Retrospective change detection in categorical time series

The aim of this paper is to propose methods of detecting change in the coefficients of a multinomial logistic regression model for categorical time series offline. The alternatives to the null hypothesis of stationarity can be either the hypothesis that it is not true, or that there is a temporary change in the sequence. We use the efficient score vector of the partial likelihood function. This has several advantages. First, the alternative value of the parameter does not have to be estimated; hence, we have a procedure that has a simple structure with only one parameter estimation using all available observations. This is in contrast with the generalized likelihood ratio-based change point tests. The efficient score vector is used in various ways. As a vector, its components correspond to the different components of the multinomial logistic regression model’s parameter vector. Using its quadratic form a test can be defined, where the presence of a change in any or all parameters is tested for. If there are too many parameters one can test for any subset while treating the rest as nuisance parameters. Our motivating example is a DNA sequence of four categories, and our test result shows that in the published data the distribution of the four categories is not stationary.     

Palm Distributions for Log Gaussian Cox Processes

This paper establishes a remarkable result regarding Palm distributions for a log Gaussian Cox process: the reduced Palm distribution for a log Gaussian Cox process is itself a log Gaussian Cox process that only differs from the original log Gaussian Cox process in the intensity function. This new result is used to study functional summaries for log Gaussian Cox processes.     

Estimation of P{X < Y} for geometric—exponential model based on complete and censored samples

This article deals with the estimation of R = P{X < Y}, where X and Y are independent random variables from geometric and exponential distribution, respectively. For complete samples, the MLE of R, its asymptotic distribution, and confidence interval based on it are obtained. The procedure for deriving bootstrap-p confidence interval is presented. The UMVUE of R and UMVUE of its variance are derived. The Bayes estimator of R is investigated and its Lindley's approximation is obtained. A simulation study is performed in order to compare these estimators. Finally, all point estimators for right censored sample from the exponential distribution, are obtained.     

Saddlepoint p-values for group of linear rank tests

Many nonparametric tests in one sample problem, matched pairs, and competingrisks under censoring have the same underlying permutation distribution. This article proposes a saddlepoint approximation to the exact p-values of these tests instead of the asymptotic approximations. The performance of the saddlepoint approximation is assessed by using simulation studies that show the superiority of the saddlepoint methods over the asymptotic approximations in several settings. The use of the saddlepoint to approximate the p-values of class of two sample tests under complete randomized design is also discussed.     

Recovery of functions from transformed moments: A unified approach

Two approximations recovering the functions from their transformed moments are proposed. The upper bounds for the uniform rate of convergence are derived. In addition, the comparisons of the estimates of the cumulative distribution function and its density function with the empirical distribution and the kernel density estimates are conducted via a simulation study. The plots of recovered functions are presented for several examples as well.     

非线性回归分析的一种有理逼近

利用有理插值逼近回归函数,把最小二乘法和插值技术结合起来,充分利用已知信息,达到最佳逼近,通过实例,获得了很好的效果。     

Confidence intervals for extreme Pareto-type quantiles

In this paper, we revisit the construction of confidence intervals for extreme quantiles of Pareto-type distributions. A novel asymptotic pivotal quantity is proposed for these quantile estimators, which leads to new asymptotic confidence intervals that exhibit more accurate coverage probability. This pivotal quantity also allows for the construction of a saddle-point approximation, from which a second set of new confidence intervals follows. The small-sample properties and utility of these confidence intervals are studied using simulations and a case study from insurance.     

三向剖分域上的二元二次样条插值与逼近

本文主要用B－网方法研究了平行六边形区域在三向剖分△_6~3下的二元二次样条插值的存在性、唯一性及逼近度问题。在本文末尾我们举例说明本方法是可行的。     

On Approximability of Boolean Formula Minimization

For a Boolean function given by a Boolean formula (or a binary circuit) S we discuss the problem of building a Boolean formula (binary circuit) of minimal size, which computes the function g equivalent to , or -equivalent to , i.e., . In this paper we prove that if P NP then this problem can not be approximated with a good approximation ratio by a polynomial time algorithm.     

On Combinatorial Approximation of Covering 0-1 Integer Programs and Partial Set Cover

The problems dealt with in this paper are generalizations of the set cover problem, min{cx | Ax b, x {0,1}ⁿ}, where c Q₊ⁿ, A {0,1}^{m × n}, b 1. The covering 0-1 integer program is the one, in this formulation, with arbitrary nonnegative entries of A and b, while the partial set cover problem requires only m–K constrains (or more) in Ax b to be satisfied when integer K is additionall specified. While many approximation algorithms have been recently developed for these problems and their special cases, using computationally rather expensive (albeit polynomial) LP-rounding (or SDP-rounding), we present a more efficient purely combinatorial algorithm and investigate its approximation capability for them. It will be shown that, when compared with the best performance known today and obtained by rounding methods, although its performance comes short in some special cases, it is at least equally good in general, extends for partial vertex cover, and improves for weighted multicover, partial set cover, and further generalizations.