The kernel regression estimation for randomly censored functional stationary ergodic data

In this paper, we investigate the asymptotic properties of the kernel estimator for non parametric regression operator when the functional stationary ergodic data with randomly censorship are considered. More precisely, we introduce the kernel-type estimator of the non parametric regression operator with the responses randomly censored and obtain the almost surely convergence with rate as well as the asymptotic normality of the estimator. As an application, the asymptotic (1 ? ζ) confidence interval of the regression operator is also presented (0 < ζ < 1). Finally, the simulation study is carried out to show the finite-sample performances of the estimator.     

A robust nonparametric estimation of the autoregression function under an ergodic hypothesis

The authors propose a family of robust nonparametric estimators for regression or autoregression functions based on kernel methods. They show the strong uniform consistency of these estimators under a general ergodicity condition when the data are unbounded and range over suitably increasing sequences of compact sets. They give some implications of these results for stating the prediction in Markovian processes with finite order and show, through simulation, the efficiency of the predictors they propose.     

Inference for ergodic diffusions plus noise

We research an adaptive maximum‐likelihood–type estimation for an ergodic diffusion process where the observation is contaminated by noise. This methodology leads to the asymptotic independence of the estimators for the variance of observation noise, the diffusion parameter, and the drift one of the latent diffusion process. Moreover, it can lessen the computational burden compared to simultaneous maximum likelihood–type estimation. In addition to adaptive estimation, we propose a test to see if noise exists or not and analyze real data as the example such that the data contain observation noise with statistical significance.     

Contrast function estimation for the drift parameter of ergodic jump diffusion process

In this paper, we consider an ergodic diffusion process with jumps whose drift coefficient depends on an unknown parameter. We suppose that the process is discretely observed. We introduce an estimator based on a contrast function, which is efficient without requiring any conditions on the rate at which the step discretization goes to zero, and where we allow the observed process to have nonsummable jumps. This extends earlier results where the condition on the step discretization was needed and where the process was supposed to have summable jumps. In general situations, our contrast function is not explicit and one has to resort to some approximation. In the case of a finite jump activity, we propose explicit approximations of the contrast function such that the efficient estimation of the drift parameter is feasible. This extends the results obtained by Kessler in the case of continuous processes.     

Universal codes as a basis for time series testing

We suggest a new approach to hypothesis testing for ergodic and stationary processes. In contrast to standard methods, the suggested approach gives a possibility to make tests, based on any lossless data compression method even if the distribution law of the codeword lengths is not known. We apply this approach to the following four problems: goodness-of-fit testing (or identity testing), testing for independence, testing of serial independence and homogeneity testing and suggest nonparametric statistical tests for these problems. It is important to note that practically used so-called archivers can be used for suggested testing.     

A Note on Consistent Estimation of Multivariate Parameters in Ergodic Diffusion Models

Certain aspects of maximum likelihood estimation for ergodic diffusions are studied via recently developed empirical process theory for martingales. This approach enables us to remove some undesirable regularity conditions that usually appear in the statistical literature on ergodic diffusions. In particular, dimension dependent conditions for the existence of a continuous likelihood and for consistency of the maximum likelihood estimator turn out to be unnecessary.     

Job Matching and the Wage Distribution

This paper brings together the microeconomic‐labor and the macroeconomic‐equilibrium views of matching in labor markets. We nest a job matching model à la Jovanovic (1984) into a Mortensen and Pissarides (1994)‐type equilibrium search environment. The resulting framework preserves the implications of job matching theory for worker turnover and wage dynamics, and it also allows for aggregation and general equilibrium analysis. We obtain two new equilibrium implications of job matching and search frictions for wage inequality. First, learning about match quality and worker turnover map Gaussian output noise into an ergodic wage distribution of empirically accurate shape: unimodal, skewed, with a Paretian right tail. Second, high idiosyncratic productivity risk hinders learning and sorting, and reduces wage inequality. The equilibrium solutions for the wage distribution and for the aggregate worker flows—quits to unemployment and to other jobs, displacements, hires—provide the likelihood function of the model in closed form.     

√n-CONSISTENT ESTIMATION IN A RANDOM COEFFICIENT AUTOREGRESSIVE MODEL

This paper deals with √n-consistent estimation of the parameter μ in the RCAR(l) model defined by the difference equation X_j=(μ+U_j)X_j-l+ej (jε Z), where {e_j: jε Z} and {U_j: jε Z} are two independent sets of i.i.d. random variables with zero means, positive finite variances and E[(μ+U₁)²] < 1. A class of asymptotically normal estimators of μ indexed by a family of bounded measurable functions is introduced. Then an estimator is constructed which is asymptotically equivalent to the best estimator in that class. This estimator, asymptotically equivalent to the quasi-maximum likelihood estimator derived in Nicholls & Quinn (1982), is much simpler to calculate and is asymptotically normal without the additional moment conditions those authors impose.