Nonparametric multistep-ahead prediction in time series analysis

Summary.  We consider the problem of multistep-ahead prediction in time series analysis by using nonparametric smoothing techniques. Forecasting is always one of the main objectives in time series analysis. Research has shown that non-linear time series models have certain advantages in multistep-ahead forecasting. Traditionally, nonparametric k -step-ahead least squares prediction for non-linear autoregressive AR( d ) models is done by estimating E ( X _{t + k}  | X _t , …,  X _{t − d +1}) via nonparametric smoothing of X _{t + k} on ( X _t , …,  X _{t − d +1}) directly. We propose a multistage nonparametric predictor. We show that the new predictor has smaller asymptotic mean-squared error than the direct smoother, though the convergence rate is the same. Hence, the predictor proposed is more efficient. Some simulation results, advice for practical bandwidth selection and a real data example are provided.     

球面径向基函数插值逼近的误差估计

研究了球面上由不同光滑度的核所生成且嵌套的两个再生核Hilbert空间之间的插值逼近问题．证明了一个空间的函数可用光滑性更好的子空间中的函数进行插值逼近，并给出了插值误差的上界估计．     

中国食用粮食消费总量的时序预测

粮食消费预测是安排粮食生产、调整粮食种植结构、制定粮食安全和农业可持续发展战略的重要理论依据。利用粮食消费量与时间之间的相关关系 ,采用SPSS程序包进行筛选 ,建立我国食用粮食消费总量的时序预测模型。研究结果表明 ,所建立的三个时序预测模型的拟合度等统计指标高度显著 ,运用所建模型对所获资料进行的内推预测比较准确 ,但外推预测结果因影响因素多 ,其准确性有待时间和实际的检验     

Estimating class-specific parametric models using finite mixtures: an application to a hedonic model of wine prices

Hedonic price models are commonly used in the study of markets for various goods, most notably those for wine, art, and jewelry. These models were developed to estimate implicit prices of product attributes within a given product class, where in the case of some goods, such as wine, substantial product differentiation exists. To address this issue, recent research on wine prices employs local polynomial regression clustering (LPRC) for estimating regression models under class uncertainty. This study demonstrates that a superior empirical approach – estimation of a mixture model – is applicable to a hedonic model of wine prices, provided only that the dependent variable in the model is rescaled. The present study also catalogues several of the advantages over LPRC modeling of estimating mixture models.     

New Developments in Statistical Computing

In 1885, Sir Francis Galton first defined the term “regression” and completed the theory of bivariate correlation. A decade later, Karl Pearson developed the index that we still use to measure correlation, Pearson's r. Our article is written in recognition of the 100th anniversary of Galton's first discussion of regression and correlation. We begin with a brief history. Then we present 13 different formulas, each of which represents a different computational and conceptual definition of r. Each formula suggests a different way of thinking about this index, from algebraic, geometric, and trigonometric settings. We show that Pearson's r (or simple functions of r) may variously be thought of as a special type of mean, a special type of variance, the ratio of two means, the ratio of two variances, the slope of a line, the cosine of an angle, and the tangent to an ellipse, and may be looked at from several other interesting perspectives.     

On the Properties of the SAVE Directions

In quadratic discriminant analysis, the use of SAVE (Cook and Weisberg, 1991 Cook, R.D., Weisberg, S. (1991). Discussion of Li (1991). J. Amer. Statist. Assoc. 86:328–32.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]; Pardoe et al., 2007 Pardoe, I., Yin, X., Cook, R. (2007). Graphical tools for quadratic discriminant analysis. Technometrics 49:172–183.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) is often recommended for dimension-reduction purposes. However, the associated directions tend to over-emphasize the differences of the groups in dispersion, ignoring at the same time those in location. This behavior makes often the plots of the corresponding canonical coordinates difficult to interpret. In this article, the properties of SAVE are investigated and related to those of the SIR and SIRII components. Applications with real data are presented. Comparisons with previous work in this area are also discussed.     

The bandpass problem: combinatorial optimization and library of problems

A combinatorial optimization problem, called the Bandpass Problem, is introduced. Given a rectangular matrix A of binary elements {0,1} and a positive integer B called the Bandpass Number, a set of B consecutive non-zero elements in any column is called a Bandpass. No two bandpasses in the same column can have common rows. The Bandpass problem consists of finding an optimal permutation of rows of the matrix, which produces the maximum total number of bandpasses having the same given bandpass number in all columns. This combinatorial problem arises in considering the optimal packing of information flows on different wavelengths into groups to obtain the highest available cost reduction in design and operating the optical communication networks using wavelength division multiplexing technology. Integer programming models of two versions of the bandpass problems are developed. For a matrix A with three or more columns the Bandpass problem is proved to be NP-hard. For matrices with two or one column a polynomial algorithm solving the problem to optimality is presented. For the general case fast performing heuristic polynomial algorithms are presented, which provide near optimal solutions, acceptable for applications. High quality of the generated heuristic solutions has been confirmed in the extensive computational experiments. As an NP-hard combinatorial optimization problem with important applications the Bandpass problem offers a challenge for researchers to develop efficient computational solution methods. To encourage the further research a Library of Bandpass Problems has been developed. The Library is open to public and consists of 90 problems of different sizes (numbers of rows, columns and density of non-zero elements of matrix A and bandpass number B), half of them with known optimal solutions and the second half, without.     

Weighted nonparametric regression

In the fixed design regression model, additional weights are considered for the Nad a ray a-Watson and Gasser-Miiller kernel estimators. We study their asymptotic behavior and the relationships between new and classical estimators. For a simple family of weights, and considering the AIMSEAS global loss criterion, we show some possible theoretical advantages. An empirical study illustrates the performance of the weighted kernel estimators in theoretical ideal situations and in simulated data sets. Also some results concerning the use of weights for local polynomial estimators are given.     

On kernel density derivative estimation

Estimators of derivatives of a density function based on polynomial multiples of kernels are compared with those based on differentiated kernels.