Parameter mixing errors within a measuring volume with applications to incoherent scatter

The effect on parameter error estimates resulting from parameter variations within the measuring volume under consideration is studied in the framework of linear statistical inversion theory. It is shown that using estimates for the parameter averages is equivalent to having the theory corrected by the covariances of the variables coupled with the second derivatives of the theory function. If the parameter distributions were known exactly, this would only introduce a bias in the linear theory and hence a systematic error in the parameter centre point estimates. When the distributions are not known exactly, there is another source of error consisting of the uncertainties in the parameter variation estimates. This leads to new error bounds on the allowed parameter variability within the volume under consideration if some prescribed accuracy in the parameter average estimates is required. These considerations are applied to incoherent scatter (IS) radar measurements, where it is important to be able to estimate the effect of integrating both in space and time over a volume with varying parameters in order to obtain spectra or autocorrelation functions. Numerical examples are given in the case of the O⁺ content estimates in measurements with the EISCAT UHF radar, when for example the ion temperature varies over the integration ranges. The results obtained may be used in the design of experiments when high resolution composition measurements are required.     

Elongation of midlatitude scintillation irregularities

This paper reports a study of the length of the midlatitude F-region irregularities which cause scintillations. The length of scintillation irregularities is usually measured by the Full Correlation Analysis (FCA) method. If observations from a typical 3-receiver array, with small spacing, are used the length is always found to he only a few kilometers. Basic ionospheric theory indicates that the irregularities should he much longer than this. In this experiment scintillations of beacon transmissions from polar-orbiting satellites were observed on a 3-receiver array with 310 m spacing, and a fourth receiver 4.6 km away was used to check the lengths measured. Analysis of the scintillation observations from the 310 m array used the FCA method. In all cases the FCA lengths, from the small array, were much shorter than those measured by the distant receiver. Measurements using the 4.6 km receiver gave an average ratio of 44.5 and a half-length (in ionosphere) of 9.4 km. It appears that random errors in the correlation functions cause the FCA to underestimate the length of the ground pattern of irregularities when the spacing of the receivers is much less than the pattern size.     

The effect of a priori knowledge on parameter estimation errors with applications to incoherent scatter

The dependence of the width of the a posteriori distribution (i.e. parameter estimation error) in a multiparameter fit on the a priori width of another parameter is studied in the framework of linear statistical inversion theory. An exact formula is given which makes it possible to estimate how accurate the a priori information on a given parameter must be in order to obtain the other parameter with a prescribed accuracy. These estimates are useful in those cases where some errors are strongly correlated, like the ion temperature and the O⁺ content in incoherent scatter measurements with the EISCAT UHF radar. The dependence of the solution on the accuracy of the power profile estimates is given. Likewise, the behaviour of the error when a linear combination of the parameters is known exactly is given. The formulae given have a very simple geometrical meaning, and together they give a complete solution to the problem of estimating the accuracies in a multiparameter fit when a linear combination of the variables is known with a prescribed accuracy. It is shown that under the conditions considered in this paper, oxygen content can be determined to an accuracy of 10 % when the ion temperature is known to within 7 %, if we can assume that the collision frequency is zero.     

Coherent-array HF Doppier sounding of traveling ionospheric disturbances: II. Assessment of errors

We examine errors which are likely to occur in the compact-array HF sounding technique for determining the velocity of traveling ionospheric disturbances. The errors arise from ionospheric irregularities (either large-scale specular facets, or fine-scale scatterers) and from the presence of multiple disturbance undulations propagating simultaneously with different velocities. The errors are either systematic (that is, not causing internal inconsistencies within the array velocimetry data) or random (that is, causing quantifiable inconsistencies between alternative velocity estimates furnished by the array). The random errors can be directly assessed using array data, as is illustrated for actual data from a 16-channel array.     

First results with the Adelaide VHF radar: spaced antenna studies of tropospheric winds

The first results from a VHF radar of the ST type located at Buckland Park near Adelaide, Australia (35°S, 138°E), are presented. The radar is designed to be versatile and can be used to measure velocities in the lower atmosphere using both the spaced antenna (SA) and Doppler beam-swinging (DBS) techniques. Here studies of irregularities and motions made with the spaced antenna technique are discussed. It is shown that the scale of the diffraction pattern formed by the backscattered radiation varies with altitude, with the mean pattern scale being smaller in the troposphere than in the stratosphere. The observations are consistent with the backscattered energy decreasing as a function of off-vertical angle by 1.5 dB per degree in the troposphere and by about 2.8 dB per degree in the lower stratosphere. An intercomparison of zonal velocities measured with the SA and DBS methods shows good agreement. In May and August 1984 an extensive comparison was made between the velocities measured by the SA method and winds determined from over 80 balloon-borne radiosondes released from Adelaide Airport, situated some 36 km to the south of the radar. The velocities were compared on a statistical basis and showed excellent agreement, although the SA speeds tended to be 1–2 m s⁻¹ smaller in magnitude than the radiosonde velocities. Overall, the rms differences between the two sets of measurements was only 3–4ms⁻¹ throughout the troposphere, a result which is consistent with the random errors inherent in each technique, as well as the spatial separation between the radar and balloon observations. The utility of the SA method for meteorological observations is illustrated by a study of both the horizontal and vertical wind fields during the passage of a cold front made in November 1984. The high time resolution available with the radar allows detailed studies of the development of the pre-frontal jet, the wind convergence into the front and associated vertical motions.     

Changes of pulsation activity during two solar cycles

Monthly and yearly averages of the pulsation activity in the mid-latitude station Nagycenk are compared to solar wind velocity and ionospheric-plasmaspheric electron concentration data. It is found that pulsation amplitudes are correlated with solar wind velocities with the exception of some month around December in solar maximum years, when they are significantly lower than computed from the corresponding solar wind velocities. This decrease can be caused either by a cutoff of the magnetospheric shell resonances or by local ionospheric damping. In addition to these effects, pulsations amplitudes slightly depend also on the geomagnetic activity and have a semi-annual activity change with maxima around equinoxes.     

Measurement of vertical phase and group velocities of atmospheric gravity waves by VHF radar

A systematic method of deriving from MST radar data the group velocity and phase velocity of the atmospheric wave along the radar beam direction is proposed and verified by a series of numerical simulations. We apply the method to two data sets measured by Chung-Li radar under different background wind conditions. It is found that the vertical group velocity and phase velocity are mostly in the opposite direction when the background wind is weak. The energy source of downgoing wave packets was evidently related to the instability in the upper height range (10.5–11.7 km) where strong wind shear existed. When the background wind and wind shear are stronger, the vertical group and phase velocities may propagate in the same direction. We also found from numerical simulation and data analysis that the wave packet of gravity waves following power law spectrum are short-lived. A by-product of the group velocity measurement is that the horizontal wavelength may also be deduced from a vertical radar beam measurement from the dispersion relation if it is valid.     

江苏省县域经济集聚和收敛的空间计量分析

通过探索性空间数据分析和空间计量分析方法,以实际人均GDP为测度指标,对江苏省65个县市的经济空间集聚、增长收敛性以及收敛机制进行讨论。研究发现1993-2009年实际人均GDP显示出越来越高的全局正相关,局部空间相关性也有增强的趋势。空间计量分析结果表明江苏省县域经济存在着β收敛,分时段研究为不同研究时段选择恰当的空间收敛模型后,收敛速度加快。技术扩散收敛机制和资本收敛机制分别在研究区间的前期和后期占主导作用,收敛机制的转变与江苏省在20世纪90年代末开始实行的区域协调发展政策密切相关。     

DIAGNOSTICS FOR REGRESSION MODELING IN SPATIAL ECONOMETRICS*

ABSTRACT. This paper describes statistics for model criticism in spatial econometrics. The purpose of these statistics is to evaluate how well a chosen model fits the data and to identify influential cases and how they affect the aggregate picture. The paper reviews results in Martin (1992) for the regression model with correlated errors where the coefficients of the variance matrix are assumed either known or fixed. The problems of applying the statistics in spatial econometric modeling are discussed. An application is reported which considers diagnostics for the mean function and highlights cases that might influence estimates of the parameter of the error model. Different ways of assessing the influence of cases are also described.     

Reducing Errors in Rainfall Estimates through Rain Gauge Location

Facility location models are examined as a framework for generating rain gauge networks designed to reduce errors in mean areal precipitation (MAP) estimation. Errors in estimating MAP may be divided into two types: (i) capture error, not observing a storm which occurs in a gauged area, and (ii) extrapolation error, using a rain gauge measurement to represent a heterogeneous area. In this paper, five rain gauge location models are developed to minimize these errors. The models include adaptations of the maximal covering location problem, the p-median model, and three models derived from multicriteria cluster analysis. The models are tested using precipitation data from an experimental watershed maintained by the U.S. Department of Agriculture in Arizona. Analysis of the results reveals, for the particular watershed, that (1) in sparse networks, location of rain gauges can play a larger role than number of rain gauges in reducing errors in MAP estimates; (2) models based on mean hydrologic data provide nearly as good networks as models based on spatially correlated data; and (3) models yielding the best networks for estimating precipitation for flood predictions are different from the models providing the best precipitation estimates for low flow forecasts.     

Heterogeneity of Attribute Sampling Error in Spatial Data Sets

This paper considers the standard error of the estimate of the mean of a spatially correlated variable in the case where data are obtained by a process of random sampling. Two distinct mean estimation problems are identified: estimating the area mean and estimating the population mean. Methods are described for obtaining standard error estimates in the two cases and, within the limits of publicly available information, the methods are implemented on average household income data at the census tract scale for Syracuse, New York. The purpose of the paper is to draw attention to issues of data precision in relation to sampled geographic information on averages and in particular to consider the problems of estimating standard errors using such data. The paper also examines the extent to which standard errors vary between census tracts.     

Statistics of incoherent scatter multiparameter fits

A new statistical inversion method to estimate the errors in incoherent scatter measurements for a given set of ionospheric parameters is presented. The possibilities to determine the ion composition in a multiparameter fit are considered. The method can also be applied to estimate the requirements on the measurement of autocorrelation functions to find the minimum possible lag resolution and lag extent for a stable inversion solution of the plasma parameters, and the temperature interval for which a stable solution exists, with or without the zero lag data. The results are illustrated in the case of a multipulse code.     

A Comparison of Spatially Varying Regression Coefficient Estimates Using Geographically Weighted and Spatial‐Filter‐Based Techniques

Geographically weighted regression (GWR) is a technique that explores spatial nonstationarity in data‐generating processes by allowing regression coefficients to vary spatially. It is a widely applied technique across domains because it is intuitive and conforms to the well‐understood framework of regression. An alternative method to GWR that has been suggested is spatial filtering, which it has been argued provides a superior alternative to GWR by producing spatially varying regression coefficients that are not correlated with each other and which display less spatial autocorrelation. It is, therefore, worthwhile to examine these claims by comparing the output from both methods. We do this by using simulated data that represent two sets of spatially varying processes and examining how well both techniques replicate the known local parameter values. The article finds no support that spatial filtering produces local parameter estimates with superior properties. The results indicate that the original spatial filtering specification is prone to overfitting and is generally inferior to GWR, while an alternative specification that minimizes the mean square error (MSE) of coefficient estimates produces results that are similar to GWR. However, since we generally do not know the true coefficients, the MSE minimizing specification is impractical for applied research.     

Errors in velocities determined from EISCAT data

It has been reported that unusually large errors are observed in velocities derived from EISCAT data in which the power in the returned signal falls to less than 2% of that in the background noise. This suggestion has been investigated using a specialised interactive analysis package, and possible causes, both in the data and in the analysis, were considered. Subsequently, an adaptation of the usual procedure for velocity determination was considered. This involved applying the normal method to the raw data without first subtracting the background noise. The advantages of this technique are discussed, in particular for data in which the returned signal is relatively weak.     

Retrieval of east-west wind in the equatorial electrojet from the local wind-generated electric field

The paper presents a method to retrieve the height-varying east-west wind U(z) in the equatorial electrojet from the local wind generated electric field E_W(z), or from the radar-measured phase velocity V_p^II(z) of the type II plasma waves. The method is found to be satisfactory when E_w ⪢ E_p, where E_p is the vertical polarization electric field generated by the global scale east-west electric field, EY, and E_y < 0.2 mV m⁻¹. Measurements of V_p^II by a VHF backscatter radar can be inverted to obtain the causative wind profile by this method. The method is tested using a simulation study in which E_w(z) and V_p^II(z) as generated by two different wind models are used. The retrieved winds are compared with the original wind profiles and it is found that the error in the retrieved winds is mostly under 5%, for the case of no errors in the model Pedersen conductivity (σ₁) profile and the E_w(z) or V_p^II(z)(z) profiles used in the inversion. Even with a ±20% error in the above profiles, the errors in the retrieved winds are found to be less than 20% over 75% of the altitude range and 20–30% for the remaining 25% of the altitude range, on the average.     

Testing child-woman ratios and the own-children method on the 1900 Sweden census: Examples of indirect fertility estimates by socioeconomic status in a historical population

Focusing on the Swedish census of 1900, the child-woman ratio and own-children method have been applied to assess socioeconomic differences in fertility. These indirect estimates of fertility have been compared to the vital statistics at the national level to assess their reliability. This comparison demonstrated that the estimated results suffered from few errors. Even if these indirect estimates of fertility could be affected by possible socioeconomic differences in mortality, the tests show that at least in the Swedish case, the impact of mortality on the indirect measures is limited. As infant mortality differences by socioeconomic status are relatively small, indirect fertility estimates are mainly affected by differences in reproductive behavior.     

Observations on Seasonality and Mortality from a Recent Catastrophic Death Assemblage

On 3 November 1991, a group of 150 pronghorn went over a cliff near Green River, Wyoming. This mortality site provides a unique opportunity to examine a number of characteristics of catastrophic death assemblages that may aid in the interpretation of archaeological bonebed sites. In 1993, the mandibles were collected for a study of seasonality and age estimation. Examination of seasonality revealed some variation in estimates by eruption/wear and cementum increments. Six percent of 86 fawn specimens exhibit eruption and wear more advanced than expected for a November third event, and 21% of 28 cementum increment estimates differ from the known November third mortality date by a month or more. These data suggest some degree of error is inherent in seasonality estimates that must be considered when interpreting seasonal distributions. Age estimates by eruption and wear reveal a distribution of pronghorn ages with many more juvenile animals than expected for a known “catastrophic” event. This may be explained by the pattern of seasonal hunting in a modern managed herd, which is likely to be very different than aboriginal hunting patterns. Age estimates by eruption/wear and cementum increment techniques failed to agree within six months in 48% of 29 test cases, with a tendency for cementum ages to be younger in 71% of specimens in which estimates of age differed. In general, the mandible assemblage exhibited more variability than one might expect for a single catastrophic kill event.     

THE SENSITIVITY OF INPUT-OUTPUT MULTIPLIERS*

The present paper derives analytical expressions for the sensitivity of input-output multipliers to errors in the data. The effects on the simple output multipliers are investigated for additive errors, multiplicative errors in the columns, multiplicative errors in the rows, error rectangles, the error couple and the single error, and price changes. In contrast to earlier investigations, the results are not obtained from the Leontief inverse. The present approach focusses on the effects of errors on the eigenvector corresponding to the dominant eigenvalue. It is indicated how similar expressions may be derived for several other multipliers.     

ISSUES IN SPATIAL DATA ANALYSIS

ABSTRACT.  Misspecified functional forms tend to produce biased estimates and spatially correlated errors. Imposing less structure than standard spatial lag models while being more amenable to large datasets, nonparametric and semiparametric methods offer significant advantages for spatial modeling. Fixed effect estimators have significant advantages when spatial effects are constant within well-defined zones, but their flexibility can produce variable, inefficient estimates while failing to account adequately for smooth spatial trends. Though estimators that are designed to measure treatment effects can potentially control for unobserved variables while eliminating the need to specify a functional form, they may be biased if the variables are not constant within discrete zones.