A nonparametric test for changing trends

Many tests of parameter change in dynamic models exhibit nonmonotonic power. An important source of the nonmonotonic power comes from the bias in estimating parameters when there is a change in the deterministic component. To avoid this bias, we propose a nonparametric test for changing trends based on nonparametrically detrended data. The tests are similar in spirit to nonparametric conditional moment tests such as Fan and Li (J. Nonparametr. Stat. 10 (1999a) 245; 11 (1999b) 251) and Zheng (J. Econometrics 75 (1996) 263). The resulting statistics have a standard normal distribution. A Monte Carlo experiment suggests that the tests have good power against changes in the deterministic component.     

A nonparametric k-sample test for data defined by intervals

Abstract  If observations are restricted in such a way that only intervals covering the true but hidden values are known and k -samples are to be compared by location, the use of a generalized K ruskal -W allis test is suggested.     

A consistent nonparametric test of affiliation in auction models

We propose a new nonparametric test of affiliation, a strong form of positive dependence with independence as a special, knife-edge, case. The test is consistent against all departures from the null of affiliation, and its null distribution is standard normal. Like most nonparametric tests, a sample-size dependent input parameter is needed. We provide an informal procedure for choosing the input parameter and evaluate the test’s performance using a simulation study. Our test can be used to test the fundamental assumptions of the auctions literature. We implement our test empirically using the Outer Continental Shelf (OCS) auction data.     

A consistent nonparametric test for nonlinear causality—Specification in time series regression

Since the pioneering work by Granger (1969), many authors have proposed tests of causality between economic time series. Most of them are concerned only with “linear causality in mean”, or if a series linearly affects the (conditional) mean of the other series. It is no doubt of primary interest, but dependence between series may be nonlinear, and/or not only through the conditional mean. Indeed conditional heteroskedastic models are widely studied recently. The purpose of this paper is to propose a nonparametric test for possibly nonlinear causality. Taking into account that dependence in higher order moments are becoming an important issue especially in financial time series, we also consider a test for causality up to the Kth conditional moment. Statistically, we can also view this test as a nonparametric omitted variable test in time series regression. A desirable property of the test is that it has nontrivial power against T^1/2-local alternatives, where T is the sample size. Also, we can form a test statistic accordingly if we have some knowledge on the alternative hypothesis. Furthermore, we show that the test statistic includes most of the omitted variable test statistics as special cases asymptotically. The null asymptotic distribution is not normal, but we can easily calculate the critical regions by simulation. Monte Carlo experiments show that the proposed test has good size and power properties.     

A nonparametric test of weak separability and consumer preferences

Two stochastic nonparametric procedures are developed to evaluate the significance of violations of weak separability. When the data have measurement error, we show that the necessary and sufficient weak separability conditions of Varian [Varian, H., 1983. Nonparametric tests of consumer behavior. Review of Economic Studies 50, 99–110] must also satisfy the Afriat inequalities. The tests detect weak separability with high probability for weakly separable data. In addition, the procedures correctly reject weak separability for both nonseparable and random utility simulated data sets. The tests also fail to reject weak separability for a monetary and consumption data set which suggests that measurement error may be the source of the observed violations.     

A general test for time dependence in parameters

A new test for time‐dependent parameters is proposed. The Trig‐test is based on a trigonometric expansion to approximate the unknown functional form of the variation in the parameters concerned. It is shown to have the correct empirical size and excellent power to detect structural breaks and stochastic parameter variation. The appropriate use of the Trig‐test is demonstrated by testing for structural breaks in the US inflation rate. The test detects a statistically significant increase in the US inflation rate beginning in the early 1970s and lasting through to the early 1980s. Copyright © 2004 John Wiley & Sons, Ltd.     

A comparison of two nonparametric k -sample slippage tests

The tests which are discussed here are Mosteller's k -sample slippage test for an extreme population [8] and the k -sample slippage analogue of the Wilcoxon two-sample test proposed by D oornbos and P rins [3]. A comparison is made between both tests in respect of their consistency against normal, exponential and uniform shifts and against Lehmann-alternatives. For some small sample sizes the powers of the two tests have been calculated.     

A test for multimodality of regression derivatives with application to nonparametric growth regressions

This paper presents a method to test for multimodality of an estimated kernel density of derivative estimates from a nonparametric regression. The test is included in a study of nonparametric growth regressions. The results show that in the estimation of unconditional β‐convergence the distribution of the partial effects is multimodal, with one mode in the negative region (primarily OECD economies) and possibly two modes in the positive region (primarily non‐OECD economies) of the estimates. The results for conditional β‐convergence show that the density is predominantly negative and there is mixed evidence that the distribution is unimodal. Copyright © 2009 John Wiley & Sons, Ltd.     

A nonparametric test for equality of distributions with mixed categorical and continuous data

In this paper we consider the problem of testing for equality of two density or two conditional density functions defined over mixed discrete and continuous variables. We smooth both the discrete and continuous variables, with the smoothing parameters chosen via least-squares cross-validation. The test statistics are shown to have (asymptotic) normal null distributions. However, we advocate the use of bootstrap methods in order to better approximate their null distribution in finite-sample settings and we provide asymptotic validity of the proposed bootstrap method. Simulations show that the proposed tests have better power than both conventional frequency-based tests and smoothing tests based on ad hoc smoothing parameter selection, while a demonstrative empirical application to the joint distribution of earnings and educational attainment underscores the utility of the proposed approach in mixed data settings.     

A remark on Lehmann-unbiased estimators for scale resp. Location parameters

Summary In this paper Lehmann-unbiased estimation of the scale and location parameter is considered. Lehmann-unbiased estimators depend strongly on the form of the loss function. Therefore quadratic and the other loss functions are discussed. Results of this paper, obtained in the class of linear statistics, can be specified to these obtained byGoodman andKiciska-Slaby [1982a, 1982b].     

A nonparametric decision approach for entrepreneurship

Credit identification is one of core issues of financing process. Enterprise credit involves a lot of financial and non-financial measures, among which entrepreneurship is an important but rarely mentioned variable. Good entrepreneur credit often leads to good enterprise credit. A comprehensive analysis of enterprise credit identification is important to avoid losses, foster excellent enterprise and make the optimal allocation of resources. The existing literature mainly studied the impact of entrepreneurship on enterprise credit from the perspective of historical information, which is about average and tendency. Hence, those models were unable to explain the function of complex human nature and, consequently, linear models are unable to well describe the relationship between enterprise credit and entrepreneur credit. Given the deficiency of parametric models when discussing the impact of entrepreneur credit, a non parametric approach are proposed to individually describe the impact path of different individuals. This paper established a decision tree based on nonparametric approach to verify the practicability of the model in the evaluation of enterprise credit recognition. In the end of this paper, we demonstrate the validity of the non parametric model and the validation method of it.     

A consistent nonparametric test of parametric regression functional form in fixed effects panel data models

We propose a consistent test for a linear functional form against a nonparametric alternative in a fixed effects panel data model. We show that the test has a limiting standard normal distribution under the null hypothesis, and show that the test is a consistent test. We also establish the asymptotic validity of a bootstrap procedure which is used to better approximate the finite sample null distribution of the test statistic. Simulation results show that the proposed test performs well for panel data with a large number of cross-sectional units and a finite number of observations across time.     

Hypothesis testing in nonparametric models of production using multiple sample splits

Several tests of model structure developed by Kneip et al. (J Bus Econ Stat 34:435–456, 2016) and Daraio et al. (Econ J 21:170–191, 2018) rely on comparing sample means of two different efficiency estimators, one appropriate under the conditions of the null hypothesis and the other appropriate under the conditions of the alternative hypothesis. These tests rely on central limit theorems developed by Kneip et al. (Econ Theory 31:394–422, 2015) and Daraio et al. (Econ J 21:170–191, 2018), but require that the original sample be split randomly into two independent subsamples. This introduces some ambiguity surrounding the sample-split, which may be determined by choice of a seed for a random number generator. We develop a method that eliminates much of this ambiguity by repeating the random splits a large number of times. We use a bootstrap algorithm to exploit the information from the multiple sample-splits. Our simulation results show that in many cases, eliminating this ambiguity results in tests with better size and power than tests that employ a single sample-split.

     

Statistical tests for multiple forecast comparison

We consider a multivariate version of the Diebold–Mariano test for equal predictive ability of three or more forecasting models. The Wald-type test, $S$, which has a null distribution that is asymptotically chi-squared, is shown to be generally invariant with respect to the ordering of the models being compared. Finite-sample corrections for the test are also developed. Monte Carlo simulations indicate that $S$ has reasonable size properties in large samples but tends to be oversized in moderate samples. The finite-sample correction succeeds in correcting for size, but only partially. For the size-adjusted tests, power increases with sample size, as expected. It is speculated that further finite-sample improvements can be achieved using Hotelling’s $T^2$ or bootstrap critical values.     

A kernel-based method for nonparametric estimation of variograms

Variogram estimation plays an important role in many areas of spatial statistics. Potential areas of application include biology, ecology, economics and meteorology. However, it is common that, for example under highly correlated patterns, traditional estimators can not reflect all the spatial features or dependencies. In this paper, we present an alternative distribution-free estimator based on nearest-neighbour estimation with a non-constant smoothing field that is better able to adapt to spatially varying features of the data pattern. We present a simulation study to compare our new estimator to a nearest-neighbour estimator built with a constant smoothing parameter and to the classical variogram estimator. We apply our method to analyze two ecological data sets.     

A test of non-identifying restrictions and confidence regions for partially identified parameters

We propose an easily implementable test of the validity of a set of theoretical restrictions on the relationship between economic variables, which do not necessarily identify the data generating process. The restrictions can be derived from any model of interactions, allowing censoring and multiple equilibria. When the restrictions are parameterized, the test can be inverted to yield confidence regions for partially identified parameters, thereby complementing other proposals, primarily Chernozhukov et al. [Chernozhukov, V., Hong, H., Tamer, E., 2007. Estimation and confidence regions for parameter sets in econometric models. Econometrica 75, 1243–1285].     

Small sample behaviour of some nonparametric multi-sample location tests in the presence of dispersion differences

This paper describes the small and moderate sample behaviour of three studentized non-parametric statistics by Sen and a modified Wilcoxon statistic by Potthoff for testing the equality of location parameters in the presence of dispersion differences. Based on the agreement between the asymptotic and small sample distributions of the statistics as well as a comparison of their power under heteroscedasticity, the studentized Wilcoxon and the studentized Brown and Mood tests arc preferred in the two-sample and c-sample situations, respectively.     

The multiple filter test for change point detection in time series

A framework for the detection of change points in the expectation in sequences of random variables is presented. Specifically, we investigate time series with general distributional assumptions that may show an unknown number of change points in the expectation occurring on multiple time scales and that may also contain change points in other parameters. To that end we propose a multiple filter test (MFT) that tests the null hypothesis of constant expectation and, in case of rejection of the null hypothesis, an algorithm that estimates the change points.The MFT has three important benefits. First, it allows for general distributional assumptions in the underlying model, assuming piecewise sequences of i.i.d. random variables, where also relaxations with regard to identical distribution or independence are possible. Second, it uses a MOSUM type statistic and an asymptotic setting in which the MOSUM process converges weakly to a functional of a Brownian motion which is then used to simulate the rejection threshold of the statistical test. This approach enables a simultaneous application of multiple MOSUM processes which improves the detection of change points that occur on different time scales. Third, we also show that the method is practically robust against changes in other distributional parameters such as the variance or higher order moments which might occur with or even without a change in expectation. A function implementing the described test and change point estimation is available in the R package MFT.     

Smooth estimators for estimating order restricted scale parameters of two gamma distributions

We consider the problem of component-wise estimation of ordered scale parameters of two gamma populations, when it is known apriori which population corresponds to each ordered parameter. Under the scale equivariant squared error loss function, smooth estimators that improve upon the best scale equivariant estimators are derived. These smooth estimators are shown to be generalized Bayes with respect to a non-informative prior. Finally, using Monte Carlo simulations, these improved smooth estimators are compared with the best scale equivariant estimators, their non-smooth improvements obtained in Vijayasree, Misra & Singh (1995), and the restricted maximum likelihood estimators. Acknowledgments. Authors are thankful to a referee for suggestions leading to improved presentation.