THE BEHAVIOR OF HEGY TESTS FOR QUARTERLY TIME SERIES WITH SEASONAL MEAN SHIFTS

ABSTRACT

This paper studies the behavior of the HEGY statistics for quarterly data, for seasonal autoregressive unit roots, when the analyzed time series is deterministic seasonal stationary but exhibits a change in the seasonal pattern. We analyze also the HEGY test for the nonseasonal unit root. the data generation process being trend stationary too. Our results show that when the break magnitudes are finite, the HEGY test statistics are not asymptotically biased toward the nonrejection of the seasonal and nonseasonal unit root hypotheses. However, the finite sample power properties may be substantially affected, the behavior of the tests depending on the type of the break.     

INFERENCE ABOUT THE MEAN OF A POISSON DISTRIBUTION IN THE PRESENCE OF A NUISANCE PARAMETER

In this note we examine the problem of estimating the mean of a Poisson distribution when a nuisance parameter is present. Using a condition of Cox (1958) about ancillarity in the presence of a nuisance parameter, we justify that inference about the parameter should be carried out using the conditional distribution given the appropriate ancillary statistics. A small simulation study has been done to compare the performance of the conditional likelihood approach and the standard likelihood approach.     

A REGRESSION APPROACH TO THE ESTIMATION OF THE FINITE POPULATION MEAN IN THE PRESENCE OF NON‐RESPONSE

This paper presents various estimators for estimating the population mean of the study variable y using information on the auxiliary variable x in the presence of non‐response. Properties of the suggested estimators are studied and compared with those of existing estimators. It is shown that the estimators suggested in this paper are among the best of all the estimators considered. An empirical study is carried out to demonstrate the performance of the suggested estimators and of others, and it is found that the empirical results support the theoretical study.     

ROBUST TESTS FOR THE SIGNIFICANCE OF ORTHANT RESTRICTED MEAN VECTOR

Mudholkar and Srivastava [1] Mudholkar, G. S. and Srivastava, D. K. A class of robust stepwise alternatives to Hotelling's T²tests. Submitted to the Journal of Applied Statistics 1999 [Google Scholar]adapted Mudholkar and Subbaiah's [2] Mudholkar, G. S. and Subbaiah, P. 1980. Testing significance of a mean vector–a possible alternative to Hotelling's T². Ann. Inst. Statist. Math., 32(A): 43–52.  [Google Scholar]modified stepwise procedure, using the trimmed means in place of the means and appropriate studentization, to construct robust tests for the significance of a mean vector. They concluded that the robust alternatives provide excellent type I error control, and a substantial gain in power over Hotelling's T ²test in case of heavy tailed populations without significant loss of power when the population is normal. In this paper we adapt the modified stepwise approach to construct simple tests for the significance of the orthant constrained mean vector of a p-variate normal population with unknown covariance matrix, and also for constructing robust tests without assuming normality. The simple normal theory tests have exact type I error, whereas the robust tests provide a reasonably type I error control and substantial power advantage over Perlman's [3] Perlman, M. D. 1969. One-sided testing problems in multivariate analysis. Annals of Mathematical Statistics, 40: 549–567. [Crossref] , [Google Scholar]likelihood ratio test.     

UNIT ROOT TESTING IN THE PRESENCE OF HEAVY‐TAILED GARCH ERRORS

We derive the asymptotic distributions of the Dickey–Fuller (DF) and augmented DF (ADF) tests for unit root processes with Generalized Autoregressive Conditional Heteroscedastic (GARCH) errors under fairly mild conditions. We show that the asymptotic distributions of the DF tests and ADF t‐type test are the same as those obtained in the independent and identically distributed Gaussian cases, regardless of whether the fourth moment of the underlying GARCH process is finite or not. Our results go beyond earlier ones by showing that the fourth moment condition on the scaled conditional errors is totally unnecessary. Some Monte Carlo simulations are provided to illustrate the finite‐sample‐size properties of the tests.     

FORECASTING VOLATILITY IN THE PRESENCE OF MODEL INSTABILITY

Recent advances in financial econometrics have allowed for the construction of efficient ex post measures of daily volatility. This paper investigates the importance of instability in models of realised volatility and their corresponding forecasts. Testing for model instability is conducted with a subsampling method. We show that removing structurally unstable data of a short duration has a negligible impact on the accuracy of conditional mean forecasts of volatility. In contrast, it does provide a substantial improvement in a model's forecast density of volatility. In addition, the forecasting performance improves, often dramatically, when we evaluate models on structurally stable data.     

SAMPLING AND ESTIMATION IN THE PRESENCE OF CUT-OFF SAMPLING

Cut-off sampling consists of deliberately excluding a set of units from possible selection in a sample, for example if the contribution of the excluded units to the total is small or if the inclusion of these units in the sample involves high costs. If the characteristics of interest of the excluded units differ from those of the rest of the population, the use of naïve estimators may result in highly biased estimates. In this paper, we discuss the use of auxiliary information to reduce the bias by means of calibration and balanced sampling. We show that the use of the available auxiliary information related to both the variable of interest and the probability of being excluded enables us to reduce the potential bias. A short numerical study supports our findings.     

ON THE CHANGE POINT OF THE MEAN RESIDUAL LIFE OF SERIES AND PARALLEL SYSTEMS

This paper considers the mean residual life in series and parallel systems with independent and identically distributed components and obtains relationships between the change points of the mean residual life of systems and that of their components. Compared with the change point for single components, should it exists, the change point for a series system occurs later. For a parallel system, however, the change point is located before that for the components, if it exists at all. Moreover, for both types of systems, the distance between the change points of the mean residual life for systems and for components increases with the number of components. These results are helpful in the determination of optimal burn-in time and related decision making in reliability analysis.     

ROBUST VARIABLE SELECTION IN REGRESSION IN THE PRESENCE OF OUTLIERS AND LEVERAGE POINTS

In linear regression, outliers and leverage points often have large influence in the model selection process. Such cases are downweighted with Mallows-type weights here, during estimation of submodel parameters by generalised M-estimation. A robust version of Mallows's Cp (Ronchetti &. Staudte, 1994) is then used to select a variety of submodels which are as informative as the full model. The methodology is illustrated on a new dataset concerning the agglomeration of alumina in Bayer precipitation.     

APPLICATION OF SEMIPARAMETRIC REGRESSION MODELS IN THE ANALYSIS OF CAPTURE-RECAPTURE EXPERIMENTS

If the capture probabilities in a capture‐recapture experiment depend on covariates, parametric models may be fitted and the population size may then be estimated. Here a semiparametric model for the capture probabilities that allows both continuous and categorical covariates is developed. Kernel smoothing and profile estimating equations are used to estimate the nonparametric and parametric components. Analytic forms of the standard errors are derived, which allows an empirical bias bandwidth selection procedure to be used to estimate the bandwidth. The method is evaluated in simulations and is applied to a real data set concerning captures of Prinia flaviventris, which is a common bird species in Southeast Asia.     

ACCOUNTING FOR NON-COMPLIANCE IN THE ANALYSIS OF RANDOMIZED RESPONSE DATA

The randomized response model is a misclassification design that is used to protect the privacy of respondents with respect to sensitive questions. Conditional misclassification probabilities are specified by the researcher and are therefore considered to be known. It is to be expected that some of the respondents do not comply with respect to the misclassification design. These respondents induce extra perturbation, which is not accounted for in the standard randomized response model. An extension of the randomized response model is presented that takes into account assumptions with respect to non-compliance under simple random sampling. The extended model is investigated using Bayesian inference. The research is motivated by randomized response data concerning violations of regulations for social benefit.     

RAO'S STATISTIC FOR THE ANALYSIS OF UNIFORM ASSOCIATION IN CROSS-CLASSIFICATIONS

In this paper we introduce a new measure for the analysis of association in cross-classifications having ordered categories. Association is measured in terms of the odd-ratios in 2 × 2 subtables formed from adjacent rows and adjacent columns. We focus our attention in the uniform association model. Our measure is based in the family of divergences introduced by Burbea and Rao [1] Burbea, J. and Rao, C. R. 1982a. On the convexity of some divergence measures based on entropy functions. IEEE Transactions on Information Theory, 28: 489–495. [Crossref], [Web of Science ®] , [Google Scholar]. Some well-known sets of data are reanalyzed and a simulation study is presented to analyze the behavior of the new families of test statistics introduced in this paper.     

ROBUST ANALYSIS OF THE BIFURCATING AUTOREGRESSIVE MODEL IN CELL LINEAGE STUDIES

A robust estimation procedure for the bifurcating autoregressive model in cell lineage studies is proposed. The method is illustrated by application to a real data set and is compared with least squares estimates in a small simulation study.     

THE EXAMINATION AND ANALYSIS OF RESIDUALS FOR SOME BIASED ESTIMATORS IN LINEAR REGRESSION

In the presence of collinearity certain biased estimation procedures like ridge regression, generalized inverse estimator, principal component regression, Liu estimator, or improved ridge and Liu estimators are used to improve the ordinary least squares (OLS) estimates in the linear regression model. In this paper new biased estimator (Liu estimator), almost unbiased (improved) Liu estimator and their residuals will be analyzed and compared with OLS residuals in terms of mean-squared error.     

ANALYSIS OF DOUBLY CENSORED DATA AND THE HIV INCUBATION PERIOD DISTRIBUTION IN WESTERN AUSTRALIA

The paper analyses the distribution of times from HIV seroconversion to the first AIDS defining illness for a subcohort of the Western Australian HIV Cohort Study for whom the seroconversion date is known to fall within a calendar time window. The analysis is based on a generalised gamma model for the incubation times and a piecewise constant distribution for the conditional times of seroconversion given the seroconversion windows. This allows flexible hazard shapes and also allows comparison of goodness of fit of the gamma and Weibull distributions which are often used for modelling incubation times. Computational issues are discussed. In these data, neither age at seroconversion, nor calendar time of seroconversion, nor the identification of a seroconversion illness appears to afFect incubation distributions. The Weibull distribution appears to provide a reasonable fit. The distribution of times from seroconversion to an HIV-related death is also briefly considered.     

THE COVERAGE PROBABILITY OF CONFIDENCE INTERVALS IN 2r FACTORIAL EXPERIMENTS AFTER PRELIMINARY HYPOTHESIS TESTING

We consider a 2^r factorial experiment with at least two replicates. Our aim is to find a confidence interval for θ, a specified linear combination of the regression parameters (for the model written as a regression, with factor levels coded as ?1 and 1). We suppose that preliminary hypothesis tests are carried out sequentially, beginning with the rth‐order interaction. After these preliminary hypothesis tests, a confidence interval for θ with nominal coverage 1 ?α is constructed under the assumption that the selected model had been given to us a priori. We describe a new efficient Monte Carlo method, which employs conditioning for variance reduction, for estimating the minimum coverage probability of the resulting confidence interval. The application of this method is demonstrated in the context of a 2³ factorial experiment with two replicates and a particular contrast θ of interest. The preliminary hypothesis tests consist of the following two‐step procedure. We first test the null hypothesis that the third‐order interaction is zero against the alternative hypothesis that it is non‐zero. If this null hypothesis is accepted, we assume that this interaction is zero and proceed to the second step; otherwise, we stop. In the second step, for each of the second‐order interactions we test the null hypothesis that the interaction is zero against the alternative hypothesis that it is non‐zero. If this null hypothesis is accepted, we assume that this interaction is zero. The resulting confidence interval, with nominal coverage probability 0.95, has a minimum coverage probability that is, to a good approximation, 0.464. This shows that this confidence interval is completely inadequate.