The asymptotic properties of parameter estimators whichare based on a model that has been selected by amodel selection procedure are investigated. Inparticular, the asymptotic distribution is derivedand the effects of the model selection process onsubsequent inference are illustrated.

The LAD estimator of the vector parameter in a linearregression is defined by minimizing the sum of theabsolute values of the residuals. This paperprovides a direct proof of asymptotic normality forthe LAD estimator. The main theorem assumesdeterministic carriers. The extension to randomcarriers includes the case of autoregressions whoseerror terms have finite second moments. For afirst-order autoregression with Cauchy errors theLAD estimator is shown to converge at a1/n rate.

We consider the limiting distributions ofM-estimates of an“autoregressive” parameter when the observationscome from an integrated linear process with infinitevariance innovations. It is shown thatM-estimates are, asymptotically,infinitely more efficient than the least-squaresestimator (in the sense that they have a faster rateof convergence) and are conditionally asymptoticallynormal.

This paper presents maximal inequalities and strong lawof large numbers for weakly dependent heterogeneousrandom variables. Specifically considered areLr mixingales forr > 1, strong mixingsequences, and near epoch dependent (NED) sequences.We provide the first strong law forLr-boundedLr mixingales and NEDsequences for 1 > r > 2. The strong lawspresented for α-mixing sequences are lessrestrictive than the laws of McLeish [8].

The exact finite sample behavior is investigated on thebias of multiperiod leastsquares forecasts in thenormal autoregressive modelyt =α +βyt–1+ ut.Necessary and sufficient conditions are given forthe existence of the bias and an expression ispresented which we use to obtain exact numericalresults for finite samples. The unit root and nearunit root behavior is studied in detail and somepopular preconceptions about the behavior of thebias are shown to be false.

We consider the least-squares estimator in a strictlystationary first-order autoregression without anestimated intercept. We study its continuous timeasymptotic distribution based on an asymptoticframework where the sampling interval converges tozero as the sample size increases. We derive amomentgenerating function which permits thecalculation of percentage points and moments of thisasymptotic distribution and assess the adequacy ofthe approximation to the finite sample distribution.In general, the approximation is excellent forvalues of the autoregressive parameter near one. Wealso consider the behavior of the power function oftests based on the normalized leastsquaresestimator. Interesting nonmonotonic properties areuncovered. This analysis extends the study of Perron[15] and helps to provide explanations for thefinite sample results established by Nankervis andSavin [13].

This paper gives simple nonuniform bounds on the tailareas of the permutation distribution of the usualStudent's t-statistic when theobservations are independent with symmetricdistributions. As opposed to uniform bounds,nonuniform bounds depend on the observed sample. Itis shown that the nonuniform bounds proposed arealways tighter than uniform exponential boundspreviously suggested. The use of the bounds toperform nonparametric t-tests isdiscussed and numerical examples are presented.Further, the bounds are extended tot-tests in the context of asimple linear regression.

Asymptotic local power analysis has become an importantand increasingly used technique in econometrics.This paper reviews the history of local poweranalysis and delineates the contribution ofJ.Neyman, E.J.G. Pitman, and G. Noether.