scholarly journals Two-sample Tests for Functional Data Using Characteristic Functions

2021 ◽  
Vol 50 (4) ◽  
pp. 53-64
Author(s):  
Mirosław Krzyśko ◽  
Łukasz Smaga
Keyword(s):  
Functional Data ◽  
Real Data ◽  
Characteristic Functions ◽  
Weight Functions ◽  
Test Statistics ◽  
Finite Sample ◽  
Testing Procedures ◽  
Two Sample Problem ◽  
Finite Sample Properties ◽  
Multivariate Functional Data

In this paper, we consider the two-sample problem for univariate and multivariate functional data. To solve this problem, we use tool of characteristic function and a basis function representation of functional data. We construct test statistics for conformity of distributions based on a weighted distance between characteristic functions of random vectors obtained in basis representation. Different weight functions result in different test statistics, whose distributions are approximated by permutation method. Testing procedures are implemented in the R program and the code is available. Simulation study shows good finite sample properties of proposed methods, while real data example illustrates the application of them.

scholarly journals DETECTION OF NONCONSTANT LONG MEMORY PARAMETER

2013 ◽  
Vol 29 (5) ◽  
pp. 1009-1056 ◽  
Author(s):  
Frédéric Lavancier ◽  
Remigijus Leipus ◽  
Anne Philippe ◽  
Donatas Surgailis
Keyword(s):  
Time Series ◽  
Long Memory ◽  
General Setting ◽  
Partial Sums ◽  
Gradual Change ◽  
Test Statistics ◽  
Finite Sample ◽  
Testing Procedures ◽  
Finite Sample Properties ◽  
Memory Parameter

This article deals with detection of a nonconstant long memory parameter in time series. The null hypothesis presumes stationary or nonstationary time series with a constant long memory parameter, typically an I (d) series with d > −.5 . The alternative corresponds to an increase in persistence and includes in particular an abrupt or gradual change from I (d1) to I (d2), −.5 < d1 < d2. We discuss several test statistics based on the ratio of forward and backward sample variances of the partial sums. The consistency of the tests is proved under a very general setting. We also study the behavior of these test statistics for some models with a changing memory parameter. A simulation study shows that our testing procedures have good finite sample properties and turn out to be more powerful than the KPSS-based tests (see Kwiatkowski, Phillips, Schmidt and Shin, 1992) considered in some previous works.

scholarly journals Goodness-of-Fit Tests for Bivariate Time Series of Counts

Econometrics ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 10
Author(s):  
Šárka Hudecová ◽  
Marie Hušková ◽  
Simos G. Meintanis
Keyword(s):  
Goodness Of Fit ◽  
Probability Generating Function ◽  
Parametric Bootstrap ◽  
Real Data ◽  
Data Sets ◽  
Test Statistics ◽  
Finite Sample ◽  
Generalized Poisson ◽  
Goodness Of Fit Tests ◽  
Monte Carlo Experiments

This article considers goodness-of-fit tests for bivariate INAR and bivariate Poisson autoregression models. The test statistics are based on an L2-type distance between two estimators of the probability generating function of the observations: one being entirely nonparametric and the second one being semiparametric computed under the corresponding null hypothesis. The asymptotic distribution of the proposed tests statistics both under the null hypotheses as well as under alternatives is derived and consistency is proved. The case of testing bivariate generalized Poisson autoregression and extension of the methods to dimension higher than two are also discussed. The finite-sample performance of a parametric bootstrap version of the tests is illustrated via a series of Monte Carlo experiments. The article concludes with applications on real data sets and discussion.

scholarly journals Estimation of the tail-index in a conditional location-scale family of heavy-tailed distributions

2019 ◽  
Vol 7 (1) ◽  
pp. 394-417
Author(s):  
Aboubacrène Ag Ahmad ◽  
El Hadji Deme ◽  
Aliou Diop ◽  
Stéphane Girard
Keyword(s):  
Asymptotic Properties ◽  
Real Data ◽  
Scale Model ◽  
Extreme Value Index ◽  
Finite Sample ◽  
Scale Functions ◽  
Nonparametric Estimators ◽  
Heavy Tailed Distributions ◽  
Finite Sample Properties ◽  
Heavy Tailed

AbstractWe introduce a location-scale model for conditional heavy-tailed distributions when the covariate is deterministic. First, nonparametric estimators of the location and scale functions are introduced. Second, an estimator of the conditional extreme-value index is derived. The asymptotic properties of the estimators are established under mild assumptions and their finite sample properties are illustrated both on simulated and real data.

scholarly journals The CUSUM statistic of change point under NA sequences

2021 ◽  
Vol 36 (4) ◽  
pp. 512-520
Author(s):  
Jin Ling ◽  
Xiao-qin Li ◽  
Wen-zhi Yang ◽  
Jian-ling Jiao
Keyword(s):  
Change Point ◽  
Brownian Bridge ◽  
Moving Average ◽  
Real Data ◽  
Normal Sample ◽  
Finite Sample ◽  
Covariance Functions ◽  
Finite Sample Properties ◽  
Moving Average Processes ◽  
Na Sequences

AbstractIn this paper, we investigate the CUSUM statistic of change point under the negatively associated (NA) sequences. By establishing the consistency estimators for mean and covariance functions respectively, the limit distribution of the CUSUM statistic is proved to be a standard Brownian bridge, which extends the results obtained under the case of an independent normal sample and the moving average processes. Finally, the finite sample properties of the CUSUM statistic are given to show the efficiency of the method by simulation studies and an application on a real data analysis.

Topp–Leone Linear Exponential Distribution

2018 ◽  
Vol 33 (1) ◽  
pp. 31-43
Author(s):  
Bol A. M. Atem ◽  
Suleman Nasiru ◽  
Kwara Nantomah
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Exponential Distribution ◽  
Likelihood Estimation ◽  
Real Data ◽  
Simulation Studies ◽  
Finite Sample ◽  
Data Set ◽  
Finite Sample Properties ◽  
Linear Exponential Distribution

Abstract This article studies the properties of the Topp–Leone linear exponential distribution. The parameters of the new model are estimated using maximum likelihood estimation, and simulation studies are performed to examine the finite sample properties of the parameters. An application of the model is demonstrated using a real data set. Finally, a bivariate extension of the model is proposed.

Some Exact Distribution Results for the Partially Restricted Reduced form Estimator

1994 ◽  
Vol 10 (1) ◽  
pp. 140-171 ◽  
Author(s):  
Terrence W. Kinal ◽  
John L. Knight
Keyword(s):  
Fractional Calculus ◽  
Linear Combination ◽  
Exact Distribution ◽  
Reduced Form ◽  
Characteristic Functions ◽  
Density Functions ◽  
Finite Sample ◽  
Invariant Polynomials ◽  
Variable Model ◽  
Finite Sample Properties

This paper considers some finite sample properties of the partially restricted reduced form estimators in a general (n + 1) endogenous variable model. In particular, the characteristic functions, density functions, and moments are examined for both the vector of estimators and a linear combination. The approach utilizes both invariant polynomials of matrix argument (see Chikuse and Davis [4] and Davis [6]) and fractional calculus techniques (see Phillips [20,25,26]).

Estimating cross-sectional regressions in event studies with conditional heteroskedasticity and regression designs that have leverage

2014 ◽  
Vol 10 (4) ◽  
pp. 418-431 ◽  
Author(s):  
Imre Karafiath
Keyword(s):  
Least Squares ◽  
Event Studies ◽  
Standard Errors ◽  
Conditional Heteroskedasticity ◽  
Test Statistics ◽  
Finite Sample ◽  
Cross Sectional ◽  
Content Type ◽  
Finite Sample Properties ◽  
Regression Design

Purpose – In the finance literature, fitting a cross-sectional regression with (estimated) abnormal returns as the dependent variable and firm-specific variables (e.g. financial ratios) as independent variables has become de rigueur for a publishable event study. In the absence of skewness and/or kurtosis the explanatory variable, the regression design does not exhibit leverage – an issue that has been addressed in the econometrics literature on the finite sample properties of heteroskedastic-consistent (HC) standard errors, but not in the finance literature on event studies. The paper aims to discuss this issue. Design/methodology/approach – In this paper, simulations are designed to evaluate the potential bias in the standard error of the regression coefficient when the regression design includes “points of high leverage” (Chesher and Jewitt, 1987) and heteroskedasticity. The empirical distributions of test statistics are tabulated from ordinary least squares, weighted least squares, and HC standard errors. Findings – None of the test statistics examined in these simulations are uniformly robust with regard to conditional heteroskedasticity when the regression includes “points of high leverage.” In some cases the bias can be quite large: an empirical rejection rate as high as 25 percent for a 5 percent nominal significance level. Further, the bias in OLS HC standard errors may be attenuated but not fully corrected with a “wild bootstrap.” Research limitations/implications – If the researcher suspects an event-induced increase in return variances, tests for conditional heteroskedasticity should be conducted and the regressor matrix should be evaluated for observations that exhibit a high degree of leverage. Originality/value – This paper is a modest step toward filling a gap on the finite sample properties of HC standard errors in the event methodology literature.

scholarly journals New Equivalence Tests for Hardy–Weinberg Equilibrium and Multiple Alleles

Stats ◽  
2020 ◽  
Vol 3 (1) ◽  
pp. 34-39
Author(s):  
Vladimir Ostrovski
Keyword(s):  
Bootstrap Method ◽  
Real Data ◽  
Data Sets ◽  
Test Statistics ◽  
Finite Sample ◽  
Multiple Alleles ◽  
Weinberg Equilibrium ◽  
Equivalence Tests ◽  
Hardy Weinberg Equilibrium ◽  
The Bootstrap Method

We consider testing equivalence to Hardy–Weinberg Equilibrium in case of multiple alleles. Two different test statistics are proposed for this test problem. The asymptotic distribution of the test statistics is derived. The corresponding tests can be carried out using asymptotic approximation. Alternatively, the variance of the test statistics can be estimated by the bootstrap method. The proposed tests are applied to three real data sets. The finite sample performance of the tests is studied by simulations, which are inspired by the real data sets.

scholarly journals HAR Testing for Spurious Regression in Trend

Econometrics ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 50
Author(s):  
Peter C. B. Phillips ◽  
Xiaohu Wang ◽  
Yonghui Zhang
Keyword(s):  
Standardized Test ◽  
Nonstationary Time Series ◽  
T Test ◽  
Test Statistics ◽  
Finite Sample ◽  
Spurious Regression ◽  
Machine Learning Methods ◽  
Stochastic Trends ◽  
Finite Sample Properties ◽  
And Control

The usual t test, the t test based on heteroskedasticity and autocorrelation consistent (HAC) covariance matrix estimators, and the heteroskedasticity and autocorrelation robust (HAR) test are three statistics that are widely used in applied econometric work. The use of these significance tests in trend regression is of particular interest given the potential for spurious relationships in trend formulations. Following a longstanding tradition in the spurious regression literature, this paper investigates the asymptotic and finite sample properties of these test statistics in several spurious regression contexts, including regression of stochastic trends on time polynomials and regressions among independent random walks. Concordant with existing theory (Phillips 1986, 1998; Sun 2004, 2014b) the usual t test and HAC standardized test fail to control size as the sample size n → ∞ in these spurious formulations, whereas HAR tests converge to well-defined limit distributions in each case and therefore have the capacity to be consistent and control size. However, it is shown that when the number of trend regressors K → ∞ , all three statistics, including the HAR test, diverge and fail to control size as n → ∞ . These findings are relevant to high-dimensional nonstationary time series regressions where machine learning methods may be employed.

scholarly journals Testing for Multiple Structural Changes with Non-Homogeneous Regressors

2015 ◽  
Vol 7 (1) ◽  
pp. 1-35 ◽  
Author(s):  
Eiji Kurozumi
Keyword(s):  
Monte Carlo ◽  
Structural Changes ◽  
Linear Trend ◽  
Critical Values ◽  
Test Statistics ◽  
Finite Sample ◽  
Multiple Structural Changes ◽  
Finite Sample Properties ◽  
Polynomial Trends ◽  
Weighted Type

AbstractThis paper investigates tests for multiple structural changes with non-homogeneous regressors, such as polynomial trends. We consider exponential-type, supremum-type and average-type tests as well as the corresponding weighted-type tests suggested in the literature. We show that the limiting distributions depend on regressors in general, and we need to tabulate critical values depending on them. Then, we focus on the linear trend case and obtain the critical values of the test statistics. The Monte Carlo simulations are conducted to investigate the finite sample properties of the tests proposed in the paper, and it is found that the specification of the number of breaks is an important factor for the finite sample performance of the tests. Since it is often the case that we cannot prespecify the number of breaks under the alternative but can suppose only the maximum number of breaks, the weighted-type tests are useful in practice.

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