Linearity Test with Unit Root in TV-ESTAR Framework

Firstly, this paper proposes F statistic whose limit distribution and critical values are also provided to test nonlinearity and structure change with unit root in TV-ESTAR model framework. The results show that the distribution of F statistic is nonstandard. Then, this paper analyzes finite sample characteristics of F statistics through the Monte Carlo simulation and founds F statistics has better power than kss statistics in Kapetanios et al to test nonlinear unit root with structure change.

On the distribution of winners’ scores in a round-robin tournament

In a classical chess round-robin tournament, each of $n$ players wins, draws, or loses a game against each of the other $n-1$ players. A win rewards a player with 1 points, a draw with 1/2 point, and a loss with 0 points. We are interested in the distribution of the scores associated with ranks of $n$ players after ${{n \choose 2}}$ games, that is, the distribution of the maximal score, second maximum, and so on. The exact distribution for a general $n$ seems impossible to obtain; we obtain a limit distribution.

Fractional Entropy-Based Test of Uniformity with Power Comparisons

In the present paper, we use the fractional and weighted cumulative residual entropy measures to test the uniformity. The limit distribution and an approximation of the distribution of the test statistic based on the fractional cumulative residual entropy are derived. Moreover, for this test statistic, percentage points and power against seven alternatives are reported. Finally, a simulation study is carried out to compare the power of the proposed tests and other tests of uniformity.

Testing the proportionality assumption for specified covariate in the cox model

In this paper, I propose a test for proportional hazards assumption for specified covariates. The testis based on a general alternative in sense that hazards rates under different values of covariates therate is not only constant as in the Cox model, but it may cross, go away, and may be monotonicwith time. The limit distribution of the test statistic is derived. Finite samples properties of thetest power are analyzed by simulation. Application of the proposed test on Real data examples areconsidered.

NEGATIVE POWERS OF INTEGRATED PROCESSES

This paper derives the limit distribution of the rescaled sum of the absolute value of an integrated process with continuously distributed innovations raised to a negative power less than $-$ 1, and of the analogous statistic that is obtained using the same function of an integrated process but only considering positive values of the integrated process. We show that the limit behavior of this statistic is determined by the values of the integrated process that are closest to 0, and find the limit behavior of the values of the integrated process that are closest to 0.

Non-local Solvable Birth–Death Processes

In this paper, we study strong solutions of some non-local difference–differential equations linked to a class of birth–death processes arising as discrete approximations of Pearson diffusions by means of a spectral decomposition in terms of orthogonal polynomials and eigenfunctions of some non-local derivatives. Moreover, we give a stochastic representation of such solutions in terms of time-changed birth–death processes and study their invariant and their limit distribution. Finally, we describe the correlation structure of the aforementioned time-changed birth–death processes.

Convergence theorems on multi-dimensional homogeneous quantum walks

We propose a general framework for quantum walks on d-dimensional spaces. We investigate asymptotic behavior of these walks. We prove that every homogeneous walks with finite degree of freedom have limit distribution. This theorem can also be applied to every crystal lattice. In this theorem, it is not necessary to assume that the support of the initial unit vector is finite. We also pay attention on 1-cocycles, which is related to Heisenberg representation of time evolution of observables. For homogeneous walks with finite degree of freedom, convergence of averages of 1-cocycles associated with the position observable is also proved.