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About 808 papers for “conditional characteristic function”

Conditional symmetry test based on empirical characteristic function

Chen, Feifei, Liang, Feng, Jiang, Qing · Figshare · 2024

In this paper, we propose a method for testing the conditional symmetry of multivariate random variables, specifically testing whether or not the conditional distribution of one random variable is symmetric around zero given another. Both the conditional symmetry test for observable data and unobserved error terms in parametric models are considered. The proposed test statistics are built on the weighted L2-distance between empirical characteristic functions and require no distributional assumption about the data distribution. The asymptotic properties of the test statistics under the null and alternative hypotheses are investigated. Since the limiting null distributions are intractable, a nonparametric Monte Carlo resampling method is used to determine critical values. Simulation results show the good performance of the proposed method in various scenarios. Two real datasets are analysed to illustrate the practical usefulness of the proposed tests.

Cited by 0Open access

Conditional symmetry test based on empirical characteristic function

Feifei Chen, Feng Liang, Qingwu Jiang · Journal of nonparametric statistics · 2024

In this paper, we propose a method for testing the conditional symmetry of multivariate random variables, specifically testing whether or not the conditional distribution of one random variable is symmetric around zero given another. Both the conditional symmetry test for observable data and unobserved error terms in parametric models are considered. The proposed test statistics are built on the weighted L2-distance between empirical characteristic functions and require no distributional assumption about the data distribution. The asymptotic properties of the test statistics under the null and alternative hypotheses are investigated. Since the limiting null distributions are intractable, a nonparametric Monte Carlo resampling method is used to determine critical values. Simulation results show the good performance of the proposed method in various scenarios. Two real datasets are analysed to illustrate the practical usefulness of the proposed tests.

Cited by 1Open access

A Consistent Characteristic Function-Based Test for Conditional Independence

Liangjun Su A, Halbert White B · 2008

Y is conditionally independent of Z given X if Pr{f(y|X, Z) =f(y|X)} =1for all y on its support, where f (. |.) denotes the conditional density of Y given (X, Z) or X. This paper proposes a nonparametric test of conditional independence based on the notion that two conditional distributions are equal if and only if the corresponding conditional characteristic functions are equal. We extend the test of Su and White (2005) in two directions: (1) our test is less sensitive to the choice of bandwidth sequences; (2) our test has power against deviations on the full support of the density of (X, Y, Z). We establish asymptotic normality for our test statistic under weak data dependence conditions. Simulation results suggest that the test is well behaved in finite samples. Applications to stock market data indicate that our test can reveal some interesting nonlinear dependence that a traditional linear Granger causality test fails to detect.

Cited by 0

Expected Conditional Characteristic Function-based Measures for Testing Independence

Ke, Chenlu, Yin, Xiangrong · Figshare · 2023

We propose a novel class of independence measures for testing independence between two random vectors based on the discrepancy between the conditional and the marginal characteristic functions. The relation between our index and other similar measures is studied, which indicates that they all belong to a large framework of reproducing kernel Hilbert space. If one of the variables is categorical, our asymmetric index extends the typical ANOVA to a kernel ANOVA that can test a more general hypothesis of equal distributions among groups. In addition, our index is also applicable when both variables are continuous. We develop two empirical estimates and obtain their respective asymptotic distributions. We illustrate the advantages of our approach by numerical studies across a variety of settings including a real data example. Supplementary materials for this article are available online.

Cited by 0Open access

Expected Conditional Characteristic Function-based Measures for Testing Independence

Chenlu Ke, Xiangrong Yin · OPAL (Open@LaTrobe) (La Trobe University) · 2021

We propose a novel class of independence measures for testing independence between two random vectors based on the discrepancy between the conditional and the marginal characteristic functions. The relation between our index and other similar measures is studied, which indicates that they all belong to a large framework of reproducing kernel Hilbert space. If one of the variables is categorical, our asymmetric index extends the typical ANOVA to a kernel ANOVA that can test a more general hypothesis of equal distributions among groups. In addition, our index is also applicable when both variables are continuous. We develop two empirical estimates and obtain their respective asymptotic distributions. We illustrate the advantages of our approach by numerical studies across a variety of settings including a real data example. Supplementary materials for this article are available online.

Cited by 0Open access

Expected Conditional Characteristic Function-based Measures for Testing Independence

Chenlu Ke, Xiangrong Yin · Figshare · 2023

We propose a novel class of independence measures for testing independence between two random vectors based on the discrepancy between the conditional and the marginal characteristic functions. The relation between our index and other similar measures is studied, which indicates that they all belong to a large framework of reproducing kernel Hilbert space. If one of the variables is categorical, our asymmetric index extends the typical ANOVA to a kernel ANOVA that can test a more general hypothesis of equal distributions among groups. In addition, our index is also applicable when both variables are continuous. We develop two empirical estimates and obtain their respective asymptotic distributions. We illustrate the advantages of our approach by numerical studies across a variety of settings including a real data example. Supplementary materials for this article are available online.

Cited by 0Open access

Expected Conditional Characteristic Function-based Measures for Testing Independence

Chenlu Ke, Xiangrong Yin · Figshare · 2019

We propose a novel class of independence measures for testing independence between two random vectors based on the discrepancy between the conditional and the marginal characteristic functions. The relation between our index and other similar measures is studied, which indicates that they all belong to a large framework of reproducing kernel Hilbert space. If one of the variables is categorical, our asymmetric index extends the typical ANOVA to a kernel ANOVA that can test a more general hypothesis of equal distributions among groups. In addition, our index is also applicable when both variables are continuous. We develop two empirical estimates and obtain their respective asymptotic distributions. We illustrate the advantages of our approach by numerical studies across a variety of settings including a real data example. Supplementary materials for this article are available online.

Cited by 0Open access

The universality of the Kalman filter: a conditional characteristic function perspective

Sandhya Rathore, Shambhu N. Sharma, Shaival H. Nagarsheth · arXiv (Cornell University) · 2019

The universality of the celebrated Kalman filtering can be found in control theory. The Kalman filter has found its striking applications in sophisticated autonomous systems and smart products, which are attributed to its realization in a single complex chip. In this paper, we revisit the Kalman filter from the perspective of conditional characteristic function evolution and Ito calculus and develop three Kalman filtering Theorems and their formal proof. Most notably, this paper reveals the following: (i) Kalman filtering equations are a consequence of the evolution of conditional characteristic function for the linear stochastic differential system coupled with the linear discrete measurement system. (ii) The Kalman filtering is a consequence of the stochastic evolution of conditional characteristic function for the linear stochastic differential system coupled with the linear continuous measurement system. (iii) The structure of the Kalman filter remains invariant under two popular stochastic interpretations, the Ito vs Stratonovich.

Cited by 0Open access

Estimation of stochastic conditional duration models by means of the empirical characteristic function.

Ferraz Junior, José Sidney, 1977- · Digital Library of Theses and Dissertations (Universidade de São Paulo) · 2008

Neste trabalho propomos a utilização do método da função característica empírica (ECF - empirical characteristic function), para estimação do modelo de duração condicional estocástica (SCD - stochastic conditional duration). Para determinação das variáveis latentes do processo utilizamos três alternativas: um filtro de Kalman, um filtro obtido por integração numérica e um filtro baseado na expansão de Gram-Charlier até 4ª ordem. Os resultados são então aplicados em séries de duração da GE, Microsoft e USD/EUR.

Cited by 0

Estimation of the Stochastic Conditional Duration Model by the Empirical Characteristic Function Method

Cathy (qiao Ning · 2004

The Stochastic conditional duration (SCD) model is a preferred model for duration data. However the model has no closed form of likelihood function and hence the maximum likelihood estimation method is unavailable. But the model has a closed form characteristic function. Since characteristic function contains the same amount of information as likelihood function, the model can be estimated by empirical characteristic function methodology. In this paper, the characteristic function of the stochastic conditional duration model is derived and the estimation approach is discussed. The empirical characteristic function approach is compared with I am very grateful to Prof. John Knight’s guidance. I also would like to thank Prof. Stephen Sapp for his helpful comments. I have further benefitted from discussion with Prof. George Jiang. All remaining errors are mine. 1 the quasi maximum likelihood approach and general method of moment approach using Monte Carlo experiments for different parameter values. It is found that the empirical characteristic function approach outperforms the quasi maximum likelihood approach and the general method of moment approach in terms of both bias and efficiency. The paper also givesinsightsastotheGMMestimationofSCDmodel. Themodeland the estimation methods are applied to IBM transaction duration. It is shown that empirical characteristic function estimators fit the data best. 1

Cited by 0

Determination of the characteristic function of discrete-time conditional linear random process and its application

Mykhailo Fryz, Bogdana Mlynko · Scientific journal of the Ternopil national technical university · 2023

The discrete-time conditional linear random process is defined, and its properties in the context of application for mathematical modelling of information signals in energy and medicine are analyzed. The relation to the continuous-time counterpart is considered on the basis of time sampling and aggregation. One-dimensional and multidimensional characteristic functions of discrete-time conditional linear random process are obtained using conditional characteristic function approach. The conditions for the investigated model to be strict sense stationary are justified.

Cited by 0Open access

INTEGRATED CONDITIONAL MOMENT TESTS FOR PARAMETRIC CONDITIONAL DISTRIBUTIONS

Herman J. Bierens, Li Wang · Econometric Theory · 2011

In this paper we propose consistent integrated conditional moment tests for the validity of parametric conditional distribution models, based on the integrated squared difference between the empirical characteristic function of the actual data and the characteristic function implied by the model. To avoid numerical evaluation of the conditional characteristic function of the model distribution, a simulated integrated conditional moment test is proposed. As an empirical application we test the validity of a few common health economic count data models.

Cited by 27

Consistent Integrated Conditional Moment Tests for Parametric Conditional Distributions of Stationary Time Series Processes (incomplete working paper, downloadable from http://econ.la. psu.edu/~hbierens/ICM_TS.PDF

Herman J. Bierens, Li Wang · 2008

This paper extends the Integrated Conditional Moment (ICM) test for the functional form of nonlinear regression models to tests for para-metric conditional distributions. This test is formed on the basis of the integrated squared difference between the empirical characteristic function of the actual data and the characteristic function implied by the model. This test is consistent, and has nontrivial power against√ n-local alternatives. To avoid numerical evaluation of the conditional characteristic function of the model distribution, a simulated integrated conditional moment (SICM) test is proposed, where each theoretical conditional characteristic function is replaced by a simulated counterpart, based on a single random drawing from the corresponding conditional dis-tribution. All the properties of the exact ICM test carry over to the SICM test. ∗A previous version of this paper was presented by Herman Bierens at the ”Symposium

Cited by 0

Generalized Wigner distributions, moments and conditional correspondence rules

Leon Cohen, Patrick J. Loughlin · Journal of Modern Optics · 2002

Methods are presented to generate conditional moments for all quasi-probability distributions, and explicit expressions for all conditional moments are given. In analogy to the generalized characteristic function operator, which generates all joint quasi-distribution functions, the conditional characteristic function operator which generates all conditional quasi-distributions is defined. This allows one to introduce the concept of conditional correspondence rules; formulations are given for all such rules.

Cited by 8

Integrated Conditional Moment Tests for Parametric Conditional Distributions ∗

Herman J. Bierens A, Li Wang B · 2011

In this paper we propose consistent integrated ionditional ioment tests for the validity of parametric conditional distribution models, based on the integrated squared difference between the empirical characteristic function of the actual data and the characteristic function implied by the model. To avoid numerical evaluation of the conditional characteristic function of the model distribution, a simulated integrated conditional moment test is proposed. As an empirical application we test the validity of a few common health economic count data models.

Cited by 0

Characteristic Function Approach to Smoothing of Linear Scalar Systems with Additive Cauchy Noises

Moshe Idan, Jason L. Speyer · 2019

The minimum conditional variance smoothing problem for a scalar linear system with additive Cauchy noises is to determine the mean of the history of the state given the measurement history over a defined time interval. Since the state history is structured as a vector, the conditional mean for additive Cauchy noises is best determined from a characteristic function approach. The derived smoothing algorithm recursively and analytically updates the characteristic function of the state history given the increasing measurement history, thereby increasing the dimension of the state history vector and the associated spectral vector, until the final stage is reached. The resulting characteristic function is then used to efficiently determine the smoothed conditional mean state history and the associated estimation error variance matrix.

Cited by 1