Interval estimation in discriminant analysis for large dimension

This paper is concerned with the interval estimation for the log odds of the posterior probability that the observation vector belongs to one of two homoscedastic multivariate normal distributions (Π₁ and Π₂). We give the limiting distribution of the unbiased estimator for the log odds as the sample sizes and the dimension jointly tend to infinity, and approximate the confidence interval based on the asymptotic distribution. Small-scale simulations are performed to check the precision of the approximation.     

Improved deviance goodness of fit statistics for a gamma regression model

A gamma regression model with an exponential link function for the means Is considered. Moment properties of the deviance statistics based on maximum likelihood and weighted least squares fits are used to define modified deviance statistics which provide alternative global goodness of fit tests. The null distribution properties of the deviances and modified deviances are compared with those of the approximating chi-square distribution and It is shown that the use of the modified deviances gives much better control over the significance levels of the tests.     

Using simulation methods for bayesian econometric models: inference,development and communication: some comments

We extend the average derivatives estimator to the case of functionally dependent regressors. We show that the proposed estimator is consistent and has a limiting normal distribution. A consistent covariance matrix estimator for the proposed estimator is provided.     

Modified minimax estimation of regression coefficients

Working with the linear regression model (1.1) and having the extraneous information (1.2) about regression coefficients the problem exists how to build estimators (1.3) with the risk (1.4) which enable to utilize the known information in order to reduce their risk as compared with the risk (1.6) of the LSE (1.5). Solution of this problem is known for the positive definite matrix T, namely in form for estimators (1.8) and (1.10).First, it is shown that the proposed estimators (2.6),(2.9) and (2.16) based on psedoinversions of the matrix L represent the solution of the problem of the positive semidefinite matrix T=L'L.Further, the problem of interpretability of estimators in the sense of the inequality (3.1) exists; it is shown that all mentioned estimators are at least partially interpretable in the sense of requirements (3.2) or (3.10).     

On square ordinal contingency tables: a comparison of social class and income mobility for the same individuals

Summary.  Square contingency tables with matching ordinal rows and columns arise in particular as empirical transition matrices and the paper considers these in the context of social class and income mobility tables. Such tables relate the socio-economic position of parents to the socio-economic position of their child in adulthood. The level of association between parental and child socio-economic position is taken as a measure of mobility. Several approaches to analysis are described and illustrated by UK data in which interest focuses on comparisons of social class and income mobility tables that are derived from the same individuals. Account is taken of the use of the same individuals in the two tables. Additionally comparisons over time are considered.     

Optimum chemical balance weighing designs for estimating the total weight

This deals with chemical balance weighing designs which attain a lower bound for the variance of the estimated total weight, The results extend those of Chacko Dey (1978).     

A generalized scheffé method of multiple comparisons

Standard resulrs on the extrema of quotients of quadratic forms are extended to the non-negative definite case. The maximum and the set over which it is achieved are characterized explicitly both in terms of generalized inverse matrices and generalized eigenvalues. These results become the basis of Scheffe type multiple comparisons in the usual way. To demonstrate their application to statistics with singular covariance matrices, the method is detailed for Mantel-Haenszel, Breslow, and Cox statistics. An example is presented illustrating a situation where the proposed Scheffe type comparisons may be better than the pairwise method.     

A Framework for Time Varying Parameter Regression Modeling

A framework for time varying parameter regression models is developed and employed in modeling and forecasting price expectations, using the Livingston data. Alternative model formulations, which include various choices for both the stochastic processes generating the varying parameters and the sets of explanatory variables, are examined and compared by using this framework. These models, some of which have appeared elsewhere and some of which are new, are estimated and used to assess the expectations formation process.     

Statistical properties of detrended fluctuation analysis

The main goal of this work is to consider the detrended fluctuation analysis (DFA), proposed by Peng et al. [Mosaic organization of DNA nucleotides, Phys. Rev. E. 49(5) (1994), 1685–1689]. This is a well-known method for analysing the long-range dependence in non-stationary time series. Here we describe the DFA method and we prove its consistency and its exact distribution, based on the usual i.i.d. assumption, as an estimator for the fractional parameter d. In the literature it is well established that the nucleotide sequences present long-range dependence property. In this work, we analyse the long dependence property in view of the autoregressive moving average fractionally integrated ARFIMA(p, d, q) processes through the analysis of four nucleotide sequences. For estimating the fractional parameter d we consider the semiparametric regression method based on the periodogram function, in both classical and robust versions; the semiparametric R/S(n) method, proposed by Hurst [Long term storage in reservoirs, Trans. Am. Soc. Civil Eng. 116 (1986), 770–779] and the maximum likelihood method (see [R. Fox and M.S. Taqqu, Large-sample properties of parameter estimates for strongly dependent stationary Gaussian time series, Ann. Statist. 14 (1986), 517–532]), by considering the approximation suggested by Whittle [Hypothesis Testing in Time Series Analysis (1953), Hafner, New York].     

Multiple Time Series Modeling and Extended Sample Cross-Correlations

This article provides an expository account of the multivariate autoregressive moving average models and proposes an extended sample cross-correlation approach for practical model identification. An iterative model building procedure for applying these models to real data is discussed and demonstrated by analyzing the 5-series U.S. Hog Data.