Equivalency and unbiasedness of grey prediction models

In order to deeply research the structure discrepancy and modeling mechanism among different grey prediction models, the equivalence and unbiasedness of grey prediction models are analyzed and verified. The results show that all the grey prediction models that are strictly derived from x^（0）（k） ＋az^（1）（k） = b have the identical model structure and simulation precision. Moreover, the unbiased simulation for the homogeneous exponential sequence can be accomplished. However, the models derived from dx^（1）/dt ＋ ax^（1）= b are only close to those derived from x^（0）（k） ＋ az^（1）（k） = b provided that ｜a｜ has to satisfy｜a｜ 0.1; neither could the unbiased simulation for the homogeneous exponential sequence be achieved. The above conclusions are proved and verified through some theorems and examples.

New construction of mutually unbiased bases for odd-dimensional state space

We study the construction of mutually unbiased bases in Hilbert space for composite dimensions d which are not prime powers.We explore the results for composite dimensions which are true for prime power dimensions.We then provide a method for selecting mutually unbiased vectors from the eigenvectors of generalized Pauli matrices to construct mutually unbiased bases.In particular,we present four mutually unbiased bases in C^(15).

On exactness and unbiasedness of confidence bands for a continuous distribution function

We define a class of confidence bands for distribution functions,named simple confidence bands.The class of bands includes the common step bands and continuous bands,some of which may perform better than the smoothed bands not belonging to the class,e.g.,the kernel smoothed bands.It is shown that under some mild assumptions,the simple bands with exact coverage for continuous distribution functions are all step bands.The unbiasedness problem of the step bands is also investigated.It is proved that most of two-sided step bands are biased and one-sided step bands are unbiased.

Non-unbiasedness of Cramer-von Mises test

This paper shows that for any given level of significance α∈ (0,1), and any sample size n, the Cramer-von Mises test is not unbiased.

Validity of non-local mean filter and novel denoising method

Background Image denoising is an important topic in the digital image processing field.This study theoretically investigates the validity of the classical nonlocal mean filter(NLM)for removing Gaussian noise from a novel statistical perspective.Method By considering the restored image as an estimator of the clear image from a statistical perspective,we gradually analyze the unbiasedness and effectiveness of the restored value obtained by the NLM filter.Subsequently,we propose an improved NLM algorithm called the clustering-based NLM filter that is derived from the conditions obtained through the theoretical analysis.The proposed filter attempts to restore an ideal value using the approximately constant intensities obtained by the image clustering process.In this study,we adopt a mixed probability model on a prefiltered image to generate an estimator of the ideal clustered components.Result The experiment yields improved peak signal-to-noise ratio values and visual results upon the removal of Gaussian noise.Conclusion However,the considerable practical performance of our filter demonstrates that our method is theoretically acceptable as it can effectively estimate ideal images.

Factors of Pumping Capacity in Some Different Types of Channel Brownian Pumps

The motion of particles in different channel Brownian pumps can be described by Langevin equations,and the pumping capacity is a useful indicator to demonstrate the strength of a pump’s transportation ability.Via the simulation,there is always an optimal value of temperature and unbiased external force for different pumps which make the concentration ratio between the right tube and left tube derive its maximum and minimum in two asymmetric tubes respectively.Besides,the concentration ratio will keep 1 regardless of radius,temperature or magnitude of force in the tube in a symmetric tube.To obtain more information about pumping capacity,exploring the average probability current(APC) of tubes in different conditions is necessary.Results indicate that as the concentration ratio is 1,the change of the APC when x_(0)=0 is similar to that when x_(0)=π.Also,when the concentration ratio is more than 1,there are optimal values of temperature,radius and magnitude of force where the APC gains a maximum,and the maximum decreases as the concentration in the right tube increases when x_(0)=0.

Study on the Prediction of Rice Blast Based on the Unbiased GM (1,1) Model

To create a new prediction model, the unbiased GM （1,1） model is optimized by the five-point slide method in this paper. Then, based on the occurrence areas of dce blast in Enshi District during 1995 -2004, the new model and unbiased GM （1, 1 ） model are applied to predict the occurrence areas of rice blast during 2005 -2010. Predicting outcomes show that the prediction accuracy of five-point unbiased sliding optimized GM （1, 1 ） model is higher than the unbiased GM （1,1） model. Finally, combined with the prediction results, the author provides some suggestion for Enshi District in the prevention and control of rice blast in 2010.

Ship motion extreme short time prediction of ship pitch based on diagonal recurrent neural network

A DRNN (diagonal recurrent neural network) and its RPE (recurrent prediction error) learning algorithm are proposed in this paper .Using of the simple structure of DRNN can reduce the capacity of calculation. The principle of RPE learning algorithm is to adjust weights along the direction of Gauss-Newton. Meanwhile, it is unnecessary to calculate the second local derivative and the inverse matrixes, whose unbiasedness is proved. With application to the extremely short time prediction of large ship pitch, satisfactory results are obtained. Prediction effect of this algorithm is compared with that of auto-regression and periodical diagram method, and comparison results show that the proposed algorithm is feasible.

基于收缩估计对投球命中率、三分球命中率和罚球命中率的预测

投球命中率、三分球命中率和罚球命中率是衡量篮球运动员表现的三个重要指标.采用多种估计方法,基于CBA 2014-2015赛季的数据对2015-2016赛季运动员投球命中率、三分球命中率和罚球命中率进行预测,结果表明:采用收缩估计和分类预测是必要的,SUREθ?M是一个非常有竞争力的收缩估计方法.

Robustness of Minimum Norm Quadratic Unbiased Estimator of Variance Under the General Linear Model

Necessary and sufficient conditions for equalities between a 2 y′(I-P Xx)y and minimum norm quadratic unbiased estimator of variance under the general linear model, where a 2 is a known positive number, are derived. Further, when the Gauss? Markov estimators and the ordinary least squares estimator are identical, a relative simply equivalent condition is obtained. At last, this condition is applied to an interesting example.

QTL mapping and QTL × environment interaction analysis of multi-seed pod in cultivated peanut(Arachis hypogaea L.)

To dissect the genetic mechanism of multi-seed pod in peanut, we explored the QTL/gene controlling multi-seed pod and analyzed the interaction effect of QTL and environment. Two hundred and forty eight recombinant inbred lines(RIL) from cross Silihong × Jinonghei 3 were used as experimental materials planted in 8 environments from 2012 to 2017. Three methods of analysis were performed. These included individual environment analysis, joint analysis in multiple environments, and epistatic interaction analysis for multi-seed pod QTL. Phenotypic data and best linear unbiased prediction(BLUP) value of the ratio of multi-seed pods per plant(RMSP) were used for QTL mapping. Seven QTL detected by the individual environmental mapping analysis and were distributed on linkage groups 1, 6, 9, 14, 19(2), and 21. Each QTL explained 4.42%–11.51% of the phenotypic variation in multi-seed pod, and synergistic alleles of5 QTL were from the Silihong parent. One QTL, explaining 4.93% of the phenotypic variation was detected using BLUP data, and this QTL mapped in the same interval as q RMSP19.1 detected in the individual environment analysis. Seventeen additive QTL were identified by joint analysis across multiple environments. A total of 43 epistatic QTL were detected by ICIM-EPI mapping in the multiple environment trials(MET) module, and involved 57 loci. Two main-effect QTL related to multi-seed pod in peanut were filtered. We also found that RMSP had a highly significant positive correlation with pod yield per plant(PY), and epistatic effects were much more important than additive effects. These results provide theoretical guidance for the genetic improvement of germplasm resources and further fine mapping of related genes in peanut.

Adaptive compensating method for Doppler frequency shift using LMS and phase estimation

The novel compensating method directly demodulates the signals without the carrier recovery processes, in which the carrier with original modulation frequency is used as the local coherent carrier. In this way, the phase offsets due to frequency shift are linear. Based on this premise, the compensation processes are： firstly, the phase offsets between the baseband neighbor-symbols after clock recovery is unbiasedly estimated among the reference symbols; then, the receiving signals symbols are adjusted by the phase estimation value; finally, the phase offsets after adjusting are compensated by the least mean squares （LMS） algorithm. In order to express the compensation processes and ability clearly, the quadrature phase shift keying （QPSK） modulation signals are regarded as examples for Matlab simulation. BER simulations are carried out using the Monte-Carlo method. The learning curves are obtained to study the algorithm＇s convergence ability. The constellation figures are also simulated to observe the compensation results directly.

Indoor INS/UWB-based Human Localization With Missing Data Utilizing Predictive UFIR Filtering

A combined algorithm for the loosely fused ultra wide band(UWB)and inertial navigation system(INS)-based measurements is designed under the indoor human navigation conditions with missing data.The scheme proposed fuses the INS-and UWB-derived positions via a data fusion filter.Since the UWB signal is prone to drift in indoor environments and its outage highly affects the integrated scheme reliability,we also consider the missing data problem in UWB measurements.To overcome this problem,the loosely-coupled INS/UWB-integrated scheme is augmented with a prediction option based on the predictive unbiased finite impulse response(UFIR)fusion filter.We show experimentally that,the standard UFIR fusion filter has higher robustness than the Kalman filter.It is also shown that the predictive UFIR fusion filter is able to produce an acceptable navigation accuracy under temporary missing UWB-data.

One compound approach combining factor-analytic model with AMMI and GGE biplot to improve multi-environment trials analysis

To improve multi-environmental trial(MET)analysis,a compound method—which combines factor analytic(FA)model with additive main effect and multiplicative interaction(AMMI)and genotype main effect plus genotype-by-environment interaction(GGE)biplot—was conducted in this study.The diameter at breast height of 36 open-pollinated(OP)families of Pinus taeda at six sites in South China was used as a raw dataset.The best linear unbiased prediction(BLUP)data of all individual trees in each site was obtained by fitting the spatial effects with the FA method from raw data.The raw data and BLUP data were analyzed and compared by using the AMMI and GGE biplot.BLUP results showed that the six sites were heterogeneous and spatial variation could be effectively fitted by spatial analysis with the FA method.AMMI analysis identified that two datasets had highly significant effects on the site,family,and their interactions,while BLUP data had a smaller residual error,but higher variation explaining ability and more credible stability than raw data.GGE biplot results revealed that raw data and BLUP data had different results in mega-environment delineation,test-environment evaluation,and genotype evaluation.In addition,BLUP data results were more reasonable due to the stronger analytical ability of the first two principal components.Our study suggests that the compound method combing the FA method with the AMMI and GGE biplot could improve the analysis result of MET data in Pinus teada as it was more reliable than direct AMMI and GGE biplot analysis on raw data.

Log-logistic parameters estimation using moving extremes ranked set sampling design

In statistical parameter estimation problems,how well the parameters are estimated largely depends on the sampling design used.In the current paper,a modification of ranked set sampling(RSS)called moving extremes RSS(MERSS)is considered for the estimation of the scale and shape parameters for the log-logistic distribution.Several traditional estimators and ad hoc estimators will be studied under MERSS.The estimators under MERSS are compared to the corresponding ones under SRS.The simulation results show that the estimators under MERSS are significantly more efficient than the ones under SRS.

Effect of Multipoint Heterogeneity on Nonlinear Transformations for Geological Modeling: Porosity-Permeability Relations Revisited

An analysis of statistical expected values for transformations is performed in this study to quantify the effect of heterogeneity on spatial geological modeling and evaluations. Algebraic transformations are frequently applied to data from logging to allow for the modeling of geological properties. Transformations may be powers, products, and exponential operations which are commonly used in well-known relations （e.g., porosity-permeability transforms）. The results of this study show that correct computations must account for residual transformation terms which arise due to lack of independence among heterogeneous geological properties. In the case of an exponential porosity-permeability transform, the values may be positive. This proves that a simple exponential model back-transformed from linear regression underestimates permeability. In the case of transformations involving two or more properties, residual terms may represent the contribution of heterogeneous components which occur when properties vary together, regardless of a pair-wise linear independence. A consequence of power- and product-transform models is that regression equations within those transformations need corrections via residual cumulants. A generalization of this result is that transformations of multivariate spatial attributes require multiple-point random variable relations. This analysis provides practical solutions leading to a methodology for nonlinear modeling using correct back transformations in geology.

EMPIRICAL LIKELIHOOD-BASED INFERENCE IN LINEAR MODELS WITH INTERVAL CENSORED DATA

An empirical likelihood approach to estimate the coefficients in linear model with interval censored responses is developed in this paper. By constructing unbiased transformation of interval censored data,an empirical log-likelihood function with asymptotic X^2 is derived. The confidence regions for the coefficients are constructed. Some simulation results indicate that the method performs better than the normal approximation method in term of coverage accuracies.

A Fusion Kalman Filter and UFIR Estimator Using the Influence Function Method

In this paper,the Kalman filter(KF)and the unbiased finite impulse response(UFIR)filter are fused in the discrete-time state-space to improve robustness against uncertainties.To avoid the problem where fusion filters may give up some advantages of UFIR filters by fusing based on noise statistics,we attempt to find a way to fuse without using noise statistics.The fusion filtering algorithm is derived using the influence function that provides a quantified measure for disturbances on the resulting filtering outputs and is termed as an influence finite impulse response(IFIR)filter.The main advantage of the proposed method is that the noise statistics of process noise and measurement noise are no longer required in the fusion process,showing that a critical feature of the UFIR filter is inherited.One numerical example and a practice-oriented case are given to illustrate the effectiveness of the proposed method.It is shown that the IFIR filter has adaptive performance and can automatically switch from the Kalman estimate to the UFIR estimates according to operating conditions.Moreover,the proposed method can reduce the effects of optimal horizon length on the UFIR estimate and can give the state estimates of best accuracy among all the compared methods.

De-correlated unbiased sequential filtering based on best unbiased linear estimation for target tracking in Doppler radar

In target tracking applications,the Doppler measurement contains information of the target range rate,which has the potential capability to improve the tracking performance.However,the nonlinear degree between the measurement and the target state increases with the introduction of the Doppler measurement.Therefore,target tracking in the Doppler radar is a nonlinear filtering problem.In order to handle this problem,the Kalman filter form of best linear unbiased estimation(BLUE)with position measurements is proposed,which is combined with the sequential filtering algorithm to handle the Doppler measurement further,where the statistic characteristic of the converted measurement error is calculated based on the predicted information in the sequential filter.Moreover,the algorithm is extended to the maneuvering target tracking case,where the interacting multiple model(IMM)algorithm is used as the basic framework and the model probabilities are updated according to the BLUE position filter and the sequential filter,and the final estimation is a weighted sum of the outputs from the sequential filters and the model probabilities.Simulation results show that compared with existing approaches,the proposed algorithm can realize target tracking with preferable tracking precision and the extended method can achieve effective maneuvering target tracking.

Nonlinear total least-squares variance component estimation for GM(1,1)model

The solution of the grey model(GM(1,1)model)generally involves equal-precision observations,and the(co)variance matrix is established from the prior information.However,the data are generally available with unequal-precision measurements in reality.To deal with the errors of all observations for GM(1,1)model with errors-in-variables(EIV)structure,we exploit the total least-squares(TLS)algorithm to estimate the parameters of GM(1,1)model in this paper.Ignoring that the effect of the improper prior stochastic model and the homologous observations may degrade the accuracy of parameter estimation,we further present a nonlinear total least-squares variance component estimation approach for GM(1,1)model,which resorts to the minimum norm quadratic unbiased estimation(MINQUE).The practical and simulative experiments indicate that the presented approach has significant merits in improving the predictive accuracy in comparison with control methods.