The asymptotic behaviour of a class of L.-estimators under long-range dependence

This paper obtains asymptotic representations of a class of L-estimators in a linear regression model when the errors are a function of long-range-dependent Gaussian random variables. These representations are then used to address some of the efficiency robustness properties of L-estimators compared to the least-squares estimator. It is observed that under the Gaussian error distribution, each member of the class has the same asymptotic efficiency as that of the least-squares estimator. The results are obtained as a consequence of the asymptotic uniform linearity of some weighted empirical processes based on long-range-dependent random variables.     

Power-law scaling behavior analysis of financial time series model by voter interacting dynamic system

We investigate the power-law scaling behaviors of returns for a financial price process which is developed by the voter interacting dynamic system in comparison with the real financial market index (Shanghai Composite Index). The voter system is a continuous time Markov process, which originally represents a voter's attitude on a particular topic, that is, voters reconsider their opinions at times distributed according to independent exponential random variables. In this paper, the detrended fluctuation analysis method is employed to explore the long range power-law correlations of return time series for different values of parameters in the financial model. The findings show no indication or very weak long-range power-law correlations for the simulated returns but strong long-range dependence for the absolute returns. The multiplier distribution is studied to demonstrate directly the existence of scale invariance in the actual data of the Shanghai Stock Exchange and the simulation data of the model by comparison. Moreover, the Zipf analysis is applied to investigate the statistical behaviors of frequency functions and the distributions of the returns. By a comparative study, the simulation data for our constructed price model exhibits very similar behaviors to the real stock index, this indicates somewhat rationality of our model to the market application.     

Large-scale simultaneous inference under dependence

Simultaneous inference allows for the exploration of data while deciding on criteria for proclaiming discoveries. It was recently proved that all admissible post hoc inference methods for the true discoveries must employ closed testing. In this paper, we investigate efficient closed testing with local tests of a special form: thresholding a function of sums of test scores for the individual hypotheses. Under this special design, we propose a new statistic that quantifies the cost of multiplicity adjustments, and we develop fast (mostly linear-time) algorithms for post hoc inference. Paired with recent advances in global null tests based on generalized means, our work instantiates a series of simultaneous inference methods that can handle many dependence structures and signal compositions. We provide guidance on the method choices via theoretical investigation of the conservativeness and sensitivity for different local tests, as well as simulations that find analogous behavior for local tests and full closed testing.     

FDR control under block dependence

In practical settings such as microarray data analysis, multiple hypotheses with dependence within but not between equal-sized blocks often need to be tested. We consider an adaptive BH procedure to test the hypotheses. Under the condition of positive regression dependence on a subset of the true null hypotheses, the proposed adaptive procedure is shown to control the false discovery rate. The proposed approach is compared to the existing methods in simulation under block dependence and totally uniform pairwise dependence. It is observed that the proposed method performs better than the existing methods in several situations.     

Hill's estimator under weak dependence

In this article, we investigate the asymptotic normality of the Hill's estimator of the tail index parameter, when the observations are weakly dependent in the sense of Doukhan and Louhichi (1999 Doukhan, P., Louhichi, S. (1999). A new weak dependence condition and applications to moment inequalities. Stochastic Process. Appl. 84:313–342.[Crossref], [Web of Science ®] , [Google Scholar]) and are drawn from a strictly linear process. We show that the previous result on Hill estimator obtained by Rootzen et al. (1990 Rootzen, H., Leadbetter, M., De Haan, L. (1990). Tail and quantile estimation for strongly mixing stationary sequences. Technical report. No. 292, Center for Stochastic Processes, Department of Statistics, University of North Carolina, Chapel Hill. [Google Scholar]) and Resnick and Starica (1997 Resnick, S., Starica, C. (1997). Asymptotic behavior of Hill's estimator for autoregressive data. Commun. Statistics-stochastic Models 13:703–723.[Taylor &; Francis Online] , [Google Scholar]) for strong mixing can be extended to weak dependence.     

Large-scale multiple testing under dependence

Summary.  The paper considers the problem of multiple testing under dependence in a compound decision theoretic framework. The observed data are assumed to be generated from an underlying two-state hidden Markov model. We propose oracle and asymptotically optimal data-driven procedures that aim to minimize the false non-discovery rate FNR subject to a constraint on the false discovery rate FDR. It is shown that the performance of a multiple-testing procedure can be substantially improved by adaptively exploiting the dependence structure among hypotheses, and hence conventional FDR procedures that ignore this structural information are inefficient. Both theoretical properties and numerical performances of the procedures proposed are investigated. It is shown that the procedures proposed control FDR at the desired level, enjoy certain optimality properties and are especially powerful in identifying clustered non-null cases. The new procedure is applied to an influenza-like illness surveillance study for detecting the timing of epidemic periods.     

Invariant dependence structure under univariate truncation

The class of all bivariate copulas that are invariant under univariate truncation is characterized. To this end, a family of bivariate copulas generated by a real-valued function is introduced. The obtained results are also used in order to show that the Clayton family of copulas (including its limiting elements) coincides with the class of copulas that are invariant under bivariate truncation and contains all exchangeable copulas which are invariant under univariate truncation.     

Some simulation results for the linear expenditure system with random marginal budget shares

The estimation of the linear expenditure system (LES) with aggregate time series data is criticized since it requires the assumption of homogeneous consumers. A cross-section random coefficient version of the LES is proposed and maximum likelihood estimators are derived. Some Monte Carlo results are described which imply that the random coefficient approach does a reasonably good job of parameter estimation in certain circumstances.     

Estimation of the limit variance for sums under a new weak dependence condition

We prove a self-normalized central limit theorem for a mixing class of processes introduced in Kacem M, Loisel S, Maume-Deschamps V. [Some mixing properties of conditionally independent processes. Commun Statist Theory Methods. 2016;45:1241–1259]. This class is larger than more classical strongly mixing processes and thus our result is more general than [Peligrad M, Shao QM. Estimation of the variance of partial sums for ρ-mixing random variables. J Multivar Anal. 1995;52:140–157; Shi S. Estimation of the variance for strongly mixing sequences. Appl Math J Chinese Univ. 2000;15(1):45–54] ones. The fact that some conditionally independent processes satisfy this kind of mixing properties motivated our study. We investigate the weak consistency as well as the asymptotic normality of the estimator of the variance that we propose.     

Complete convergence of weighted sums under negative dependence

In this paper, we study the complete convergence of weighted sums. In fact, we extend the result of Amini and Bozorgnia (J Appl Math Stoch Anal 16(2):121–126, 2003) on unweighted average to a weighted average under mild conditions.     

Preservation of dependence concepts under bivariate weighted distributions

ABSTRACT

In this paper, we provide conditions under which some bivariate dependence structures are preserved under bivariate weighted distributions. Bivariate weighted distributions whose dependence structure is the same as the original distribution are characterized. Finally, we discuss some examples to show the usefulness of our results.     

Modified Simes’ critical values under positive dependence

A modification of the critical values of Simes’ test is suggested in this article when the underlying test statistics are multivariate normal with a common non-negative correlation, yielding a more powerful test than the original Simes’ test. A step-up multiple testing procedure with these modified critical values, which is shown to control false discovery rate (FDR), is presented as a modification of the traditional Benjamini–Hochberg (BH) procedure. Simulations were carried out to compare this modified BH procedure with the BH and other modified BH procedures in terms of false non-discovery rate (FNR), 1–FDR–FNR and average power. The present modified BH procedure is observed to perform well compared to others when the test statistics are highly correlated and most of the hypotheses are true.     

Nonparametric estimation of the hazard function under dependence conditions

The estimation of the hazard rate has a great number of practical appli¬cations in dependence situations (seismicity analysis, reliability, economics), Based on kernel estimates of the density and the distribution function, we study the properties of the nonparametric estimator of the hazard function as-sociated with a strongly mixing time series. We prove consistency and asymp¬totic normality properties, and a cross-validation method for the smoothing parameter selection is studied. Some simulations and a practical application to real data are also shown.     

Stationary bootstrapping for panel cointegration tests under cross-sectional dependence

Stationary bootstrapping is applied to panel cointegration tests which are based on the ordinary least-squares estimator and the seemingly unrelated regression (SUR) estimator of the residual unit root. Large sample validity of stationary bootstrapping is established. A finite sample experiment reveals that size performances of the bootstrap tests are much less sensitive to cross-sectional correlation than those of existing tests and a test based on the SUR estimator has substantially better power than existing tests.     

Frequency domain bootstrap for ratio statistics under long-range dependence

A frequency domain bootstrap (FDB) is a common technique to apply Efron’s independent and identically distributed resampling technique (Efron, 1979) to periodogram ordinates – especially normalized periodogram ordinates – by using spectral density estimates. The FDB method is applicable to several classes of statistics, such as estimators of the normalized spectral mean, the autocorrelation (but not autocovariance), the normalized spectral density function, and Whittle parameters. While this FDB method has been extensively studied with respect to short-range dependent time processes, there is a dearth of research on its use with long-range dependent time processes. Therefore, we propose an FDB methodology for ratio statistics under long-range dependence, using semi- and nonparametric spectral density estimates as a normalizing factor. It is shown that the FDB approximation allows for valid distribution estimation for a broad class of stationary, long-range (or short-range) dependent linear processes, without any stringent assumptions on the distribution of the underlying process. The results of a large simulation study show that the FDB approximation using a semi- or nonparametric spectral density estimator is often robust for various values of a long-memory parameter reflecting magnitude of dependence. We apply the proposed procedure to two data examples.     

On the expected discounted penalty function for a risk model with dependence under a multi-layer dividend strategy

In this article, we consider a dependent risk model in the presence of a multi-laydividend strategy. We construct the dependence structure between the claim size and interclaim time by a Farlie–Gumbel–Morgenstern copula. A piecewise integro-differential equations for the expected discounted penalty function with boundary conditions are established. A renewal equation satisfied by the expected discounted penalty function is obtained via the translation operator. Then, we provide a recursive approach to derive the analytical solution of the expected discounted penalty function. Finally, a numerical example is presented to illustrate the solution procedure.