Corrected Phase-Type Approximations of Heavy-Tailed Queueing Models in a Markovian Environment

We develop accurate approximations for the delay distribution of the MArP/G/1 queue that capture the exact tail behavior and provide bounded relative errors. Motivated by statistical analysis, we consider the service times as a mixture of a phase-type and a heavy-tailed distribution. With the aid of perturbation analysis, we derive corrected phase-type approximations as a sum of the delay in a MArP/PH/1 queue and a heavy-tailed component depending on the perturbation parameter. We exhibit their performance with numerical examples.     

On the least-squares model averaging interval estimator

In many applications of linear regression models, randomness due to model selection is commonly ignored in post-model selection inference. In order to account for the model selection uncertainty, least-squares frequentist model averaging has been proposed recently. We show that the confidence interval from model averaging is asymptotically equivalent to the confidence interval from the full model. The finite-sample confidence intervals based on approximations to the asymptotic distributions are also equivalent if the parameter of interest is a linear function of the regression coefficients. Furthermore, we demonstrate that this equivalence also holds for prediction intervals constructed in the same fashion.     

On Expected Lengths of Predictive Intervals

Abstract.  We consider the problem of comparing predictive intervals for a future observation via their expected lengths at a given confidence level. A higher order asymptotic theory is developed. This yields an explicit formula for expected length comparison and associated admissibility results. Illustrative examples are given.     

Asymptotic confidence interval of power spectrum of a continuous time process through progressively faster sampling

If the power spectral density of a continuous time stationary stochastic process is not limited to a finite bandwidth, data sampled from that process at any uniform sampling rate leads to biased and inconsistent spectrum estimators, which are unsuitable for constructing confidence intervals. In this paper, we use the smoothed periodogram estimator to construct asymptotic confidence intervals shrinking to the true spectra, by allowing the sampling rate to go to infinity suitably fast as the sample size goes to infinity. The proposed method requires minimal computation, as it does not involve bootstrap or other resampling. The method is illustrated through a Monte-Carlo simulation study, and its performance is compared with that of the corresponding method based on uniform sampling at a fixed rate.     

Unit Root Testing in Heteroscedastic Panels Using the Cauchy Estimator

The Cauchy estimator of an autoregressive root uses the sign of the first lag as instrumental variable. The resulting IV t-type statistic follows a standard normal limiting distribution under a unit root case even under unconditional heteroscedasticity, if the series to be tested has no deterministic trends. The standard normality of the Cauchy test is exploited to obtain a standard normal panel unit root test under cross-sectional dependence and time-varying volatility with an orthogonalization procedure. The article’s analysis of the joint N, T asymptotics of the test suggests that (1) N should be smaller than T and (2) its local power is competitive with other popular tests. To render the test applicable when N is comparable with, or larger than, T, shrinkage estimators of the involved covariance matrix are used. The finite-sample performance of the discussed procedures is found to be satisfactory.     

Exact tests based on pre-estimation and second order pivotals: non-inferiority trials

Pre-estimation is a technique for adjusting a standard approximate P-value to be close to exact. While conceptually simple, it can become computationally intensive. Second order pivotals [N. Reid, Asymptotics and the theory of inference, Ann. Statist. 31 (2003), pp. 1695–1731] are constructed to be closer to exact than standard approximate pivotals. The theory behind these pivotals is complex, and their properties are unclear for discrete models. However, since they are typically given in closed form they are easy to compute. For the special case of non-inferiority trials, we investigate Wald, Score, likelihood ratio and second order pivotals. Each of the basic pivotals are used to generate an exact test by maximising with respect to the nuisance parameter. We also study the effect of pre-estimating the nuisance parameter, as described in Lloyd [C.J. Lloyd, Exact P-values for discrete models obtained by estimation and maximisation, Aust. N. Z. J. Statist. 50 (2008), pp. 329–346]. It appears that second order methods are not as close to exact as might have been hoped. On the other hand, P-values, based on pre-estimation are very close to exact, are more powerful than competitors and are hardly affected by the basic generating statistic chosen.     

Detection of a change-point in variance by a weighted sum of powers of variances test

This paper proposes a weighted sum of powers of variances test for detecting changes in variance of a data sequence. Asymptotic critical value formulas are derived for this test. The modified weighted sum of powers of variances test is also introduced so that the accuracy of change-point detection is highly improved for a sample of small size. Simulation studies and real data analysis are presented to assess the proposed tests.     

On asymptotics of multivariate integrals with applications to records

Let { X _n ,n≥1} be a sequence of iid. Gaussian random vectors in R ^d , d≥2, with nonsingular distribution function F. In this paper the asymptotics for the sequence of integrals I _F,n (G _n )?n∫ _{R ^d} G _n ^n?1( X ) dF( X ) is considered with G _n some distribution function on R ^d . In the case G _n =F the integral I _F,n (F)/n is the probability that a record occurs in X ₁,…, X _n at index n. [1] Gnedin, A.V. 1998. Records from a Multivariate Normal Sample. Statist. Probab. Lett., 39: 11–15. [Crossref], [Web of Science ®] , [Google Scholar] obtained lower and upper asymptotic bounds for this case, whereas [2] Ledford, W.A. and Twan, A.J. 1998. On the Tail Concomitant Behaviour for Extremes. Adv. Appl. Probab., 30: 197–215. [Crossref], [Web of Science ®] , [Google Scholar] showed the rate of convergence if d=2. In this paper we derive the exact rate of convergence of I _F,n (G _n ) for d≥2 under some restrictions on the distribution function G _n . Some related results for multivariate Gaussian tails are discussed also.     

Estimating Housing Infill Potential: Developing a Case for Floorspace Pooling in Ahmedabad,India

This paper demonstrates a rapid and inexpensive methodology (using minimal data) for estimating housing infill potential and develops the idea of residential floorspace pooling to deliver the infill. Estimates are based on surveying 11 km2 of the residential land in Ahmedabad. The analysis suggests that Ahmedabad has a huge potential for infill development, which could accommodate significantly more than its new housing requirements for 2031, within the existing footprint of the city. The second part of the paper discusses development of the idea of floorspace pooling as a tool to enable supply of the new housing infill floorspace in the market.     

Subsampling Intervals in Autoregressive Models with Linear Time Trend

A new method is proposed for constructing confidence intervals in autoregressive models with linear time trend. Interest focuses on the sum of the autoregressive coefficients because this parameter provides a useful scalar measure of the long‐run persistence properties of an economic time series. Since the type of the limiting distribution of the corresponding OLS estimator, as well as the rate of its convergence, depend in a discontinuous fashion upon whether the true parameter is less than one or equal to one (that is, trend‐stationary case or unit root case), the construction of confidence intervals is notoriously difficult. The crux of our method is to recompute the OLS estimator on smaller blocks of the observed data, according to the general subsampling idea of Politis and Romano (1994a), although some extensions of the standard theory are needed. The method is more general than previous approaches in that it works for arbitrary parameter values, but also because it allows the innovations to be a martingale difference sequence rather than i.i.d. Some simulation studies examine the finite sample performance.