On the estimation of non linear functions in stochastic volatility models

Abstract

This paper focuses on the inference of suitable generally non linear functions in stochastic volatility models. In this context, in order to estimate the variance of the proposed estimators, a moving block bootstrap (MBB) approach is suggested and discussed. Under mild assumptions, we show that the MBB procedure is weakly consistent. Moreover, a methodology to choose the optimal length block in the MBB is proposed. Some examples and simulations on the model are also made to show the performance of the proposed procedure.     

一类混合指数型算子的一致逼近

主要讨论了一类混合指数型算子的一致逼近问题，并给出了逼近阶的估计和特征刻划。     

一类Kermack—Mckandrick方程组初值问题

本文研究描述传染病现象的一类Kermack—Mekandrick方程组初值问题光滑解整体存在唯一性及渐近性质。     

Efficient Estimation of a Distribution Function under Quadrant Dependence

LetX₁,X₂, ..., be real-valued random variables forming a strictly stationary sequence, and satisfying the basic requirement of being either pairwise positively quadrant dependent or pairwise negatively quadrant dependent. LetF^ be the marginal distribution function of theX_ips, which is estimated by the empirical distribution functionF_n and also by a smooth kernel-type estimateF_n, by means of the segmentX₁, ...,X_n. These estimates are compared on the basis of their mean squared errors (MSE). The main results of this paper are the following. Under certain regularity conditions, the optimal bandwidth (in the MSE sense) is determined, and is found to be the same as that in the independent identically distributed case. It is also shown thatn MSE(F_n(t)) andnMSE (F^_n(t)) tend to the same constant, asn→∞ so that one can not discriminate be tween the two estimates on the basis of the MSE. Next, ifi(n) = min {k∈{1, 2, ...}; MSE (F_k(t)) ≤ MSE (F_n(t))}, then it is proved thati(n)/n tends to 1, asn→∞. Thus, once again, one can not choose one estimate over the other in terms of their asymptotic relative efficiency. If, however, the squared bias ofF^_n(t) tends to 0 sufficiently fast, or equivalently, the bandwidthh_n satisfies the requirement thatnh³_n→ 0, asn→∞, it is shown that, for a suitable choice of the kernel, (i(n) ?n)/(nh_n) tends to a positive number, asn→∞ It follows that the deficiency ofF_n(t) with respect toF^_n(t),i(n) ?n, is substantial, and, actually, tends to ∞, asn→∞. In terms of deficiency, the smooth estimateF^_n(t) is preferable to the empirical distribution functionF_n(t)     

Smoothed bootstrap bandwidth selection for nonparametric hazard rate estimation

A smoothed bootstrap method is presented for the purpose of bandwidth selection in nonparametric hazard rate estimation for iid data. In this context, two new bootstrap bandwidth selectors are established based on the exact expression of the bootstrap version of the mean integrated squared error of some approximations of the kernel hazard rate estimator. This is very useful since Monte Carlo approximation is no longer needed for the implementation of the two bootstrap selectors. A simulation study is carried out in order to show the empirical performance of the new bootstrap bandwidths and to compare them with other existing selectors. The methods are illustrated by applying them to a diabetes data set.     

Robust bootstrap forecast densities for GARCH returns and volatilities

Bootstrap procedures are useful to obtain forecast densities for both returns and volatilities in the context of generalized autoregressive conditional heteroscedasticity models. In this paper, we analyse the effect of additive outliers on the finite sample properties of these bootstrap densities and show that, when obtained using maximum likelihood estimates of the parameters and standard filters for the volatilities, they are badly affected with dramatic consequences on the estimation of Value-at-Risk. We propose constructing bootstrap densities for returns and volatilities using a robust parameter estimator based on variance targeting implemented together with an adequate modification of the volatility filter. We show that the performance of the proposed procedure is adequate when compared with available robust alternatives. The results are illustrated with both simulated and real data.     

《周易》中正之道与人生

中正之道是《周易》全文倡导的一种思想,也是当代人趋吉避凶、和谐生活的一种有效方法.有中正继而达到合和,而要达到中正合和就需要人们日常的言行当位,当位进而处顺；而要达到中正合和、当位处顺,则需要正确把握时机,时行则行,时止则止.中正和合、当位处顺、时行则行、时止则止,强调的都是时、位、度的重要性,在合适的时间、合适的地点、做合适的事情关系到对度的把握,而度的把握更多的是需要一种智慧.     

Generalized additive mixed models

Following the extension from linear mixed models to additive mixed models, extension from generalized linear mixed models to generalized additive mixed models is made, Algorithms are developed to compute the MLE's of the nonlinear effects and the covariance structures based on the penalized marginal likelihood. Convergence of the algorithms and selection of the smooth param¬eters are discussed.     

Smooth goodness of fit tests for the weibull distribution with singly censored data

The smooth goodness of fit tests are generalized to singly censored data and applied to the problem of testing Weibull (or extreme value) fit. Smooth tests, Pearson-type tests, and the spacings tests proposed by Mann, Schemer, and Fertig (1973) are compared on the basis of local asymptotic relative efficiency with respect to the asymptotic best test against generalized gamma alternatives, The smooth test of order one Is found to be most efficient for the generalized gamma alternatives.     

近代报刊"喉舌论"考辨

在近代报刊发展初期,自由主义是使“喉舌”获得自由的主义,“喉舌论”是使言论自由成为现实的理论。戊戌变法前后,维新变法人士的报刊“喉舌论”,首先是要求封建专制统治者还民众以话语权,给民众以监督官吏、监督政治、监督社会、变法图强的政治权力;其次,他们还十分强调报刊“去塞求通”的“喉舌”功能,这是他们对启蒙民众,宣讲民主、科学的真理,沟通社会上下和国家内外信息以变革社会的话语制权的强调。辛亥革命前后,资产阶级民主革命派的报刊“喉舌论”,则是要求其报刊成为宣传革命思想、推翻帝制统治、建立资产阶级民主共和国的“喉舌”,掌控革命舆论的话语制权。