CAPM with fuzzy returns and hypothesis testing

Over the last four decades, several estimation issues of the beta have been discussed extensively in many articles. An emerging consensus is that the betas are time-dependent and their estimates are impacted by the return interval and the length of the estimation period. These findings lead to the prominence of the practical implementation of the Capital Asset Pricing Model. Our goal in this paper is two-fold. After studying the impact of the return interval on the beta estimates, we analyze the sample size effects on the preceding estimation. Working in the framework of fuzzy set theory, we first associate the returns based on closing prices with the intraperiod volatility for the representation by the means of a fuzzy random variable in order to incorporate the effect of the interval period over which the returns are measured in the analysis. Next, we use these fuzzy returns to estimate the beta via fuzzy least square method in order to deal efficiently with outliers in returns, often caused by structural breaks and regime switches in the asset prices. A bootstrap test is carried out to investigate whether there is a linear relationship between the market portfolio fuzzy return and the given asset fuzzy return. Finally, the empirical results on French stocks suggest that our beta estimates seem to be more stable than the ordinary least square (OLS) estimates when the return intervals and the sample size change.     

A Bootstrap Approach to Nonparametric Regression for Right Censored Data

In this paper a two-stage bootstrap method is proposed for nonparametric regression with right censored data. The method is applied to construct confidence intervals and bands for a conditional survival function. Its asymptotic validity is established using counting process techniques and martingale central limit theory. The performance of the bootstrap method is investigated in a Monte Carlo study. An illustration is given using a real data.     

条件t-分位数核估计的逼近速度

该文研究了条件狋 分位数核估计的逼近速度问题．在适当的条件下,给出了核估计的强收敛速度、正态逼近速度和Ｂｏｏｔｓｔｒａｐ逼近速度．     

非参数回归函数的kn近邻估计的渐近性质及其Bootstrap逼近

本文研究回归函数的kn-近邻估计的渐近性质,得到了回归函数的kn－近邻估计的渐近正态性和它的Bootstrap统计量的相合性,在高阶矩存在的条件下,我们证明了回归函数的kn-近邻估计的Bootstrap逼近比正态逼近更精确。     

Data-driven local bandwidth selection for additive models with missing data

This paper deals in the nonparametric estimation of additive models in the presence of missing data in the response variable. Specifically in the case of additive models estimated by the Backfitting algorithm with local polynomial smoothers [1]. Three estimators are presented, one based on the available data and two based on a complete sample from imputation techniques. We also develop a data-driven local bandwidth selector based on a Wild Bootstrap approximation of the mean squared error of the estimators. The performance of the estimators and the local bootstrap bandwidth selection method are explored through simulation experiments.     

Assessing the Effect of Individual Data Points on Inference From Empirical Likelihood

An oft-cited advantage of empirical likelihood is that the confidence intervals that are produced by this nonparametric technique are not necessarily symmetric. Rather, they reflect the nature of the underlying data and hence give a more representative way of reaching inferences about the functional of interest. However, this advantage can easily become a disadvantage if the resultant intervals are unduly influenced by one of the data points. This article proposes simple methods for evaluating the effect of single points on empirical likelihood confidence intervals. In addition to suggesting diagnostics for detecting important observations, we examine the use of bootstrap and of jackknife influence functions to assess the extremity of suspect points.     

Bootstrap and empirical likelihood methods in extremes

One of the major interests in extreme-value statistics is to infer the tail properties of the distribution functions in the domain of attraction of an extreme-value distribution and to predict rare events. In recent years, much effort in developing new methodologies has been made by many researchers in this area so as to diminish the impact of the bias in the estimation and achieve some asymptotic optimality in inference problems such as estimating the optimal sample fractions and constructing confidence intervals of various quantities. In particular, bootstrap and empirical likelihood methods, which have been widely used in many areas of statistics, have drawn attention. This paper reviews some novel applications of the bootstrap and the empirical likelihood techniques in extreme-value statistics. Dedicated to Professor Laurens de Haan on the occasion of his 70th birthday.     

Theoretical and empirical estimates of mean–variance portfolio sensitivity

This paper studies properties of an estimator of mean–variance portfolio weights in a market model with multiple risky assets and a riskless asset. Theoretical formulas for the mean square error are derived in the case when asset excess returns are multivariate normally distributed and serially independent. The sensitivity of the portfolio estimator to errors arising from the estimation of the covariance matrix and the mean vector is quantified. It turns out that the relative contribution of the covariance matrix error depends mainly on the Sharpe ratio of the market portfolio and the sampling frequency of historical data. Theoretical studies are complemented by an investigation of the distribution of portfolio estimator for empirical datasets. An appropriately crafted bootstrapping method is employed to compute the empirical mean square error. Empirical and theoretical estimates are in good agreement, with the empirical values being, in general, higher.     

On the Cost of Data Analysis

Abstract

A regression analysis usually consists of several stages, such as variable selection, transformation and residual diagnosis. Inference is often made from the selected model without regard to the model selection methods that preceeded it. This can result in overoptimistic and biased inferences. We first characterize data-analytic actions as functions acting on regression models. We investigate the extent of the problem and test bootstrap, jackknife, and sample-splitting methods for ameliorating it. We also demonstrate an interactive LISP-STAT system for assessing the cost of the data analysis while it is taking place.     

应用积分经验过程检验多元分布函数的相等性

本文引进投影积分经验过程用于检验两个或K个多元分布函数的相等性，自助法用于确定临界值的逼近，数论方法有效地计算自动法确定的临界值，且进行了一些模拟试验．