Characteristic Function‐based Semiparametric Inference for Skew‐symmetric Models

Skew‐symmetric models offer a very flexible class of distributions for modelling data. These distributions can also be viewed as selection models for the symmetric component of the specified skew‐symmetric distribution. The estimation of the location and scale parameters corresponding to the symmetric component is considered here, with the symmetric component known. Emphasis is placed on using the empirical characteristic function to estimate these parameters. This is made possible by an invariance property of the skew‐symmetric family of distributions, namely that even transformations of random variables that are skew‐symmetric have a distribution only depending on the symmetric density. A distance metric between the real components of the empirical and true characteristic functions is minimized to obtain the estimators. The method is semiparametric, in that the symmetric component is specified, but the skewing function is assumed unknown. Furthermore, the methodology is extended to hypothesis testing. Two tests for a null hypothesis of specific parameter values are considered, as well as a test for the hypothesis that the symmetric component has a specific parametric form. A resampling algorithm is described for practical implementation of these tests. The outcomes of various numerical experiments are presented.     

Importance of the prior mass for agreement between frequentist and Bayesian approaches in the two-sided test

We study distributional properties of generalized order statistics (gos) related by a random shift or scaling scheme in the continuous and discrete case, respectively. In the continuous case, we obtain new characterizations of distributions relating non-neighbouring gos extending some results given in the literature for the neighbouring cases. On the other hand, in the discrete case, we investigate the existence and uniqueness of a discrete parent distribution supported on the integers whose gos are related by a random translation.     

Inference of the derivative of nonparametric curve based on confidence distribution

Abstract

This paper focuses on inference based on the confidence distributions of the nonparametric regression function and its derivatives, in which dependent inferences are combined by obtaining information about their dependency structure. We first give a motivating example in production operation system to illustrate the necessity of the problems studied in this paper in practical applications. A goodness-of-fit test for polynomial regression model is proposed on the basis of the idea of combined confidence distribution inference, which is the Fisher’s combination statistic in some cases. On the basis of this testing results, a combined estimator for the p-order derivative of nonparametric regression function is provided as well as its large sample size properties. Consequently, the performances of the proposed test and estimation method are illustrated by three specific examples. Finally, the motivating example is analyzed in detail. The simulated and real data examples illustrate the good performance and practicability of the proposed methods based on confidence distribution.     

Wavelet‐Based Testing for Serial Correlation of Unknown Form in Panel Models

Wavelet analysis is a new mathematical method developed as a unified field of science over the last decade or so. As a spatially adaptive analytic tool, wavelets are useful for capturing serial correlation where the spectrum has peaks or kinks, as can arise from persistent dependence, seasonality, and other kinds of periodicity. This paper proposes a new class of generally applicable wavelet‐based tests for serial correlation of unknown form in the estimated residuals of a panel regression model, where error components can be one‐way or two‐way, individual and time effects can be fixed or random, and regressors may contain lagged dependent variables or deterministic/stochastic trending variables. Our tests are applicable to unbalanced heterogenous panel data. They have a convenient null limit N(0,1) distribution. No formulation of an alternative model is required, and our tests are consistent against serial correlation of unknown form even in the presence of substantial inhomogeneity in serial correlation across individuals. This is in contrast to existing serial correlation tests for panel models, which ignore inhomogeneity in serial correlation across individuals by assuming a common alternative, and thus have no power against the alternatives where the average of serial correlations among individuals is close to zero. We propose and justify a data‐driven method to choose the smoothing parameter—the finest scale in wavelet spectral estimation, making the tests completely operational in practice. The data‐driven finest scale automatically converges to zero under the null hypothesis of no serial correlation and diverges to infinity as the sample size increases under the alternative, ensuring the consistency of our tests. Simulation shows that our tests perform well in small and finite samples relative to some existing tests.     

Does Market Incompleteness Matter?

This paper argues that incompleteness of intertemporal financial markets has little effect (on welfare, prices, or consumption) in an economy with a single consumption good, provided that traders are long–lived and patient, a riskless bond is traded, shocks are transitory, and there is no aggregate risk. In an economy with aggregate risk, a similar conclusion holds, provided traders share the same CRRA utility function and the right assets are traded. Examples demonstrate that these conclusions need not hold if the wrong assets are traded or if the economy has multiple consumption goods.     

论宪政设计的可能性及其理论预设

人类社会可以通过政治设计来建立一个良好的政府,而宪政设计就是一个实现人间至善、建立美好现代社会的基本途径。人类具有主体性,政治具有向善性,这就使得宪政设计成为可能。进行宪政设计必须遵循一些理论预设,那就是关于人性的幽暗意识假定和关于权力的必要的恶的假定。     

Multiperiod Forecasts of Interest Rates

The accuracy of forecasts of interest rates over different forecast horizons and time periods is examined. The results indicate a deterioration in “absolute” forecast accuracy measured by the mean absolute error and the root mean squared error but no decrease in “relative” accuracy measured by the Theil coefficient with an increase in the forecast span. The results also indicate a decline in accuracy in periods of volatile interest rates. Support is found for the hypothesis that the ratio of the variability of predicted changes to that of actual changes falls with an increase in the forecast horizon.     

On the asymptotic distribution of cramer-von mises one-sample test statistics under an alternative

The asymptotic normality of the Cramer-von Mises one-sample test statistic and one of its variants under an alternative cdf is demonstrated. The derivation herein is unique in that it does not require knowledge of the theory of weak convergence of probability measures defined on metrized function spaces, and thus is accessible to a broader class of students and practitioners.     

On concurrence of several linear regressions and applications to problems of enzyme kinetics

In comparing several regressions E(y_ij) =α_i + β_ix_ij i = 1, 2, ..., k, j = 1,2, ..., n_i, researchers are generally interested in the following five problems: whether they have (1) equal slope, (2) equal intercept, (3) coincidence, (4) common intersection on X-axis, and (5) common intersection on (X,Y) - plane. Problems (1) - (3) can be put into the framework of the general linear hypothesis and the F-test can be used. However, problems (4) and (5) cannot be put into the general linear hypothesis because they are ratios of parameters. Hence, in this paper we consider the generalized likelihood ratio test for hypothesis testing. An application to an enzyme kinetics problem in Aniline Metabolism is demonstrated