Modified whittle estimation of multilateral spatial models

We consider the estimation of parametric models for stationary spatial or spatio-temporal data on a d-dimensional lattice, for d = 2. The achievement of asymptotic efficiency under Gaussianity, and asymptotic normality more generally, with standard convergence rate, faces two obstacles. One is the 'edge effect', which worsens with increasing d. The other is the difficulty of computing a continuous-frequency form of Whittle estimate or a time domain Gaussian maximum likelihood estimate, especially in case of multilateral models, due mainly to the Jacobian term. An extension of the discrete-frequency Whittle estimate from the time series literature deals conveniently with the latter problem, but when subjected to a standard device for avoiding the edge effect has disastrous asymptotic performance, along with finite sample numerical drawbacks, the objective function lacking a minimum-distance interpretation and losing any global convexity properties. We overcome these problems by first optimizing a standard, guaranteed non-negative, discrete-frequency, Whittle function, without edge-effect correction, providing an estimate with a slow convergence rate, then improving this by a sequence of computationally convenient approximate Newton iterations using a modified, almost-unbiased periodogram, the desired asymptotic properties being achieved after finitely many steps. A Monte Carlo study of finite sample behaviour is included. The asymptotic regime allows increase in both directions, unlike the usual random fields formulation, with the central limit theorem established after re-ordering as a triangular array. When the data are non-Gaussian, the asymptotic variances of all parameter estimates are likely to be affected, and we provide a consistent, non-negative definite, estimate of the asymptotic variance matrix.Spatial data, multilateral models, Whittle estimation,

Cointegration in fractional systems with unknown integration orders.

Cointegrated bivariate nonstationary time series are considered in a fractional context, without allowance for deterministic trends. Both the observable series and the cointegrating error can be fractional processes. The familiar situation in which the respective integration orders are 1 and 0 is nested, but these values have typically been assumed known. We allow one or more of them to be unknown real values, in which case Robinson and Marinucci (1997,2001) have justified least squares estimates of the cointegrating vector, as well as narrow-band frequency-domain estimates, which may be less biased. While consistent, these estimates do not always have optimal convergence rates, and they have non-standard limit distributional behaviour. We consider estimates formulated in the frequency domain, that consequently allow for a wide variety of (parametric) autocorrelation in the short memory input series, as well as time-domain estimates based on autoregressive transformation. Both can be interpreted as approximating generalized least squares and Gaussian maximum likelihood estimates. The estimates share the same limiting distribution, having mixed normal asymptotics (yielding Wald test statistics with χ2 null limit distributions), irrespective of whether the integration orders are known or unknown, subject in the latter case to their estimation with adequate rates of convergence. The parameters describing the short memory stationary input series are √n-consistently estimable, but the assumptions imposed on these series are much more general than ones of autoregressive moving average type. A Monte Carlo study of finite-sample performance is included.

Modified Whittle Estimation of Multilateral Models on a Lattice

In the estimation of parametric models for stationary spatial or spatio-temporal data on a d-dimensional lattice, for d >= 2, the achievement of asymptotic efficiency under Gaussianity, and asymptotic normality more generally, with standard convergence rate, faces two obstacles. One is the "edge effect", which worsens with increasing d. The other is the possible difficulty of computing a continuous-frequency form of Whittle estimate or a time domain Gaussian maximum likelihood estimate, due mainly to the Jacobian term. This is especially a problem in "multilateral" models, which are naturally expressed in terms of lagged values in both directions for one or more of the d dimensions. An extension of the discrete-frequency Whittle estimate from the time series literature deals conveniently with the computational problem, but when subjected to a standard device for avoiding the edge effect has disastrous asymptotic performance, along with finite sample numerical drawbacks, the objective function lacking a minimum-distance interpretation and losing any global convexity properties. We overcome these problems by first optimizing a standard, guaranteed non-negative, discrete-frequency, Whittle function, without edge-effect correction, providing an estimate with a slow convergence rate, then improving this by a sequence of computationally convenient approximate Newton iterations using a modified, almost-unbiased periodogram, the desired asymptotic properties being achieved after finitely many steps. The asymptotic regime allows increase in both directions of all d dimensions, with the central limit theorem established after re-ordering as a triangular array. However our work offers something new for "unilateral" models also. When the data are non-Gaussian, asymptotic variances of all parameter estimates may be affected, and we propose consistent, non-negative definite estimates of the asymptotic variance matrix.spatial data, multilateral modelling, Whittle estimation, edge effect, consistent variance estimation

Evolutionary history of LINE-1 in the major clades of placental mammals

BACKGROUND: LINE-1 constitutes an important component of mammalian genomes. It has a dynamic evolutionary history characterized by the rise, fall and replacement of subfamilies. Most data concerning LINE-1 biology and evolution are derived from the human and mouse genomes and are often assumed to hold for all placentals. METHODOLOGY: To examine LINE-1 relationships, sequences from the 3′ region of the reverse transcriptase from 21 species (representing 13 orders across Afrotheria, Xenarthra, Supraprimates and Laurasiatheria) were obtained from whole genome sequence assemblies, or by PCR with degenerate primers. These sequences were aligned and analysed. PRINCIPAL FINDINGS: Our analysis reflects accepted placental relationships suggesting mostly lineage-specific LINE-1 families. The data provide clear support for several clades including Glires, Supraprimates, Laurasiatheria, Boreoeutheria, Xenarthra and Afrotheria. Within the afrotherian LINE-1 (AfroLINE) clade, our tree supports Paenungulata, Afroinsectivora and Afroinsectiphillia. Xenarthran LINE-1 (XenaLINE) falls sister to AfroLINE, providing some support for the Atlantogenata (Xenarthra+Afrotheria) hypothesis. SIGNIFICANCE: LINEs and SINEs make up approximately half of all placental genomes, so understanding their dynamics is an essential aspect of comparative genomics. Importantly, a tree of LINE-1 offers a different view of the root, as long edges (branches) such as that to marsupials are shortened and/or broken up. Additionally, a robust phylogeny of diverse LINE-1 is essential in testing that site-specific LINE-1 insertions, often regarded as homoplasy-free phylogenetic markers, are indeed unique and not convergent

Universals of Word Formation Processes: Noun Incorporated in the Acquisition of Sāmoan as a Second Language

Studies of sccond language syntactic acquisition (e.g., Gass 1979; Flynn 1991; White 1989) have been motivated by research into language universals within both typological (Creenberg 1966), and universal grammar (Chomsky 1981) frameworks. In the typological framework learning difficulty is predicted by the relative markedness of the second languagc, when comparcd with the leamer's first languagc (Eckman 1985). In the universal grammar framework learning difficulty is Predicted where there are differences in the paramcter settings of the first and second language (Flynn 1989). Some support exists for the influence of markedness on learning difficulty (e.g., Gass 1979; Pavesi 1986; Doughtye199.1), but there is disagreement about the influence exerted by universal grammar (Bley-Vroman & Chaudron 1990; Flynn & Lust 1990). To date no studies of second language word forrnation processes have been motivated by language universals research from either of these perspectives. This study examines the influence of a proposed implicational hicrarchy (Mithun 1984) and constraints of universal Srammar (Baker 1988) on the acquisition of noun incorporation processes by second language learners of Samoan. The methodology involved reaction time, grammaticality iudgement and response certainty measures of the processing difficulty and acceptability of examples of noun incorporation for English speaking learners of Samoan, with the latter measure guving the clearest support for two hypothesized orders of difficulty

Sequence of the mouse Q4 class I gene and characterization of the gene product

The Q4 class I gene has been shown to participate in gene conversion events within the mouse major histocompatibility complex. Its complete genomic nucleotide sequence has been determined. The 5' half of Q4 resembles H-2 genes more strongly than other Q genes. Its 3' end, in contrast, is Q-like and contains a translational stop signal in exon 5 which predicts a polypeptide with an incomplete membrane spanning segment. The presence of two inverted B1 repeats suggests that part of the Q4 gene may be mobile within the genome. Gene transfer experiments have shown that the Q4 gene encodes a ß2-microglobulin associated polypeptide of Mr 41 000. A similar protein was found in activated mouse spleen cells. The Q4 polypeptide was found to be secreted both by spleen cells and by transfected fibroblasts and was not detectable on the cell surface. Antibody binding and twodimensional gel electrophoresis indicate that the Q4 molecule is identical to a mouse class I polypeptide, Qb-1, which has been previously described

Saturn Forms by Core Accretion in 3.4 Myr

We present two new in situ core accretion simulations of Saturn with planet formation timescales of 3.37 Myr (model S0) and 3.48 Myr (model S1), consistent with observed protostellar disk lifetimes. In model S0, we assume rapid grain settling reduces opacity due to grains from full interstellar values (Podolak 2003). In model S1, we do not invoke grain settling, instead assigning full interstellar opacities to grains in the envelope. Surprisingly, the two models produce nearly identical formation timescales and core/atmosphere mass ratios. We therefore observe a new manifestation of core accretion theory: at large heliocentric distances, the solid core growth rate (limited by Keplerian orbital velocity) controls the planet formation timescale. We argue that this paradigm should apply to Uranus and Neptune as well.Comment: 4 pages, including 1 figure, submitted to ApJ Letter

Evolution of the Olympus Mons Caldera, Mars

Extensive high-resolution (15 to 20 m/pixel) coverage of Olympus Mons volcano permits the investigation of the sequence of events associated with the evolution of the nested summit caldera. The sequence of the intra-caldera events is well illustrated by image data collected on orbits 473S and 474S of Viking Orbiter 1. These data cover both the oldest and youngest portions of the caldera floor. The chronology inferred from the observations is presented which in turn can be interpreted in terms of the internal structure of the volcano (i.e., magma chamber depth and the existence of dikes)