samples. Under the sequence of translation alternatives the proposed tests are equally efficient when the distributions belong to the same location and scale family. Some indications are provided about the significance levels of the tests based on simulation results.     

Smooth Goodness-of-Fit Specification Tests Under the Lagrange Multiplier Principle

This article generalizes Neyman's smooth test for the goodness-of-fit hypothesis using orthogonal polynomials of the density function under the null hypothesis, and derives a Lagrange Multiplier (LM) statistic based on the generalized form of the smooth test. Under the null hypothesis, using the joint limiting normality of the orthogonal functions imbedded into the smooth alternative density function and the restricted parameter estimators, the covariance matrix of the LM statistic can be estimated. The procedure of constructing monic orthogonal polynomials from a given moment function is developed. This procedure is applied to examples of testing for normal, Poisson, and gamma distributions.     

Goodness of fit tests for Nakagami distribution based on smooth tests

ABSTRACT

Nakagami distribution is one of the most common distributions used to model positive valued and right skewed data. In this study, we interest goodness of fit problem for Nakagami distribution. Thus, we propose smooth tests for Nakagami distribution based on orthonormal functions. We also compare these tests with some classical goodness of fit tests such as Cramer–von Mises, Anderson–Darling, and Kolmogorov–Smirnov tests in respect to type-I error rates and powers of tests. Simulation study indicates that smooth tests give better results than these classical tests give in respect to almost all cases considered.     

An R package for testing goodness of fit: goft

This R package implements three types of goodness-of-fit tests for some widely used probability distributions where there are unknown parameters, namely tests based on data transformations, on the ratio of two estimators of a dispersion parameter, and correlation tests. Most of the considered tests have been proved to be powerful against a wide range of alternatives and some new ones are proposed here. The package's functionality is illustrated with several examples by using some data sets from the areas of environmental studies, biology and finance, among others.     

GOODNESS-OF-FIT AND DISCORDANCY TESTS FOR SAMPLES FROM THE WATSON DISTRIBUTION ON THE SPHERE

The only parametric model in current use for axial data from a rotationally symmetric bipolar or girdle distribution on the sphere is the Watson distribution. This paper develops methods for evaluating the model as a fit to data using graphical and formal goodness-of-fit tests, and tests of discordancy.     

Tests of symmetry derived as components of pearson's phi-squared distance measure

Rank statistics which arise as estimates of the first and third components of a frequency decomposition of Pearson's phi-squared distance measure, introduced by Eubank, LaRiccia, and Rosenstein (1987), are examined for their usefulness as tests of symmetry about a known median against various asymmetric alternatives, Pitman asymptotic relative efficiencies are used to compare the efficacies of the new statistics with classical test procedures, and empirical powers of the new tests are compared via simulation for a variety of asymmetric distributions. Statistics which arise from components based on Legendre polynomials are of particular interest. The first component is the familiar Wilcoxon signed rank statistic. The third component, which is a new statistic for this problem, exhibits a high level of sensitivity to a variety of asymmetric alternatives both asymptotically and in small sample studies.     

Jacobi and Laguerre polynomial approximations for the distributions of statistics useful in testing for outliers in exponential and gamma samples

Recently, Sanjel and Balakrishnan [A Laguerre Polynomial Approximation for a goodness-of-fit test for exponential distribution based on progressively censored data, J. Stat. Comput. Simul. 78 (2008), pp. 503–513] proposed the use of Laguerre orthogonal polynomials for a goodness-of-fit test for the exponential distribution based on progressively censored data. In this paper, we use Jacobi and Laguerre orthogonal polynomials in order to obtain density approximants for some test statistics useful in testing for outliers in gamma and exponential samples. We first obtain the exact moments of the statistics and then the density approximants, based on these moments, are expressed in terms of Jacobi and Laguerre polynomials. A comparative study is carried out of the critical values obtained by using the proposed methods to the corresponding results given by Barnett and Lewis [Outliers in Statistical Data, 3rd ed., John Wiley & Sons, New York, 1993]. This reveals that the proposed techniques provide very accurate approximations to the distributions. Finally, we present some numerical examples to illustrate the proposed approximations. Monte Carlo simulations suggest that the proposed approximate densities are very accurate.     

Default Bayesian goodness-of-fit tests for the skew-normal model

In this paper we propose a series of goodness-of-fit tests for the family of skew-normal models when all parameters are unknown. As the null distributions of the considered test statistics depend only on asymmetry parameter, we used a default and proper prior on skewness parameter leading to the prior predictive p-value advocated by G. Box. Goodness-of-fit tests, here proposed, depend only on sample size and exhibit full agreement between nominal and actual size. They also have good power against local alternative models which also account for asymmetry in the data.     

Orthogonal polynomials,repeated measures,and SPSS

We discuss the construction of discrete orthonormal polynomials, using MAPLE procedures. We also study two important applications of these polynomials in statistics: in multiple linear regression and in repeated measures analysis. In particular, it is argued that the tests given by SPSS for linear and other trends in a within-subject factor are inefficient. Examples are given, including two (from psychology and medicine, respectively) which involve repeated measures and SPSS. Extensive tables of discrete orthornormal polynomials are given in the Appendix.     

Testing Supremacy or Inferiority of Multinomial Cell Probabilities with Application to Biting Preferences of Loggerhead Marine Turtles

We propose exact tests for uniform superiority or uniform inferiority of a multinomial cell probability. We extend the approach to testing supremacy or inferiority in multivariate settings. We also show how to perform superiority or inferiority tests in presence of covariates, and discuss the different interpretations of the proposed tests. The tests are illustrated on an original data set on biting behavior of loggerhead marine turtles.     

Testing equality of variances for several normal populations

In this study, we develop a test based on computational approach for the equality of variances of several normal populations. The proposed method is numerically compared with the existing methods. The numeric results demonstrate that the proposed method performs very well in terms of type I error rate and power of test. Furthermore we study the robustness of the tests by using simulation study when the underlying data are from t, exponential and uniform distributions. Finally we analyze a real dataset that motivated our study using the proposed test.     

Detection of non-Gaussianity

We develop two tests sensitive to various departures from composite goodness-of-fit hypothesis of normality. The tests are based on the sums of squares of some components naturally arising in decomposition of the Shapiro–Wilk-type statistic. Each component itself has diagnostic properties. The numbers of squared components in sums are determined via some novel selection rules based on the data. The new solutions prove to be effective tools in detecting a broad spectrum of sources of non-Gaussianity. We also discuss two variants of the new tests adjusted to verification of simple goodness-of-fit hypothesis of normality. These variants also compare well to popular competitors.