A general approximation to quantiles

For many continuous distributions, a closed-form expression for their quantiles does not exist. Numerical approximations for their quantiles are developed on a distribution-by-distribution basis. This work develops a general approximation for quantiles using the Taylor expansion. Our method only requires that the distribution has a continuous probability density function and its derivatives can be derived to a certain order (usually 3 or 4). We demonstrate our unified approach by approximating the quantiles of the normal, exponential, and chi-square distributions. The approximation works well for these distributions.     

Spectral Estimation of Covolatility from Noisy Observations Using Local Weights

We propose localized spectral estimators for the quadratic covariation and the spot covolatility of diffusion processes, which are observed discretely with additive observation noise. The appropriate estimation for time‐varying volatilities is based on an asymptotic equivalence of the underlying statistical model to a white‐noise model with correlation and volatility processes being constant over small time intervals. The asymptotic equivalence of the continuous‐time and discrete‐time experiments is proved by a construction with linear interpolation in one direction and local means for the other. The new estimator outperforms earlier non‐parametric methods in the literature for the considered model. We investigate its finite sample size characteristics in simulations and draw a comparison between various proposed methods.     

Sums of powers of binomial coefficients

An asymptotic series for sums of powers of binomial coefficients is derived, the general term being defined and usable with a computer symbolic language. Sums of squares of coefficients in the symmetric case are shown to have a link with classical moment problems, but this property breaks down for cubes and higher powers. Problems of remainders for the asymptotic series are mentioned. Using the reflection formula for I'(.), a continuous form for a binomial function is set up, and this becomes oscillatory outstde the usual range. A new contmued fraction emerges for the logarithm of an adjusted sum of binomial squares. The note is a contribution to the problem of the interpretation of asymptotic series and processes for their convergence acceleration.     

Asymptotic expansions for sequential confidence levels in inverse linear regression

Non-linear renewal theory is used to derive second order asymptotic expansions for the coverage probability of a fixed-width sequential confidence interval for an unknown parameter xin the inverse linear regression model. These expansions are obtained for a two-stage sequential procedure, proposed by Perng and Tong (1974) for the construction of a confidence interval for x.     

The estimation of treatment effect for the censored bivariate data under the univariate censoring

This paper establishes a nonparametric estimator for the treatment effect on censored bivariate data under unvariate censoring. This proposed estimator is based on the one from Lin and Ying(1993)'s nonparametric bivariate survival function estimator, which is itself a generalized version of Park and Park(1995)' quantile estimator. A Bahadur type representation of quantile functions were obtained from the marginal survival distribution estimator of Lin and Ying' model. The asymptotic property of this estimator is shown below and the simulation studies are also given     

Cumulants of random sum distributions

Consider a random variable S being the sum of a number N of independent and identically distributed random variables X_j (j = 1, 2, ...) where the number N is itself a non-negative integer-valued random variable independent of the X_j An explicit expression of the r-th cumulant of S is given in terms of the cumulants of N and X_j, Asymptotic properties of the distribution of S are also discussed.     

A new goodness of fit test for the equality of multinomial cell probabilities versus trend alternatives

In this paper, a new test statistic is presented for testing the null hypothesis of equal multinomial cell probabilities versus various trend alternatives. Exact asymptotic critical values are obtained, The power of the test is compared with several other statistics considered by Choulakian et al (1995), The test is shown to have better power for certain trend alternatives.     

Testing for exponentiality against monotone failure rate average alternatives

We propose a test for exponentiality against the class of non-exponential distributions having monotone failure rate averages. The test statistic, which is a U-statistic and hence asymptotically normally distributed, is much simpler than its competitors yet compares favorably with them in efficiency and power comparisons.     

中国居民代际收入流动性的变化趋势及影响机制研究

基于1989~2015年共计10轮CHNS数据,本文采用代际收入弹性和代际收入秩关联系数双重测度指标对我国居民代际收入流动性进行了测算,发现代际收入流动性在1991~2004年期间基本保持稳定,2004年以后呈现出不断上升的变化趋势。基于收入分组视角的研究发现,各收入组2004年以后代际收入阶层固化程度均有所降低,但高收入组和低收入组的固化程度远高于其他各组,中等收入群体是目前我国保持较高代际收入流动性的主要动力来源。从城乡差异视角看,受大规模农村劳动力向城镇流动的影响,2000年后农村家庭的代际流动性显著提升,且持续高于城市居民的代际流动性。进一步,基于人力资本分析框架对我国代际收入传递机制进行了探究,发现父亲的非教育因素在代际收入传递中起到主导作用。受整体社会制度环境不断改善的积极影响,2004年以后非教育传递机制不断减弱,对代际收入流动性的提升起到较大助推作用;而受高等教育扩张政策的影响,教育因素在2004年左右一定程度上削弱了代际收入流动性。     

A Note on the Large Sample Properties of Estimators Based on Generalized Linear Models for Correlated Pseudo‐observations

Pseudo‐values have proven very useful in censored data analysis in complex settings such as multi‐state models. It was originally suggested by Andersen et al., Biometrika, 90, 2003, 335 who also suggested to estimate standard errors using classical generalized estimating equation results. These results were studied more formally in Graw et al., Lifetime Data Anal., 15, 2009, 241 that derived some key results based on a second‐order von Mises expansion. However, results concerning large sample properties of estimates based on regression models for pseudo‐values still seem unclear. In this paper, we study these large sample properties in the simple setting of survival probabilities and show that the estimating function can be written as a U‐statistic of second order giving rise to an additional term that does not vanish asymptotically. We further show that previously advocated standard error estimates will typically be too large, although in many practical applications the difference will be of minor importance. We show how to estimate correctly the variability of the estimator. This is further studied in some simulation studies.