In this present paper, considering a linear regression model with nonspherical disturbances, improved confidence sets for the regression coefficients vector are developed using the Stein rule estimators. We derive the large-sample approximations for the coverage probabilities and the expected volumes of the confidence sets based on the feasible generalized least-squares estimator and the Stein rule estimator and discuss their ranking.

In the AR(2) model, with a double root at unity, we consider the asymptotic distribution of the likelihood ratio with respect to a nearly nonstationary alternative. It is shown how the distribution can be represented as a Radon-Nikodym derivative of an Ito process with respect to Brownian motion. Using this result, we point out how standard contiguity arguments can be applied to obtain a representation of the asymptotic power function in nearly nonstationary alternatives.

It is shown that the Cox modified likelihood-ratio statistic for testing partially non-nested hypotheses H0 and H1 is asymptotically equivalent to a bilinear form in nondegenerate asymptotically normal random vectors for sequences of data-generating processes converging to the intersection of H0 and H1 but not necessarily belonging to either H0 or H1. One of the asymptotically normal vectors is the complete parametric encompassing vector of Mizon and Richard, while the other is a close relative. The results are valid regardless of whether or not the data-generating process is exponential and imply that the Cox statistic is not generally asymptotically locally normal. This corrects an assumption made in recent literature.

We propose a method, alternative to that of Estrella (2003, Econometric Theory 19, 1128–1143), of obtaining exact asymptotic p-values and critical values for the popular Andrews (1993, Econometrica 61, 821–856) test for structural stability. The method is based on inverting an integral equation that determines the intensity of crossing a boundary by the asymptotic process underlying the test statistic. Further integration of the crossing intensity yields a p-value. The proposed method can potentially be applied to other stability tests that employ the supremum functional.

Upper and lower bounds on the order of magnitude of $\sum\nolimits_{t = 1}^n {\lefttnq#x007C; {x_t } \righttnq#x007C;^{ - \alpha } } $, where xt is an integrated process, are obtained. Furthermore, upper bounds for the order of magnitude of the related quantity $\sum\nolimits_{t = 1}^n {v_t } \lefttnq#x007C; {x_t } \righttnq#x007C;^{ - \alpha } $, where vt are random variables satisfying certain conditions, are also derived.

This paper proposes bootstrap assisted specification tests for the autoregressive fractionally integrated moving average model based on the Bartlett Tp-process with estimated parameters whose limiting distribution under the null depends on the estimated model and the estimation method employed. The computation of the asymptotic critical values is not easy if at all possible under these circumstances. To circumvent this problem Delgado, Hidalgo, and Velasco (2005, Annals of Statistics 33, 2568–2609) proposed an asymptotically pivotal transformation of the Tp-process with estimated parameters. The aim of this paper is twofold. First, to examine alternative methods based on bootstrap algorithms for estimating the distribution of the test under the null, showing its validity. And second, to study the finite-sample performance of the different alternative procedures via Monte Carlo simulation.

We study the properties of the integrated score estimator (ISE), which is the Laplace version of Manski’s maximum score estimator (MMSE). The ISE belongs to a class of estimators whose basic asymptotic properties were studied in Jun, Pinkse, and Wan (2015, Journal of Econometrics 187(1), 201–216). Here, we establish that the MMSE, or more precisely $$\root 3 \of n |\hat \theta _M - \theta _0 |$$, (locally first order) stochastically dominates the ISE under the conditions necessary for the MMSE to attain its $\root 3 \of n $ convergence rate and that the ISE has the same convergence rate as Horowitz’s smoothed maximum score estimator (SMSE) under somewhat weaker conditions. An implication of the stochastic dominance result is that the confidence intervals of the MMSE are for any given coverage rate wider than those of the ISE, provided that the input parameter αn is not chosen too large. Further, we introduce an inference procedure that is not only rate adaptive as established in Jun et al. (2015), but also uniform in the choice of αn. We propose three different first order bias elimination procedures and we discuss the choice of input parameters. We develop a computational algorithm for the ISE based on the Gibbs sampler and we examine implementational issues in detail. We argue in favor of normalizing the norm of the parameter vector as opposed to fixing one of the coefficients. Finally, we evaluate the computational efficiency of the ISE and the performance of the ISE and the proposed inference procedure in an extensive Monte Carlo study.

In nonstationary heterogeneous panels where the number of units is finite and where each unit cointegrates, a large number of conditions needs to be satisfied for cointegration to be preserved in the aggregate relationship. In reality, the conditions most likely will not hold. This paper takes a closer look at what happens when the conditions are violated. In this case, the question of whether an aggregate relationship is observationally equivalent to a cointegrating equation is of particular interest. We derive a measure of the degree of noncointegration of the aggregate estimates, and we explore its asymptotic properties.We thank Stephen Hall for inspiring discussions and comments during the initial stage of this research. We are grateful to participants in the 9th Conference on Panel Data (Geneva, June 22–23, 2000) and the 2000 Meeting of the Society for Economic Dynamics (San José, Costa Rica, June 29–July 2, 2000) and to colleagues at the University of Bergamo (Italy), London Business School (UK), and Cass Business School (UK) for useful comments. We have enormously benefited from comments and suggestions from two anonymous referees, the editor, Peter C.B. Phillips, and the co-editor, Bruce Hansen. The usual disclaimer applies. G. Urga acknowledges ESRC (Project R022251032) for financial support. Lorenzo Trapani acknowledges financial support from Cass Business School (RAE Development Funds Scheme) and ESRC Postdoctoral Fellowship Scheme (A.N. PTA-026-27-1107).

In this paper, we present a new nonparametric method for estimating a conditional quantile function and develop its weak convergence theory. The proposed estimator is computationally easy to implement and automatically ensures quantile monotonicity by construction. For inference, we propose to use a residual bootstrap method. Our Monte Carlo simulations show that this new estimator compares well with the check-function-based estimator in terms of estimation mean squared error. The bootstrap confidence bands yield adequate coverage probabilities. An empirical example uses a dataset of Canadian high school graduate earnings, illustrating the usefulness of the proposed method in applications.