Estimation du comportement asymptotique des autocovariances et autocorrelations empiriques de processus multivariéeas

Statistics based on the sample autocovariances are widely used in time-series analysis. Estimators of the asymptotic covariance between the sample autocovariances are commonly derived from the so-called Bartlett's formula. However, this formula essentially holds for linear processes. This entails that for a wide range of nonlinear time series the above-mentioned estimators are not suitable. In this paper the behaviour of an alternative estimator is studied within the framework of centered or uncentered multivariate strongly mixing processes. Applications to differential functions of sample autocovariances, such as the sample autocorrelations, are considered.     

The Comparative Statics of Constrained Optimization Problems

This paper develops and applies some new results in the theory of monotone comparative statics. Let f be a real‐valued function defined on R^l and consider the problem of maximizing f(x) when x is constrained to lie in some subset C of R^l. We develop a natural way to order the constraint sets C and find the corresponding restrictions on the objective function f that guarantee that optimal solutions increase with the constraint set. We apply our techniques to problems in consumer, producer, and portfolio theory. We also use them to generalize Rybcsynski's theorem and the LeChatelier principle.     

Analyzing partially paired data: when can the unpaired portion(s) be safely ignored?

Partially paired data, either with incompleteness in one or both arms, are common in practice. For testing equality of means of two arms, practitioners often use only the portion of data with complete pairs and perform paired tests. Although such tests (referred as ‘naive paired tests’) are legitimate, their powers might be low as only partial data are utilized. The recently proposed ‘P-value pooling methods’, based on combining P-values from two tests, use all data, have reasonable type-I error control and good power property. While it is generally believed that ‘P-value pooling methods’ are superior to ‘naive paired tests’ in terms of power as the former use more data than the latter, no detailed power comparison has been done. This paper aims to compare powers of ‘naive paired tests’ and ‘P-value pooling methods’ analytically and our findings are counterintuitive, i.e. the ‘P-value pooling methods’ do not always outperform the naive paired tests in terms of power. Based on these results, we present guidance on how to select the best test for testing equality of means with partially paired data.     

Goodness-of-fit testing of a weak memoryless property of life distributions

A life distribution is said to have a weak memoryless property if its conditional probability of survival beyond a fixed time point is equal to its (unconditional) survival probability at that point. Goodness‐of‐fit testing of this notion is proposed in the current investigation, both when the fixed time point is known and when it is unknown but estimable from the data. The limiting behaviour of the proposed test statistic is obtained and the null variance is explicitly given. The empirical power of the test is evaluated for a commonly known alternative using Monte Carlo methods, showing that the test performs well. The case when the fixed time point t₀ equals a quantile of the distribution F gives a distribution‐free test procedure. The procedure works even if t₀ is unknown but is estimable.     

Some nonparametric methods for changepoint problems

A general model for changepoint problems is discussed from a nonparametric viewpoint. The test statistics introduced are based on Cramér-von Mises functionals of certain processes and are shown to converge in distribution to corresponding Gaussian functionals (under the assumption of no change in distribution, H₀). We also demonstrate how the distribution of the limiting Gaussian functionals may be tabulated. Finally, properties of the tests under the alternative hypothesis of exactly one changepoint occurring are studied, and some examples are given.     

Contributions to-asymptotic theory in regression models with linear covariance structure 1

Asymptotic results are .presented- for estimating the parameters in variance-components models both with linear and with nonlinear regression functions.     

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.     

SELECTION PROCEDURES FOR SCALE PARAMETERS USING TWO-SAMPLE U-STATISTICS

Let be k independent populations having the same known quantile of order p (0 p 1) and let F(x)=F(x/_i) be the absolutely continuous cumulative distribution function of the ith population indexed by the scale parameter ₁, i = 1,…, k. We propose subset selection procedures based on two-sample U-statistics for selecting a subset of k populations containing the one associated with the smallest scale parameter. These procedures are compared with the subset selection procedures based on two-sample linear rank statistics given by Gill & Mehta (1989) in the sense of Pitman asymptotic relative efficiency, with interesting results.     

A NOTE ON ASYMPTOTIC POSTERIOR NORMALITY FOR STOCHASTIC PROCESSES

In a recent paper, Sweeting & Adekola (1987) presented a fairly general set of conditions for asymptotic posterior normality which covers a wide class of problems. In this paper we present an example of an explosive autoregressive model where our condition A4 does not hold.