Estimating good discrete partitions from observed data: symbolic false nearest neighbors

A symbolic analysis of observed time series data requires making a discrete partition of a continuous state space containing observations of the dynamics. A particular kind of partition, called ``generating'', preserves all dynamical information of a deterministic map in the symbolic representation, but such partitions are not obvious beyond one dimension, and existing methods to find them require significant knowledge of the dynamical evolution operator or the spectrum of unstable periodic orbits. We introduce a statistic and algorithm to refine empirical partitions for symbolic state reconstruction. This method optimizes an essential property of a generating partition: avoiding topological degeneracies. It requires only the observed time series and is sensible even in the presence of noise when no truly generating partition is possible. Because of its resemblance to a geometrical statistic frequently used for reconstructing valid time-delay embeddings, we call the algorithm ``symbolic false nearest neighbors''

Scheduling for next generation WLANs: filling the gap between offered and observed data rates

In wireless networks, opportunistic scheduling is used to increase system throughput by exploiting multi-user diversity. Although recent advances have increased physical layer data rates supported in wireless local area networks (WLANs), actual throughput realized are significantly lower due to overhead. Accordingly, the frame aggregation concept is used in next generation WLANs to improve efficiency. However, with frame aggregation, traditional opportunistic schemes are no longer optimal. In this paper, we propose schedulers that take queue and channel conditions into account jointly, to maximize throughput observed at the users for next generation WLANs. We also extend this work to design two schedulers that perform block scheduling for maximizing network throughput over multiple transmission sequences. For these schedulers, which make decisions over long time durations, we model the system using queueing theory and determine users' temporal access proportions according to this model. Through detailed simulations, we show that all our proposed algorithms offer significant throughput improvement, better fairness, and much lower delay compared with traditional opportunistic schedulers, facilitating the practical use of the evolving standard for next generation wireless networks

Combined constraints on modified Chaplygin gas model from cosmological observed data: Markov Chain Monte Carlo approach

We use the Markov Chain Monte Carlo method to investigate a global constraints on the modified Chaplygin gas (MCG) model as the unification of dark matter and dark energy from the latest observational data: the Union2 dataset of type supernovae Ia (SNIa), the observational Hubble data (OHD), the cluster X-ray gas mass fraction, the baryon acoustic oscillation (BAO), and the cosmic microwave background (CMB) data. In a flat universe, the constraint results for MCG model are, $\Omega_{b}h^{2}=0.02263^{+0.00184}_{-0.00162}$ ($1\sigma$) $^{+0.00213}_{-0.00195}$ $(2\sigma)$, $B_{s}=0.7788^{+0.0736}_{-0.0723}$ ($1\sigma$) $^{+0.0918}_{-0.0904}$ $(2\sigma)$, $\alpha=0.1079^{+0.3397}_{-0.2539}$ ($1\sigma$) $^{+0.4678}_{-0.2911}$ $(2\sigma)$, $B=0.00189^{+0.00583}_{-0.00756}$ ($1\sigma$) $^{+0.00660}_{-0.00915}$ $(2\sigma)$, and $H_{0}=70.711^{+4.188}_{-3.142}$ ($1\sigma$) $^{+5.281}_{-4.149}$ $(2\sigma)$.Comment: 12 pages, 1figur

Nonparametric detection of changepoints for sequentially observed data

AbstractAssume that independent data Xn1,…,Xnk(n) are observed sequentially in time, where k(n) < ∞ is a finite horizon. Suppose also that there existsθ ∈ (0, 1] such that Xn1,…, Xn[k(n)θ] have distribution ν1,n and Xn[k(n)θ]+1,…,Xnk(n) have distribution ν2,n. The distributions and the changepoint θ are unknown. Our aim is to react as soon as possible after the change has taken place. We propose a nonparametric stopping rule which attains a given probability of “false alarm” on the one hand and, on the other hand, is less than or equal to k(n)θ + (Ok(n)) with probability one

Essays on statistical inference with imperfectly observed data

Missing data is a common problem encountered by empirical researchers and practitioners. This dissertation is a collection of three essays on handling imperfectly observed economic data. The first essay addresses temporal aggregation where some high frequency data are missing but their sum or average are observed in the form of low frequency data. In a vector autoregression model with varied frequency data, the explicit form of the likelihood function and the posterior distribution of missing values are found without resorting to the recursive Kalman filter. The second essay further discusses data aggregation in a two-equation model in which the missing values are imputed by a regression. In two scenarios, the likelihood function is shown to be separable and the analytic maximum likelihood estimator can be obtained by two auxiliary regressions, which is advantageous to the conventional least squares imputation approach in terms of both efficiency and computability. The third essay concerns the finite-sample bias of estimators associated with the monotone instrumental variables, which is a useful assumption to partially identify the counterfactual outcomes. It is shown that a multi-level bootstrap procedure can reduce and gradually eliminate the bias. A simultaneous simulation strategy is also proposed to make multi-level bootstrap computationally feasible

An alternate algorithm for correction of the scanning multichannel microwave radiometer polarization radiances using Nimbus-7 observed data

The manner in which Nimbus-7 scanning multichannel microwave radiometer (SMMR) scan radiance data was used to determine its operational characteristics is described. The predicted SMMR scan radiance was found to be in disagreement at all wavelengths with a large area of average measured ocean radiances. A modified model incorporating a different phase shift for each of the SMMR horizontal and vertical polarization channels was developed and found to provide good data correlation. Additional study is required to determine the validity and accuracy of this model