Alwell J. Oyet

A note on the properties of some time varying bilinear models

In this note, a sufficient condition is given for the existence and uniqueness of a stable causal solution for bilinear time series with time-varying coefficients; also some conditions for invertibility and the optimal prediction procedure are given. The notions of controllability, observability and minimality are discussed.

Estimation of Some Bilinear Time Series Models with Time Varying Coefficients

Abstract We discuss the problem of estimating the coefficients of the time-varying bilinear model where (ξ t ) t∈ℤ is an independent white noise process, with zero mean and variance and a t (a), b t (b) are the coefficients of the model. The consistency and asymptotic normality of the least squares estimates are established. Applications to seasonal and conditionally heteroscedastic bilinear models are considered.

Testing variances in wavelet regression models

In this paper we develop an asymptotically locally optimal partial score test for testing the suitability of a homoscedastic wavelet model against a general heteroscedastic wavelet model. As the construction of the partial score test requires a consistent estimate for the nuisance parameter, namely the constant variance estimate under the null hypothesis, we conduct a comprehensive investigation in order to choose its best possible estimate among some competitors. The size and power performances of the partial score test are reported for testing for heteroscedasticity in a time series of finite length.

On exact minimax wavelet designs obtained by simulated annealing

We construct minimax robust designs for estimating wavelet regression models. Such models arise from approximating an unknown nonparametric response by a wavelet expansion. The designs are robust against errors in such an approximation, and against heteroscedasticity. We aim for exact, rather than approximate, designs; this is facilitated by our use of simulated annealing. The relative simplicity of annealing allows for a much more complete treatment of some hitherto intractable problems initially addressed in Oyet and Wiens (J. Nonparametric Stat. 12 (2000) 837). Thus, we are able to exhibit integer-valued designs for estimating higher order wavelet approximations of nonparametric curves. The exact designs constructed for multiwavelet approximations of various orders are found to be symmetric and periodic, as anticipated in Oyet and Wiens (J. Nonparametric Stat. 12 (2000) 837). We also construct integer-valued designs based on the Daubechies wavelet system with a wavelet number of 5.

Minimax A‐ and D‐optimal integer‐valued wavelet designs for estimation

The author discusses integer-valued designs for wavelet estimation of nonparametric response curves in the possible presence of heteroscedastic noise using a modified wavelet version of the Gasser- Muller kernel estimator or weighted least squares estimation. The designs are constructed using a minimax treatment and the simulated annealing algorithm. The author presents designs for three case studies in ex- periments for investigating Gompertzs theory on mortality rates, nitrite utilization in bush beans and the impact of crash helmets in motorcycle accidents.

ON WAVELET METHODS FOR TESTING EQUALITY OF MEAN RESPONSE CURVES

In this article, we exploit the adaptive properties of wavelets to develop some procedures for testing the equality of nonlinear and nonparametric mean response curves which are assumed by an experimenter to be the underlying functions generating several groups of data with possibly hetereoscedastic errors. The essential feature of the techniques is the transformation of the problem from the domain of the input variable to the wavelet domain through an orthogonal discrete wavelet transformation or a multiresolution expansion. We shall see that this greatly simplifies the testing problem into either a wavelet thresholding problem or a linear wavelet regression problem. The size and power performances of the tests are reported and compared to some existing methods. The tests are also applied to data on dose response curves for vascular relaxation in the absence or presence of a nitric oxide inhibitor.

Maximum studentized score tests for the detection of outliers in time series regression models

Efficient score tests exist among others, for testing the presence of additive and/or innovative outliers that are the result of the shifted mean of the error process under the regression model. A sample influence function of autocorrelation-based diagnostic technique also exists for the detection of outliers that are the result of the shifted autocorrelations. The later diagnostic technique is however not useful if the outlying observation does not affect the autocorrelation structure but is generated due to an inflation in the variance of the error process under the regression model. In this paper, we develop a unified maximum studentized type test which is applicable for testing the additive and innovative outliers as well as variance shifted outliers that may or may not affect the autocorrelation structure of the outlier free time series observations. Since the computation of the p-values for the maximum studentized type test is not easy in general, we propose a Satterthwaite type approximation based on suitable doubly non-central F-distributions for finding such p-values [F.E. Satterthwaite, An approximate distribution of estimates of variance components, Biometrics 2 (1946), pp. 110–114]. The approximations are evaluated through a simulation study, for example, for the detection of additive and innovative outliers as well as variance shifted outliers that do not affect the autocorrelation structure of the outlier free time series observations. Some simulation results on model misspecification effects on outlier detection are also provided.

Score Test for Homogeneity of Variances in Longitudinal Time Series Via Wavelets

We discuss the problem of testing for homogeneity of variances in a nonstationary longitudinal time series. The nonstationarity is assumed to arise from the dependence of the mean function on time and possibly nonconstancy in variance. We develop a partial score statistic for testing for equality of variances between the series in the longitudinal setup. We study the effect of using both the discrete wavelet transformation (DWT) approach and wavelet regression based on multiresolution analysis in estimating the time dependent mean function on the size and power of the test. We found that the DWT estimate is not consistent. Thus, the score test based on this approach fails in controlling the size of the test, whereas the score test based on the wavelet regression estimate performs well in controlling the size of the test. The power of the test is, however, not affected by the estimation method.

Wavelet designs for estimating nonparametric curves with heteroscedastic error

In this paper, we discuss the problem of constructing designs in order to maximize the accuracy of nonparametric curve estimation in the possible presence of heteroscedastic errors. Our approach is to exploit the flexibility of wavelet approximations to approximate the unknown response curve by its wavelet expansion thereby eliminating the mathematical difficulty associated with the unknown structure. It is expected that only finitely many parameters in the resulting wavelet response can be estimated by weighted least squares. The bias arising from this, compounds the natural variation of the estimates. Robust minimax designs and weights are then constructed to minimize mean-squared-error-based loss functions of the estimates. We find the periodic and symmetric properties of the Euclidean norm of the multiwavelet system useful in eliminating some of the mathematical difficulties involved. These properties lead us to restrict the search for robust minimax designs to a specific class of symmetric designs. We also construct minimum variance unbiased designs and weights which minimize the loss functions subject to a side condition of unbiasedness. We discuss an example from the nonparametric literature.

Association between early history of asthma and COPD diagnosis in later life: a systematic review and meta-analysis

Background Whereas most studies have reported prior history/diagnosis of asthma as an independent risk factor for chronic obstructive pulmonary disease (COPD) development in later life, no systematic review and meta-analysis has been conducted to synthesize these observational studies. The aim of this review is to investigate associations between prior history of asthma and later development of COPD. Methods We conducted a comprehensive search in PubMed, CINAHL and EMBASE for studies related to prior history of asthma and COPD diagnosis. Articles were screened for relevance by two independent reviewers. Methodological quality was independently assessed and data extracted for qualitative and quantitative review. We explored heterogeneity and performed a publication bias check. Results From the 1260 articles retrieved, 9 were included in the qualitative review and 7 in the meta-analysis. History of asthma was associated with developing COPD in later life (Inverse Variance Random-effects model, odds ratio: 7.87, 95% confidence interval: 5.40-11.45, p < 0.00001). Conclusions Studies with high methodological quality provided sufficient evidence to suggest that individuals with previous history of asthma have an increasing likelihood of developing COPD in later life.