TESTING OF CORRELATION AND HETEROSCEDASTICITY IN NONLINEAR REGRESSION MODELS WITH DBL(p,q,1) RANDOM ERRORS

Chaos theory has taught us that a system which has both nonlinearity and random input will most likely produce irregular data. If random errors are irregular data, then random error process will raise nonlinearity （Kantz and Schreiber （1997））. Tsai （1986） introduced a composite test for autocorrelation and heteroscedasticity in linear models with AR（1） errors. Liu （2003） introduced a composite test for correlation and heteroscedasticity in nonlinear models with DBL（p, 0, 1） errors. Therefore, the important problems in regression model axe detections of bilinearity, correlation and heteroscedasticity. In this article, the authors discuss more general case of nonlinear models with DBL（p, q, 1） random errors by score test. Several statistics for the test of bilinearity, correlation, and heteroscedasticity are obtained, and expressed in simple matrix formulas. The results of regression models with linear errors are extended to those with bilinear errors. The simulation study is carried out to investigate the powers of the test statistics. All results of this article extend and develop results of Tsai （1986）, Wei, et al （1995）, and Liu, et al （2003）.

Estimation of random errors for lidar based on noise scale factor

Estimation of random errors, which are due to shot noise of photomultiplier tube(PMT) or avalanche photodiode(APD) detectors, is very necessary in lidar observation. Due to the Poisson distribution of incident electrons, there still exists a proportional relationship between standard deviation and square root of its mean value. Based on this relationship,noise scale factor(NSF) is introduced into the estimation, which only needs a single data sample. This method overcomes the distractions of atmospheric fluctuations during calculation of random errors. The results show that this method is feasible and reliable.

ON DESIGN METHOD OF THE PRECISION CAM PROFILE WITH RANDOM PROCESSING ERRORS

Based on probability and statistic, a design method of precision cam profileconcerning the influence of random processing errors is advanced. Combining the design with theprocess, which can be used to predict that cam profiles will be successfully processed or not in thedesign stage, design of the cam can be done by balancing the economization and reliability. Inaddition, an fuzzy deduction method based on Bayers formula is advanced to estimate processingreasonable of the designed precision cam profile, and it take few samples.

Error Threshold of Fully Random Eigen Model

Species evolution is essentially a random process of interaction between biological populations and their environ- ments. As a result, some physical parameters in evolution models are subject to statistical fluctuations. In this work, two important parameters in the Eigen model, the fitness and mutation rate, are treated as Gaassian dis- tributed random variables simultaneously to examine the property of the error threshold. Numerical simulation results show that the error threshold in the fully random model appears as a crossover region instead of a phase transition point, and ＆s the fluctuation strength increases the crossover region becomes smoother and smoother. Furthermore, it is shown that the randomization of the mutation rate plays a dominant role in changing the error threshold in the fully random model, which is consistent with the existing experimental data. The implication of the threshold change due to the randomization for antiviral strategies is discussed.

Effect of random phase error and baseline roll angle error on eddy identification by interferometric imaging altimeter

To achieve better observation for sea surface,a new generation of wide-swath interferometric altimeter satellites is proposed.Before satellite launch,it is particularly important to study the data processing methods and carry out the detailed error analysis of ocean satellites,because it is directly related to the ultimate ability of satellites to capture ocean information.For this purpose,ocean eddies are considered a specific case of ocean signals,and it can cause significant changes in sea surface elevation.It is suitable for theoretical simulation of the sea surface and systematic simulation of the altimeter.We analyzed the impacts of random error and baseline error on the sea surface and ocean signals and proposed a combined strategy of low-pass filtering,empirical orthogonal function(EOF)decomposition,and linear fitting to remove the errors.Through this strategy,sea surface anomalies caused by errors were considerably improved,and the capability of satellite for capturing ocean information was enhanced.Notably,we found that the baseline error in sea surface height data was likely to cause inaccuracy in eddy boundary detection,as well as false eddy detection.These abnormalities could be prevented for"clean"sea surface height after the errors removal.

THE APPLICATION OF RANDOM METRIC SPACE IN ERROR ESTIMATE

Throughout this paper,let(Ω,ι,μ)be a probability space,D the collection of allleft-continuous distribution functions,and D^+={F(0)=0|F∈D},and L(Ω)the collec-tion of all random variables which is a.s.finite on Ω,and L^+={ξ≥0 a.s.|ξ∈L(Ω)}.For random metric (normed) spaces,see [1]or[2].Theorem 1 Let(M,d)be a complete metric space f:M→M,a contract mappingwith contract coefficient α∈[0,1),L(Ω,m)the collection of all M-valued random vari-

Intercomparison of GPS radiosonde soundings during the eastern tropical Indian Ocean experiment

Temperature and relative humidity profiles derived from two China-made global positioning system（GPS） radiosondes（GPS-TK and CF-06-A） during the east tropical Indian Ocean（ETIO） experiment were compared with Vaisala RS92-SGP to assess the performances of China-made radiosondes over the tropical ocean.The results show that there have relative large biases in temperature observations between the GPSTK and the RS92-SGP in the low troposphere,with a warm bias of greater than 2 K in the day and a cooling bias of 0.6 K at night.The temperature differences of the CF-06-A were small in the troposphere both in daytime and nighttime,and became large peak-to-peak fluctuations in the stratosphere.The intercomparison of the relative humidity showed that the CF-06-A had large random errors due to the limitation of sensors and the lack of correction scheme,and the GPS-TK had large systematic biases in the low troposphere which might be related to the temperature impact.GPS height measurements are clearly suitable for China-made radiosonde systems operation.At night,the CF-06-A and the GPS-TK could provide virtual potential temperature and atmospheric boundary layer height measurements of suitable quality for both weather and climate research.As a result of the intercomparison experiment,major errors in the Chinamade radiosonde systems were well indentified and subsequently rectified to ensure improving accuracy for historical and future radiosondes.

A Report on a Biotite-Calcic Hornblende Geothermometer

This paper presents a biotite-calcic hornblende geothermometer which wasempirically calibrated based on the garnet-biotite geothermometer and thegarnet-plagioclase-hornblende-quartz geobarometer, in the ranges of 560-800 deg C (T) and 0.26-l.4GPa (P) using the data of metadolerite, amphibolite, metagabbro, and metapelite collected from theliterature. Biotite was treated as symmetric Fe-Mg-Al^VI-Ti quaternary solid solution, and calcichornblende was simplified as symmetric Fe-Mg binary solid solution. The resulting thermometer mayrebuild the input garnet-biotite temperatures well within an uncertainty of + - 50 deg C. Errors of+- 0.2 GPa for input pressure, along with analytical errors of = - 5 percent for the relevantmineral compositions, may lead to a random error of + - 16 deg C for this thermometer, so that thethermometer is almost independent of pressure estimates. The thermometer may clearly discriminatedifferent rocks of lower amphibolite, upper amphibolite and granulite facies on a high confidencelevel. It is assumed that there is a ferric iron content of 11.6 percent in biotite, and that theiron content in calcic hornblende may be calculated according to the method of Dale et al. (2000).This thermometer can be used for medium- to high-grade metabasites and metapelites.

Unitary Noise and the Mermin-GHZ Game

Communication complexity is an area of classical computer science which studies how much communication is necessary to solve various distributed computational problems.Quantum information processing can be used to reduce the amount of communication required to carry out some distributed problems.We speak of pseudo-telepathy when it is able to completely eliminate the need for communication.Since it is generally very hard to perfectly implement a quantum winning strategy for a pseudo-telepathy game,quantum players are almost certain to make errors even though they use a winning strategy.After introducing a model for pseudotelepathy games,we investigate the impact of erroneously performed unitary transformations on the quantum winning strategy for the Mermin-GHZ game.The question of how strong the unitary noise can be so that quantum players would still be better than classical ones is also dealt with.

Assessment of the State of Forests Based on Joint Statistical Processing of Sentinel-2B Remote Sensing Data and the Data from Network of Ground-Based ICP-Forests Sample Plots

The research was carried out on the territory of the Karelian Isthmus of the Leningrad Region using Sentinel-2B images and data from a network of ground sample plots. The ground sample plots are located in the studied territory mainly in a regular manner, laid and surveyed according to the ICP-Forests methodology with some additions. The total area of the sample plots is a small part of the entire study area. One of the objectives of the study was to determine the possibility of using the k-NN (nearest neighbor method) to assess the state of forests throughout the whole studied territory by joint statistical processing of data from ground sample plots and Sentinel-2B imagery. The data of the ground-based sample plots were divided into 2 equal parts, one for the application of the k-NN method, the second for checking the results of the method application. The systematic error in determining the mean damage class of the tree stands on sample plots by the k-NN method turned out to be zero, the random error is equal to one point. These results offer a possibility to determine the state of the forest in the entire study area. The second objective of the study was to examine the possibility of using the short-wave vegetation index (SWVI) to assess the state of forests. As a result, a close statistically reliable dependence of the average score of the state of plantations and the value of the SWVI index was established, which makes it possible to use the established relationship to determine the state of forests throughout the studied territory. The joint use and statistical processing of remotely sensed data and ground-based test areas by the two studied methods make it possible to assess the state of forests throughout the large studied area within the image. The results obtained can be used to monitor the state of forests in large areas and design appropriate forestry protective measures.

Non-piece-wise error compensation for grating displacement measurement system with absolute zero mark

A method for compensating the measuring error of the grating displacement measurement system with absolute zero mark is presented. It divides the full scale range into piece-wise subsections and compares the maximum variation of the measuring errors of two adjacent subsections with the threshold. Whether the specified subsection is divided into smaller subsections is determined by the comparison result. After different compensation parameters and weighted average values of the random errors are obtained, the error compensation algorithm is implemented in the left and right subsections, and the whole measuring error of the grating displacement measurement system is reduced by about 73%. Experimental results show that the method may not only effectively compensate the spike error but also greatly improve the precision of the measuring system.

A PARAMETRIC METHOD OF SITE ERROR ESTIMATION FOR A LIGHTNING LOCATION SYSTEM

In this paper,a parametric method of site error estimation is developed for a lightning location system (LLS) which consists of three or more direction finders (DFs) and one position analyzer (PA). The site error for each DF is a function of bearings measured by the DF, and is assumed to be limited-term harmonics. The problem of site error estimation is reduced to a non-linear unconstrained minimization problem by employing the eigen technique (Orville Jr., 1987). The site error can be found directly by minimizing the objective function. By using the data set obtained with the LLS of three DFs in Beijing area during the summer of 1988, the site error correction curves for all DFs were found. About 4900 lightning flashes detected by the three DFs were used. The results showed that about 95% of the flash residuals of the sample were within ± 1 degree after corrections. The lightning locations with site error corrections were more consistent with the corresponding radar echoes than those without corrections.

Error Sensitivity Analysis in 10–30-Day Extended Range Forecasting by Using a Nonlinear Cross-Prediction Error Model

Extended range forecasting of 10-30 days, which lies between medium-term and climate prediction in terms of timescale, plays a significant role in decision-making processes for the prevention and mitigation of disastrous met- eorological events. The sensitivity of initial error, model parameter error, and random error in a nonlinear cross- prediction error （NCPE） model, and their stability in the prediction validity period in 1 0-30-day extended range fore- casting, are analyzed quantitatively. The associated sensitivity of precipitable water, temperature, and geopotential height during cases of heavy rain and hurricane is also discussed. The results are summarized as follows. First, the initial error and random error interact. When the ratio of random error to initial error is small （10＂5-10-2）, minor vari- ation in random error cannot significantly change the dynamic features of a chaotic system, and therefore random er- ror has minimal effect on the prediction. When the ratio is in the range of 10-1-2 （i.e., random error dominates）, at- tention should be paid to the random error instead of only the initial error. When the ratio is around 10 2-10-1, both influences must be considered. Their mutual effects may bring considerable uncertainty to extended range forecast- ing, and de-noising is therefore necessary. Second, in terms of model parameter error, the embedding dimension m should be determined by the factual nonlinear time series. The dynamic features of a chaotic system cannot be depic- ted because of the incomplete structure of the attractor when m is small. When m is large, prediction indicators can vanish because of the scarcity of phase points in phase space. A method for overcoming the cut-off effect （m 〉 4） is proposed. Third, for heavy rains, precipitable water is more sensitive to the prediction validity period than temperat- ure or geopotential height; however, for hurricanes, geopotential height is most sensitive, followed by precipitable water.