33,648 research outputs found

    Estimating Knots and Their Association in Parallel Bilinear Spline Growth Curve Models in the Framework of Individual Measurement Occasions

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    Latent growth curve models with spline functions are flexible and accessible statistical tools for investigating nonlinear change patterns that exhibit distinct phases of development in manifested variables. Among such models, the bilinear spline growth model (BLSGM) is the most straightforward and intuitive but useful. An existing study has demonstrated that the BLSGM allows the knot (or change-point), at which two linear segments join together, to be an additional growth factor other than the intercept and slopes so that researchers can estimate the knot and its variability in the framework of individual measurement occasions. However, developmental processes usually unfold in a joint development where two or more outcomes and their change patterns are correlated over time. As an extension of the existing BLSGM with an unknown knot, this study considers a parallel BLSGM (PBLSGM) for investigating multiple nonlinear growth processes and estimating the knot with its variability of each process as well as the knot-knot association in the framework of individual measurement occasions. We present the proposed model by simulation studies and a real-world data analysis. Our simulation studies demonstrate that the proposed PBLSGM generally estimate the parameters of interest unbiasedly, precisely and exhibit appropriate confidence interval coverage. An empirical example using longitudinal reading scores, mathematics scores, and science scores shows that the model can estimate the knot with its variance for each growth curve and the covariance between two knots. We also provide the corresponding code for the proposed model.Comment: \c{opyright} 2020, American Psychological Association. This paper is not the copy of record and may not exactly replicate the final, authoritative version of the article. Please do not copy or cite without authors' permission. The final article will be available, upon publication, via its DOI: 10.1037/met000030

    On generating functions of Hausdorff moment sequences

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    The class of generating functions for completely monotone sequences (moments of finite positive measures on [0,1][0,1]) has an elegant characterization as the class of Pick functions analytic and positive on (βˆ’βˆž,1)(-\infty,1). We establish this and another such characterization and develop a variety of consequences. In particular, we characterize generating functions for moments of convex and concave probability distribution functions on [0,1][0,1]. Also we provide a simple analytic proof that for any real pp and rr with p>0p>0, the Fuss-Catalan or Raney numbers rpn+r(pn+rn)\frac{r}{pn+r}\binom{pn+r}{n}, n=0,1,…n=0,1,\ldots are the moments of a probability distribution on some interval [0,Ο„][0,\tau] {if and only if} pβ‰₯1p\ge1 and pβ‰₯rβ‰₯0p\ge r\ge 0. The same statement holds for the binomial coefficients (pn+rβˆ’1n)\binom{pn+r-1}n, n=0,1,…n=0,1,\ldots.Comment: 23 pages, LaTeX; Minor corrections and explanations added, literature update. To appear in Transactions Amer. Math. So

    A generalised sidelobe canceller architecture based on oversampled subband decompositions

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    Adaptive broadband beamforming can be performed in oversampled subband signals, whereby an independent beamformer is operated in each frequency band. This has been shown to result in a considerably reduced computational complexity. In this paper, we primarily investigate the convergence behaviour of the generalised sidelobe canceller (GSC) based on normalised least mean squares algorithm (NLMS) when operated in subbands. The minimum mean squared error can be limited, amongst other factors, by the aliasing present in the subbands. With regard to convergence speed, there is strong indication that the subband-GSC converges faster than a fullband counterpart of similar modelling capabilities. Simulations are presented

    Continued Field Evaluation of Precutting for Maintaining Asphalt Concrete Pavements with Thermal Cracking

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    In continuation of a previously completed project entitled Evaluate Presawn Transverse Thermal Cracks for Asphalt Concrete Pavement, this project was a further effort to understand important variables in the thermal cracking process through continued field monitoring of three precutting test sites in Interior Alaska. The test sites included (1) Phillips Field Road, precut in 1984 (β‰ˆ west ΒΌ mile of this road), (2) Richardson Highway precut in 2012 (β‰ˆ MP 343–344), and (3) Parks Highway precut in 2014 (β‰ˆ MP 245–252). Preliminary results at relatively short periods (up to 4 years) indicate that precutting is an economically promising way to control natural thermal cracks. Even short-term economic benefits appear to range between about 2% and 21%. The degree to which precutting works for an AC pavement appears to be a function of the thickness and general structural robustness of new construction. Shorter precut spacing, along with stronger and/or thicker pavement structures, looks promising with respect to crack control. Continuing evaluation and monitoring of test sections are needed to recommend an effective design methodology and construction practice for Alaska and cold areas of other northern states.Alaska Department of Transportatio
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