多项式的一种无重因式的分解方法

本文利用多项或重因式的判定法，论证一种更接近ｆ（ｘ）典型分解式的一种既无相同重数，又无重因式的分解方法。     

A note on general quadratic forms of nonstationary stochastic processes

In this paper, general quadratic forms of nonstationary, α-mixing time series are considered. Under mixing and moment assumptions, asymptotically normality of these forms are derived. These results do not assume that the variance of the generalized quadratic form has a limit, thus allowing for general types of nonstationarity. However, without well-defined limits, it is not possible to understand the differences in sampling properties of quadratic forms of nonstationary and stationary processes. To understand these differences, the nonstationary process is placed within the locally stationary framework. Under the assumption that the nonstationary process is locally stationary the asymptotic expectation and variance of the weighted sample covariance of the discrete Fourier transforms (an important class of quadratic forms) is derived and shown to be very different to its stationary counterpart.     

Fractional Age Assumption Based on Cubic Polynomial Interpolation

This article proposes a new fractional age assumption (FAA) based on the cubic polynomial interpolation (CPI) and applies it to estimate the mortality rate and related actuarial quantities. The validity of the method under CPI is proved theoretically and the valuable advantages of CPI assumption are discussed based on three different perspectives—utilized death information, property of mortality force, and optimality criterion. The results show that CPI assumption has distinct valuable superiority compared with other FAAs in references. Finally under CPI assumption we study the calculations of some important actuarial quantities in life contingencies.     

A variant of K nearest neighbor quantile regression

Compared with local polynomial quantile regression, K nearest neighbor quantile regression (KNNQR) has many advantages, such as not assuming smoothness of functions. The paper summarizes the research of KNNQR and has carried out further research on the selection of k, algorithm and Monte Carlo simulations. Additionally, simulated functions are Blocks, Bumps, HeaviSine and Doppler, which stand for jumping, volatility, mutagenicity slope and high frequency function. When function to be estimated has some jump points or catastrophe points, KNNQR is superior to local linear quantile regression in the sense of the mean squared error and mean absolute error criteria. To be mentioned, even high frequency, the superiority of KNNQR could be observed. A real data is analyzed as an illustration.     

Variable selection for semiparametric errors-in-variables regression model with longitudinal data

In this paper, we focus on the variable selection for the semiparametric regression model with longitudinal data when some covariates are measured with errors. A new bias-corrected variable selection procedure is proposed based on the combination of the quadratic inference functions and shrinkage estimations. With appropriate selection of the tuning parameters, we establish the consistency and asymptotic normality of the resulting estimators. Extensive Monte Carlo simulation studies are conducted to examine the finite sample performance of the proposed variable selection procedure. We further illustrate the proposed procedure with an application.     

A Scale-space Approach for Detecting Non-stationarities in Time Series

Abstract.  The presented method called Significant Non-stationarities, represents an exploratory tool for identifying significant changes in the mean, the variance, and the first-lag autocorrelation coefficient of a time series. The changes are detected on different time scales. The statistical inference for each scale is based on accurate approximation of the probability distribution, using test statistics being ratios of quadratic forms. No assumptions concerning the autocovariance function of the time series are made as the dependence structure is estimated non-parametrically. The results of the analyses are summarized in significance maps showing at which time points and on which time scales significant changes in the parameters occur. The performance of the given method is thoroughly studied by simulations in terms of observed significance level and power. Several examples, including a real temperature data set, are studied. The examples illustrate that it is important to carry out the analysis on several time horizons.     

The three-parameter two-piece normal family of distributions and its fitting

This note introduces a family of skew and symmetric distributions containing the normal family and indexed by three parameters with clear meanings. Another respect in which this family compares favourably with families like the Pearson family, the Bessel-Gram-Charlier family and the Johnson family is ease of maximum likelihood fitting. Fitting by the method of moments is also considered. Asymptotic distributions of maximum likelihood and moment estimators are worked out. A test of symmetry and normality is suggested.     

On matric variate-T distribution

In this paper matric variate-t distribution has been studied. A factorization of the density is obtained in terms of the product of independent multivariate t- and F-densities. Further, the distributions of TAT1 and ATB, for given non-singular matrices A and B, are derived.     

Comparison of some common ratio estimators using pitman measure of nearness

In this article we compare some common ratio estimators for estimating the population total of a given characteristic. The sampling schemes considered are simple random sampling (S.R.S.) and S.R.S.under stratification. The comparisons are made using the Pitman Nearness criterion under the model-based approach. The error term is assumed normal with mean zero and variance σg(x). The function g(x) is a known function of the auxiliary variable x. Special interest is on the cases of g(x) =l and x. The result is found the same as that using MSE criterion, although the PN is very different from the MSE intrinsically.     

Independence distribution preserving joint covariance structures for the multivariate two-group case

We characterize the general nonnegative-definite and positive-definite joint observation covariance structures for the two-group case such that the two sample mean vectors are independent of the two corresponding sample covariance matrices. Also, the sample covariance matrices are distributed as independent noncentral or central Wishart random matrices. We derive and utilize a representation of the general common non-negative-definite solution to a particular system of matrix equations with idempotent coefficient matrices.