Unknown Order Research Articles

Persistence-robust surplus-lag Granger causality testing

Previous literature has introduced causality tests with conventional limiting distributions in I(0)/I(1) vector autoregressive (VAR) models with unknown integration orders, based on an additional surplus lag in the specification of the estimated equation, which is not included in the tests. By extending this surplus lag approach to an infinite order VARX framework, we show that it can provide a highly persistence-robust Granger causality test that accommodates i.a stationary, nonstationary, local-to-unity, long-memory, and certain (unmodelled) structural break processes in the forcing variables within the context of a single χ2 null limiting distribution.

Automated Estimation of Vector Error Correction Models

Model selection and associated issues of post-model selection inference present well known challenges in empirical econometric research. These modeling issues are manifest in all applied work but they are particularly acute in multivariate time series settings such as cointegrated systems where multiple interconnected decisions can materially affect the form of the model and its interpretation. In cointegrated system modeling, empirical estimation typically proceeds in a stepwise manner that involves the determination of cointegrating rank and autoregressive lag order in a reduced rank vector autoregression followed by estimation and inference. This paper proposes an automated approach to cointegrated system modeling that uses adaptive shrinkage techniques to estimate vector error correction models with unknown cointegrating rank structure and unknown transient lag dynamic order. These methods enable simultaneous order estimation of the cointegrating rank and autoregressive order in conjunction with oracle-like efficient estimation of the cointegrating matrix and transient dynamics. As such they offer considerable advantages to the practitioner as an automated approach to the estimation of cointegrated systems. The paper develops the new methods, derives their limit theory, reports simulations and presents an empirical illustration with macroeconomic aggregates.

A Per-Survivor Processing Receiver for MIMO Transmission Systems With One Unknown Channel Order Per Output

The order of a communications channel is the length of its impulse response. Recently, several works have tackled the problem of estimating the order of a frequency-selective multiple-input-multiple-output (MIMO) channel. However, all of them consider a single order, despite the fact that a MIMO channel comprises several subchannels (specifically, as many as the number of inputs times the number of outputs), each one possibly with its own order. In this paper, we introduce an algorithm for maximum-likelihood sequence detection (MLSD) in frequency- and time-selective MIMO channels that incorporates full estimation of the MIMO channel impulse response (CIR) coefficients, including one channel order per output. Simulation results following the analytical derivation of the algorithm suggest that the proposed receiver can achieve significant improvements in performance when transmitting through a MIMO channel that effectively comprises subchannels of different lengths.

The OMERACT Psoriatic Arthritis Magnetic Resonance Imaging Score (PsAMRIS) Is Reliable and Sensitive to Change: Results from an OMERACT Workshop

The aim of this multireader exercise was to assess the reliability and sensitivity to change of the psoriatic arthritis magnetic resonance imaging score (PsAMRIS) in PsA patients followed for 1 year. MRI was acquired from 12 patients with PsA before initiation of treatment and after 12 months. MR images were scored according to PsAMRIS (for synovitis, tenosynovitis, periarticular inflammation, bone marrow edema, bone erosion, and bone proliferation) under standardized conditions, in unknown chronological order. Intraobserver/interobserver reliability was examined by intraclass correlation coefficients (ICC) and sensitivity to change by standardized response means (SRM). The interobserver reliability of PsAMRIS was high for synovitis, tenosynovitis, periarticular inflammation, and bone edema status and change scores (interobserver ICC 0.87-0.97). The intraobserver reliability was moderate to high (ICC 0.60-0.98) for status and change scores, except for change in periarticular inflammation (ICC 0.33). PsAMRIS sensitivity to change was moderate for synovitis, tenosynovitis, and periarticular inflammation (SRM 0.5-0.8), while poor (SRM 0.1-0.3) for bone marrow edema, erosion, and bone proliferation. Rare occurrence and minimal change contributed to poor SRM and change-score ICC for bone parameters. This multireader exercise, performed under standardized conditions, confirmed PsAMRIS to have high interobserver and intraobserver reliability for hand PsA. Measures of inflammation were sensitive to change, implying that PsAMRIS may be a valuable tool for monitoring change in inflammation during PsA clinical trials.

Testing for variance changes in autoregressive models with unknown order

The problem of change point in autoregressive process is studied in this article. We propose a Bayesian information criterion-iterated cumulative sums of squares algorithm to detect the variance changes in an autoregressive series with unknown order. Simulation results and two examples are presented, where it is shown to have good performances when the sample size is relatively small.

Robust Sign-Based and Hodges-Lehmann Estimators in Linear Median Regressions with Heterogenous Serially Dependent Errors

We propose estimators for the parameters of a linear median regression without any assumption on the shape of the error distribution – including no condition on the existence of moments – allowing for heterogeneity (or heteroskedasticity) of unknown form, noncontinuous distributions, and very general serial dependence (linear or nonlinear) including GARCH-type and stochastic volatility of unknown order. The estimators follow from a reverse inference approach, based on the class of distribution-free sign tests proposed in Coudin and Dufour (2009, Econometrics J.) under a median gale assumption. As a result, the estimators inherit strong robustness properties from their generating tests. Since the proposed estimators are based on maximizing a test statistic (or a p-value function) over different null hypotheses, they can be interpreted as Hodges-Lehmann-type (HL) estimators. It is easy to adapt the sign-based estimators to account for linear serial dependence. Both finite-sample and large-sample properties are established under weak regularity conditions. The proposed estimators are median unbiased (under symmetry and estimator unicity) and satisfy natural equivariance properties. Consistency and asymptotic normality are established without any condition on error moment existence, allowing for heterogeneity (or heteroskedasticity) of unknown form, noncontinuous distributions, and very general serial dependence (linear or nonlinear). These conditions are considerably weaker than those used to show corresponding results for LAD estimators. In a Monte Carlo study on bias and mean square error, we find that sign-based estimators perform better than LAD-type estimators, especially in heteroskedastic settings. The proposed procedures are applied to a trend model of the Standard and Poor’s composite price index, where disturbances are affected by both heavy tails (non-normality) and heteroskedasticity.

Online Sparse System Identification and Signal Reconstruction Using Projections Onto Weighted $\ell_{1}$ Balls

This paper presents a novel projection-based adaptive algorithm for sparse signal and system identification. The sequentially observed data are used to generate an equivalent sequence of closed convex sets, namely hyperslabs. Each hyperslab is the geometric equivalent of a cost criterion, that quantifies "data mismatch". Sparsity is imposed by the introduction of appropriately designed weighted $\ell_1$ balls. The algorithm develops around projections onto the sequence of the generated hyperslabs as well as the weighted $\ell_1$ balls. The resulting scheme exhibits linear dependence, with respect to the unknown system's order, on the number of multiplications/additions and an $\mathcal{O}(L\log_2L)$ dependence on sorting operations, where $L$ is the length of the system/signal to be estimated. Numerical results are also given to validate the performance of the proposed method against the LASSO algorithm and two very recently developed adaptive sparse LMS and LS-type of adaptive algorithms, which are considered to belong to the same algorithmic family.

An adaptive learning regulator for uncertain minimum phase systems with undermodeled unknown exosystems

The design of an adaptive learning regulator is addressed for uncertain minimum phase linear systems (with known bounds, known upper bound on system order, known relative degree, known high frequency gain sign) and for unknown exosystems (with unknown order, uncertain frequencies). On the basis of a known bound on system uncertainties and a known bound on the modeled exosystem frequencies, a new adaptive output error feedback control algorithm is proposed which guarantees exponential convergence of both the output and the control input errors into residual bounds which decrease as the exosystem modeling error decreases. Exponential convergence of both errors to zero is obtained when the regulator exactly models all exosystem excited frequencies, while asymptotic convergence of both errors to zero is achieved when the actual exosystem is overmodeled by the regulator. The new algorithm generalizes existing learning controllers since, in the case of periodic references and/or disturbances, the knowledge of the period is not required.

Instability detection of ARMA systems based on AR system identification

The ability of parametric autoregressive (AR) system identification methods to detect the instability of an autoregressive moving average (ARMA) system of an unknown order is investigated. The collection of least squares AR estimators of various orders is shown to have the capacity to detect the instability of the underlying system. Necessary information is not the order of the system but, instead, an upper bound of the number of unstable poles with the maximal magnitude outside the unit circle.

A strategy analysis for genetic association studies with known inbreeding

BackgroundAssociation studies consist in identifying the genetic variants which are related to a specific disease through the use of statistical multiple hypothesis testing or segregation analysis in pedigrees. This type of studies has been very successful in the case of Mendelian monogenic disorders while it has been less successful in identifying genetic variants related to complex diseases where the insurgence depends on the interactions between different genes and the environment. The current technology allows to genotype more than a million of markers and this number has been rapidly increasing in the last years with the imputation based on templates sets and whole genome sequencing. This type of data introduces a great amount of noise in the statistical analysis and usually requires a great number of samples. Current methods seldom take into account gene-gene and gene-environment interactions which are fundamental especially in complex diseases. In this paper we propose to use a non-parametric additive model to detect the genetic variants related to diseases which accounts for interactions of unknown order. Although this is not new to the current literature, we show that in an isolated population, where the most related subjects share also most of their genetic code, the use of additive models may be improved if the available genealogical tree is taken into account. Specifically, we form a sample of cases and controls with the highest inbreeding by means of the Hungarian method, and estimate the set of genes/environmental variables, associated with the disease, by means of Random Forest.ResultsWe have evidence, from statistical theory, simulations and two applications, that we build a suitable procedure to eliminate stratification between cases and controls and that it also has enough precision in identifying genetic variants responsible for a disease. This procedure has been successfully used for the beta-thalassemia, which is a well known Mendelian disease, and also to the common asthma where we have identified candidate genes that underlie to the susceptibility of the asthma. Some of such candidate genes have been also found related to common asthma in the current literature.ConclusionsThe data analysis approach, based on selecting the most related cases and controls along with the Random Forest model, is a powerful tool for detecting genetic variants associated to a disease in isolated populations. Moreover, this method provides also a prediction model that has accuracy in estimating the unknown disease status and that can be generally used to build kit tests for a wide class of Mendelian diseases.

Higher-Order Derivative Compensators for Controlling the Systems With Higher Dynamics

The PID controller is a popular choice for the control of industrial processes. The PDN controller introduced in this paper is a better alternative to PIDN. The paper presents the design and computer simulation of the PDN controller. The PDN controller is a simpler and more effective choice when dealing with higher-order dynamic systems. The gain components of the controller are introduced to improve transient characteristics of the higher-order industrial systems or processes by directly modifying the components of their characteristic equations. As a result the system under control becomes stable and able to respond faster to the inputs as compared to PID-based systems. The tunable command feed-forward steady-state gain (K S ) of the PDN controller helps to track the constant or time-varying input commands much faster and more precisely than the integral component of the PID controller. The paper discusses the steady-state performance, stability problems and the gain tuning strategies to improve the transient responses of the feedback system. The quality of the PDN performance is demonstrated by solving the set point input (step) and tracking a time-varying input (ramp) problems. The paper also presents the detailed higher-order derivative compensators tuning procedures for the general case of unknown order, stable/unstable plant and particular case of unknown order but stable plant.

New method for parameter estimation of polynomial phase signals

In this correspondence, a linear transform called polynomial to Hermite polynomial transform (PHPT) is proposed, and the PHPT-based method for parameter estimation of polynomial phase signals (PPS) embedded in additive white Gaussian noise is addressed. The first advantage is the low computational complexity. If the number of samples is N, the computational complexity is O(3N log2N) regardless of the order or the component number of PPS. The second advantage is that there is no non-linear operation in PHPT algorithm; therefore there is no cross-term interference in between the various components. In addition, the proposed method can well process the PPS with unknown order phase. Simulations illustrate that the proposed algorithm is more effective as compared with the existing ones.

Predictions for Higgs production at the Tevatron and the associated uncertainties

We update the theoretical predictions for the production cross sections of the Standard Model Higgs boson at the Fermilab Tevatron collider, focusing on the two main search channels, the gluon-gluon fusion mechanism $gg \to H$ and the Higgs-strahlung processes $q \bar q \to VH$ with $V=W/Z$, including all relevant higher order QCD and electroweak corrections in perturbation theory. We then estimate the various uncertainties affecting these predictions: the scale uncertainties which are viewed as a measure of the unknown higher order effects, the uncertainties from the parton distribution functions and the related errors on the strong coupling constant, as well as the uncertainties due to the use of an effective theory approach in the determination of the radiative corrections in the $gg \to H$ process at next-to-next-to-leading order. We find that while the cross sections are well under control in the Higgs--strahlung processes, the theoretical uncertainties are rather large in the case of the gluon-gluon fusion channel, possibly shifting the central values of the next-to-next-to-leading order cross sections by more than $\approx 40%$. These uncertainties are thus significantly larger than the $\approx 10%$ error assumed by the CDF and D0 experiments in their recent analysis that has excluded the Higgs mass range $M_H=$162-166 GeV at the 95% confidence level. These exclusion limits should be, therefore, reconsidered in the light of these large theoretical uncertainties.

Twice-Universal Simulation of Markov Sources and Individual Sequences

The problem of universal simulation given a training sequence is studied both in a stochastic setting and for individual sequences. In the stochastic setting, the training sequence is assumed to be emitted by a Markov source of unknown order, extending previous work where the order is assumed known and leading to the notion of twice-universal simulation. A simulation scheme, which partitions the set of sequences of a given length into classes, is proposed for this setting and shown to be asymptotically optimal. This partition extends the notion of type classes to the twice-universal setting. In the individual sequence scenario, the same simulation scheme is shown to generate sequences which are statistically similar, in a strong sense, to the training sequence, for statistics of any order, while essentially maximizing the uncertainty on the output.

Bootstrapping the likelihood ratio cointegration test in error correction models with unknown lag order

The finite-sample size and power properties of bootstrapped likelihood ratio system cointegration tests are investigated via Monte Carlo simulations when the true lag order of the data generating process is unknown. Recursive bootstrap schemes are employed which differ in the way in which the lag order is chosen. The order is estimated by minimizing different information criteria and by combining the corresponding order estimates. It is found that, in comparison to the standard asymptotic likelihood ratio test based on an estimated lag order, bootstrapping can lead to improvements in small samples even when the true lag order is unknown, while the power loss is moderate.

IDENTIFIKASI DAN ESTIMASI RUNTUN WAKTU MODEL AR MENGGUNAKAN ALGORITMA SIMULATED ANNEALING

When fitting a Autoregressive (AR) model to real data, the correct model order and the model parameter often unknown. Our aim is to find estimators of the order and the parameter based on the data. In this paper the model identification and parameter estimation for AR model is posed within a Bayesian framework. Within this framework the unknown order and parameter are assumed to be distributed according to a prior distribution, which incorporates all the available information about the process. All the information concerning the order andparameter characterising the model is then contained in the posterior distribution. Obtaining the posterior model order probabilities and the posterior model parameter probabilitiesrequires integration of the resulting posterior distribution, an operation which is analytically intractable. Here stochastic simulated annealing algorithm is developed to perform therequired integration by simulating from the posterior distribution. The methods developed are evaluated in simulation studies on number of synthetic and real data sets.Keywords : simulated annealing, autoregressive, order identification, parameter estimation.

Blind noise variance and SNR estimation for OFDM systems based on information theoretic criteria

Blind noise variance and SNR estimators based on information theoretic criteria for orthogonal frequency division multiplexing (OFDM) systems are proposed in this paper. By using the redundancy induced by the cyclic-prefix, the unknown channel order is estimated via minimum length description (MDL) or Akaike information criterion (AIC), and the noise variance and SNR can be obtained subsequently. The proposed methods do not require any pilot symbols and therefore improve the spectrum efficiency. Simulation results are presented to highlight the benefit of the proposed algorithms compared with the other existing blind methods.

Tests of analytical hadronisation models using event shape moments in e+e− annihilation

Predictions of analytical models for hadronisation, namely the dispersive model, the shape function and the single dressed gluon approximation, are compared with moments of hadronic event shape distributions measured in e+e− annihilation at centre-of-mass energies between 14 and 209 GeV. In contrast to Monte Carlo models for hadronisation, analytical models require to adjust only two universal parameters, the strong coupling and a second quantity parametrising non-perturbative corrections. The extracted values of α S are consistent with the world average and competitive with previous measurements. The variance of event shape distributions is compared with predictions given by some of these models. Limitations of the models, probably due to unknown higher order corrections, are demonstrated and discussed.

Nonparametric cointegration analysis of fractional systems with unknown integration orders

In this paper a nonparametric variance ratio testing approach is proposed for determining the cointegration rank in fractionally integrated systems. The test statistic is easily calculated without prior knowledge of the integration order of the data, the strength of the cointegrating relations, or the cointegration vector(s). The latter property makes it easier to implement than regression-based approaches, especially when examining relationships between several variables with possibly multiple cointegrating vectors. Since the test is nonparametric, it does not require the specification of a particular model and is invariant to short-run dynamics. Nor does it require the choice of any smoothing parameters that change the test statistic without being reflected in the asymptotic distribution. Furthermore, a consistent estimator of the cointegration space can be obtained from the procedure. The asymptotic distribution theory for the proposed test is non-standard but easily tabulated or simulated. Monte Carlo simulations demonstrate excellent finite sample properties, even rivaling those of well-specified parametric tests. The proposed methodology is applied to the term structure of interest rates, where, contrary to both fractional- and integer-based parametric approaches, evidence in favor of the expectations hypothesis is found using the nonparametric approach.

New results on large sets of Kirkman triple systems

The existence problem on the large sets of Kirkman triple systems (LKTS) was posed by Sylvester in 1850's as an extension of Kirkman's 15 schoolgirls problem. An LKTS(15) was constructed by Denniston in 1974. However, up to now the smallest unknown order for the existence of LKTS is still 21. In this paper we construct the two smallest unknown LKTS(v)s with v = 21 and v = 39 by using multiplier automorphism groups. Applying known recursive constructions, we show the existence of more infinite classes of large sets of Kirkman triple systems.