Test for randomness of the technology parameter in a stochastic frontier regression model

This paper considers the problem of testing for randomness of the technology parameter in a stochastic frontier regression model. A test statistic is proposed and its asymptotic distribution theory is discussed. Simulation results show that the proposed test maintains its level and also quite powerful against various alternatives. An empirical investigation has been carried out by applying the suggested test procedure to the data set on electric utility companies. The results are consistent with the general finding that the technology parameter of the stochastic frontier model used for modeling these data is random.     

An approximate entropy test for randomness

We develop an entropy-based test for randomness of binary time series of finite length. The test uses the frequencies of contiguous blocks of different lengths. A simple condition ib the block lengths and the length of the time series enables one to estimate the entropy rate for the data, and this information is used to develop a statistic to test the hypothesis of randomness. This static measures the deviation of the estimated entropy of the observed data from the theoretical maximum under the randomness hypothesis. This test offers a real alternative to the conventional runs test. Critical percentage points, based on simulations, are provided for testing the hypothesis of randomness. Power calculations using dependent data show that the proposed test has higher power against the runs test for short series, and it is similar to the runs test for long series. The test is applied to two published data sets that wree investigated by others with respect to their randomness.     

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.     

Approximate entropy: Statistical properties and applications

ApEn, approximate entropy, is a recently developed family of parameters and statistics quantifying regularity (complexity) in data, providing an information-theoretic quantity for continuous-state processes. We provide the motivation for ApEn development, and indicate the superiority of ApEn to the K-S entropy for statistical application, and for discrimination of both correlated stochastic and noisy deterministic processes. We study the variation of ApEn with input parameter choices, reemphasizing that ApEn is a relative measure of regularity. We study the bias in the ApEn statistic, and present evidence for asymptotic normality in the ApEn distributions, assuming weak dependence. We provide a new test for the hypothesis that an underlying time-series is generated by i.i.d. variables, which does not require distribution specification. We introduce randomized ApEn, which derives an empirical significance probability that two processes differ, based on one data set from each process.     

Nonparametric test for checking lack of fit of the quantité regression model under random censoring

The author proposes a nonparametric test for checking the lack of fit of the quantile function of survival time given the covariates; she assumes that survival time is subjected to random right censoring. Her test statistic is a kemel‐based smoothing estimator of a moment condition. The test statistic is asymptotically Gaussian under the null hypothesis. The author investigates its behavior under local alternative sequences. She assesses its finite‐sample power through simulations and illustrates its use with the Stanford heart transplant data.     

Two‐Sample Test Against One‐Sided Alternatives

Abstract. This paper proposes, implements and investigates a new non‐parametric two‐sample test for detecting stochastic dominance. We pose the question of detecting the stochastic dominance in a non‐standard way. This is motivated by existing evidence showing that standard formulations and pertaining procedures may lead to serious errors in inference. The procedure that we introduce matches testing and model selection. More precisely, we reparametrize the testing problem in terms of Fourier coefficients of well‐known comparison densities. Next, the estimated Fourier coefficients are used to form a kind of signed smooth rank statistic. In such a setting, the number of Fourier coefficients incorporated into the statistic is a smoothing parameter. We determine this parameter via some flexible selection rule. We establish the asymptotic properties of the new test under null and alternative hypotheses. The finite sample performance of the new solution is demonstrated through Monte Carlo studies and an application to a set of survival times.     

Likelihood ratio test against simple stochastic ordering among several multinomial populations

Stochastic ordering between probability distributions has been widely studied in the past 50 years. Because it is often easy to make valuable judgments when such orderings exist, it is desirable to recognize their existence and to model distributional structures under them. Likelihood ratio test is the most commonly used method to test hypotheses involving stochastic orderings. Among the various formally defined notions of stochastic ordering, the least stringent is simple stochastic ordering. In this paper, we consider testing the hypothesis that all multinomial populations are identically distributed against the alternative that they are in simple stochastic ordering. We construct likelihood ratio test statistic for this hypothesis test problem, provide limit form of the objective function corresponding to the test statistic and show that the test statistic is asymptotically distributed as a mixture of chi-squared distributions, i.e., a chi-bar-squared distribution.     

A test for randomness of the environments in a branching process

This paper discusses an approximate score test for testing randomness of environments in a branching process without observing the environments. Using an appropriate martingale central limit theorem the asymptotic null distribution of test statistic is shown to be normal. When the offspring distribution is Poisson, the detail derivation of asymptotic distribution of the test statistic is presented.     

A new family of random graphs for testing spatial segregation

The authors discuss a graph‐based approach for testing spatial point patterns. This approach falls under the category of data‐random graphs, which have been introduced and used for statistical pattern recognition in recent years. The authors address specifically the problem of testing complete spatial randomness against spatial patterns of segregation or association between two or more classes of points on the plane. To this end, they use a particular type of parameterized random digraph called a proximity catch digraph (PCD) which is based on relative positions of the data points from various classes. The statistic employed is the relative density of the PCD, which is a U‐statistic when scaled properly. The authors derive the limiting distribution of the relative density, using the standard asymptotic theory of U‐statistics. They evaluate the finite‐sample performance of their test statistic by Monte Carlo simulations and assess its asymptotic performance via Pitman's asymptotic efficiency, thereby yielding the optimal parameters for testing. They further stress that their methodology remains valid for data in higher dimensions.     

因子模型的一种结构突变检验及其统计性质研究

为了内生地识别动态因子模型因子载荷矩阵的结构突变（包括因子个数的变化）,本文利用主成分估计得伪因子序列构造累积平方和统计量检验因子载荷矩阵的结构突变性,进一步利用迭代累积平方和算法对多个结构突变点的位置进行探测。研究发现,本文提出的检验统计量对于因子个数误设具有稳健性;并且该检验具有良好的有限样本性质和渐近性;另外,实证分析发现,中国沪市A股市场制造业上市公司的对数收益率序列存在结构突变的共同因子。     

Generalized sequential ranks and tests of randomness

Generalized sequential ranks are defined and are proved to be independent and uniformly distributed under the hypothesis of randomness. By comparison with a Spear-MAsr-type statistic it is shown that in certain cases the test based on the sum of all sequential ranks is an asymptotically optimum test for trend against logistic regression. The test is equivalent to tests proposed by Jonckheere and Terpstra and has a high efficiency when compared with the optimal parametric test for normal regression alternatives.     

蒙特卡罗方法在经济学中的应用——基于河南省农业持续度的实证分析

首先利用蒙特卡罗方法研究小样本或有限样本的统计性质,然后计算ADF检验式中时间趋势项的τ统计量的值,最后用蒙特卡罗方法进行实证分析。通过分析可以看出蒙特卡罗方法在经济中的应用非常广泛,特别是用于解决随机性问题,使得这种方法成为一种优于其它方法的工具。     

A TEST FOR THE NONPARAMETRIC TWO SAMPLE SCALE PROBLEM

We propose a distribution-free test for the nonparametric two sample scale problem. Unlike the other tests for this problem, we do not assume that the two distribution functions have a common median. We assume that they have a common quantile of order a (not necessarily 1/2). The test statistic is a modification of the Sukhatme statistic for the scale problem and the Wilcoxon-Mann-Whitney statistic for stochastic dominance. It is shown that the new test is uniformly more efficient (in the Pitman sense) than the Sukhatme test and has very good efficiency when compared to the Mood test.     

Spatial Clustering Tests Based on the Domination Number of a New Random Digraph Family

We use the domination number of a parametrized random digraph family called proportional-edge proximity catch digraphs (PCDs) for testing multivariate spatial point patterns. This digraph family is based on relative positions of data points from various classes. We extend the results on the distribution of the domination number of proportional-edge PCDs, and use the domination number as a statistic for testing segregation and association against complete spatial randomness. We demonstrate that the domination number of the PCD has binomial distribution when size of one class is fixed while the size of the other (whose points constitute the vertices of the digraph) tends to infinity and has asymptotic normality when sizes of both classes tend to infinity. We evaluate the finite sample performance of the test by Monte Carlo simulations and prove the consistency of the test under the alternatives. We find the optimal parameters for testing each of the segregation and association alternatives. Furthermore, the methodology discussed in this article is valid for data in higher dimensions also.     

An Approximate Bayesian Marginal Likelihood Approach for Estimating Finite Mixtures

Estimation of finite mixture models when the mixing distribution support is unknown is an important problem. This article gives a new approach based on a marginal likelihood for the unknown support. Motivated by a Bayesian Dirichlet prior model, a computationally efficient stochastic approximation version of the marginal likelihood is proposed and large-sample theory is presented. By restricting the support to a finite grid, a simulated annealing method is employed to maximize the marginal likelihood and estimate the support. Real and simulated data examples show that this novel stochastic approximation and simulated annealing procedure compares favorably with existing methods.     

Conditional Stochastic Dominance Testing

This article proposes bootstrap-based stochastic dominance tests for nonparametric conditional distributions and their moments. We exploit the fact that a conditional distribution dominates the other if and only if the difference between the marginal joint distributions is monotonic in the explanatory variable at each value of the dependent variable. The proposed test statistic compares restricted and unrestricted estimators of the difference between the joint distributions, and it can be implemented under minimal smoothness requirements on the underlying nonparametric curves and without resorting to smooth estimation. The finite sample properties of the proposed test are examined by means of a Monte Carlo study. We illustrate the test by studying the impact on postintervention earnings of the National Supported Work Demonstration, a randomized labor training program carried out in the 1970s.     

A new test for residual randomness in a class of dynamic autocorrelated econometric models

This paper presents a new test statistic for dynamic or stochastic mis-specification for the dynamic demand or dynamic adjustment class of economic models. The test statistic is based on residual autocorrelations, asymptotically X² and is suspected to be of low power. The test is illustrated with an example from recent econometric literature.     

Nonparametric analysis of treatment effects with missing observations

This paper develops a test for comparing treatment effects when observations are missing at random for repeated measures data on independent subjects. It is assumed that missingness at any occasion follows a Bernoulli distribution. It is shown that the distribution of the vector of linear rank statistics depends on the unknown parameters of the probability law that governs missingness, which is absent in the existing conditional methods employing rank statistics. This dependence is through the variance–covariance matrix of the vector of linear ranks. The test statistic is a quadratic form in the linear rank statistics when the variance–covariance matrix is estimated. The limiting distribution of the test statistic is derived under the null hypothesis. Several methods of estimating the unknown components of the variance–covariance matrix are considered. The estimate that produces stable empirical Type I error rate while maintaining the highest power among the competing tests is recommended for implementation in practice. Simulation studies are also presented to show the advantage of the proposed test over other rank-based tests that do not account for the randomness in the missing data pattern. Our method is shown to have the highest power while also maintaining near-nominal Type I error rates. Our results clearly illustrate that even for an ignorable missingness mechanism, the randomness in the pattern of missingness cannot be ignored. A real data example is presented to highlight the effectiveness of the proposed method.     

Prequential omnibus goodness-of-fit tests for stochastic processes: A numerical study

This article is a contribution to the study of an omnibus goodness-of-fit (Gof) test based on Rosenblatt Probability Integral Transform (RPIT) within Dawid's prequential framework. This Gof test is easy to use since it has a common test statistic (with apparently the same asymptotic distribution) for a wide range of stochastic models. Intensive Monte-Carlo simulations are presented to investigate the behavior of this test for several stochastic models: renewal, autoregressive (AR, ARMA, ARCH, GARCH) and Poisson processes, generalized linear models... These simulations suggest that the RPIT test could be used to test the fit of a wide range of stochastic models but it may be not powerful when compared to Gof tests specifically designed for the tested processes. It is also conjectured that this test is still appropriate for testing the Gof of any discrete-time stochastic process provided that efficient estimators are used.     

A permutation test for randomness with power against smooth variation

A permutation test for the white noise hypothesis is described, offering power against a general class of smooth alternatives. Simulation results show that it performs well, as compared with similar tests available in the literature, in terms of power. An example demonstrates its use in a particular problem in which a test for randomness was sought without any specific alternative.