Uniform consistency rate of kNN regression estimation for functional time series data

In this paper, we investigate the k-nearest neighbours (kNN) estimation of nonparametric regression model for strong mixing functional time series data. More precisely, we establish the uniform almost complete convergence rate of the kNN estimator under some mild conditions. Furthermore, a simulation study and an empirical application to the real data analysis of sea surface temperature (SST) are carried out to illustrate the finite sample performances and the usefulness of the kNN approach.     

The impact of the European Youth Guarantee on active labour market policies: A convergence analysis

The European Union’s (EU) Youth Guarantee aims to improve the labour market situation of young people. Rather than prescribing a uniform policy model, it acknowledges that supportive measures need to align with national, regional and local circumstances. It thus seeks to promote mutual policy learning through the open method of coordination. As an innovative measure, the EU has deployed funding programmes to support the domestic measures related to the Youth Guarantee. We therefore examined in this study whether this mix of recommendations and financial incentives has entailed a convergence of member state policies. Our analysis of policy outputs for the period 2007?2014 yields a mixed empirical picture. There is catching‐up convergence regarding policies’ sectoral coverage but increasing divergence concerning the number of adopted policy instruments. The first two years of financial incentives did not produce any effect on enhancing policy experimentation among less active member states. We offer an optimistic and a pessimistic interpretation of these findings.     

Parameter estimation of the censored δ-shock model on uniform interval

The censored δ-shock model is a special kind of shock model and it has very important research values in the reliability theory. In this paper, we discuss the parameter estimation of the censored δ-shock model when the inter-arrival times between two successive shocks follows uniform distribution on [a, b]. With the maximum likelihood estimation, we obtain the parameter estimator and expectation of estimator and lifetime of the model. By numerical simulation, we get the empirical result on the estimator of δ and the relationship between δ and other parameters.     

Complete moment convergence of widely orthant dependent random variables

It is known that the dependence structure of widely orthant dependent (WOD) random variables is weaker than those of negatively associated (NA) random variables, negatively superadditive dependent (NSD) random variables, negatively orthant dependent (NOD) random variables, and extended negatively dependent (END) random variables. In this article, the results of complete moment convergence and complete convergence are presented for WOD sequence under the same moment conditions as independent sequence in classical result (Chow 1988 Chow, Y. (1988). On the rate of moment convergence of sample sums and extremes. Bull. Inst. Math. Acad. Sin. 16(3):177–201. [Google Scholar]).     

Efficiency of the generalized-difference-based weighted mixed almost unbiased two-parameter estimator in partially linear model

In this paper, a generalized difference-based estimator is introduced for the vector parameter β in partially linear model when the errors are correlated. A generalized-difference-based almost unbiased two-parameter estimator is defined for the vector parameter β. Under the linear stochastic constraint r = Rβ + e, we introduce a new generalized-difference-based weighted mixed almost unbiased two-parameter estimator. The performance of this new estimator over the generalized-difference-based estimator and generalized- difference-based almost unbiased two-parameter estimator in terms of the MSEM criterion is investigated. The efficiency properties of the new estimator is illustrated by a simulation study. Finally, the performance of the new estimator is evaluated for a real dataset.     

Varying kernel marginal density estimator for a positive time series

This paper analyses the large sample behaviour of a varying kernel density estimator of the marginal density of a non-negative stationary and ergodic time series that is also strongly mixing. In particular we obtain an approximation for bias, mean square error and establish asymptotic normality of this density estimator. We also derive an almost sure uniform consistency rate over bounded intervals of this estimator. A finite sample simulation shows some superiority of the proposed density estimator over the one based on a symmetric kernel.     

A note on mixingale limit theorems and stable convergence in law

A gap in the proof of a non stationary mixingale invariance principle is identified and fixed by introducing a skipped subsampling of a partial sum process and letting the skipped interval vanish asymptotically at an appropriate rate as the sample size increases. The corrected proof produces a mixingale limit theorem in the form of a mixing convergence in law, occurring jointly with the stable convergence in law for the same σ-field relative to which they are stable and mixing. The applicability of established results to a high-frequency estimation of the quadratic variation of financial price process is discussed.     

基于贝叶斯SDM模型的中国城镇居民收入收敛性分析

随着中国经济的高速增长,中国区域间贫富差距也日渐加大,在此背景下对中国城镇居民收入是否收敛进行检验并探究其影响原因十分必要。基于一个包括物质资本和人力资本投入的新古典增长模型,根据中国31个省市的1987—2013年数据,利用SDM模型和贝叶斯MCMC统计分析方法,研究城镇居民收入的收敛性问题,结果发现:中国城镇居民人均收入具有显著的空间差异,且在1987—2008年为发散、在2008—2013年以及1987—2013年为存在β收敛的变化趋势;物质资本对中国城镇居民收入增长的β收敛具有正向促进作用,而人力资本对其具有反向促进作用,增加物质资本投入有利于缩小地区收入差距,二者的不匹配可能是导致中国收入增长差距的原因。     

Asymptotic behaviour of proportions of observations in random regions determined by central order statistics from stationary processes

In this paper, we show that proportions of observations that fall into a random region determined by a given Borel set and a central order statistic converge almost surely, provided that the corresponding population quantile is unique. We also describe three types of possible asymptotic behaviour of these proportions in the case of non-unique population quantile. As an application of our findings we establish limiting properties of numbers of ties with a central order statistics in a discrete sample. Our results are derived not only for independent and identically distributed observations but more generally for strictly stationary and ergodic sequences of random variables.     

Threshold Estimation for Stochastic Processes with Small Noise

Consider a process satisfying a stochastic differential equation with unknown drift parameter, and suppose that discrete observations are given. It is known that a simple least squares estimator (LSE) can be consistent but numerically unstable in the sense of large standard deviations under finite samples when the noise process has jumps. We propose a filter to cut large shocks from data and construct the same LSE from data selected by the filter. The proposed estimator can be asymptotically equivalent to the usual LSE, whose asymptotic distribution strongly depends on the noise process. However, in numerical study, it looked asymptotically normal in an example where filter was chosen suitably, and the noise was a Lévy process. We will try to justify this phenomenon mathematically, under certain restricted assumptions.