Kinds Of Estimates Research Articles

Statistical asymptotic theory of active learning

We study a parametric estimation problem. Our aim is to estimate or to identify the conditional probability which is called the system. We suppose that we can select appropriate inputs to the system when we gather the training data. This kind of estimation is called active learning in the context of the artificial neural networks. In this paper we suggest new active learning algorithms and evaluate the risk of the algorithms by using statistical asymptotic theory. The algorithms are regarded as a version of the experimental design with two-stage sampling. We verify the efficiency of the active learning by simple computer simulations.

Some new applications of the pointwise relations for the relative rearrangement

Let $V=V(\Omega)$ be a set satisfying the Poincaré-Sobolev pointwise inequalities for the relative rearrangement and $\rho$ an arbitrary norm on the set of measurable functions on the interval $\Omega_*=(0,measure(\Omega))$. Then using the associate norm of $\rho$, we give some sufficient conditions to ensure that a function $u$ of $V$ has to be bounded or integrable in an Orlicz space. We show similar results for a solution of quasilinear equation under some conditions between the data and $\rho$. We then give an unified approach for many kinds of estimates. Using a main relation involving some pointwise relations for the relative rearrangement, we prove a regularity result for the time derivative of a parabolic system well posed in a Grand Sobolev space.

Isotropy vs anisotropy in small-scale turbulence

The decay of large-scale anisotropies in small-scale turbulent flow is investigated. By introducing two different kinds of estimators we discuss the relation between the presence of a hierarchy for the isotropic and the anisotropic scaling exponents and the persistence of anisotropies. By direct measurements on a channel flow numerical simulation we show that the presence of a hierarchy for the isotropic and the anisotropic scaling exponent is not in contradiction with the persistence of anisotropies at small scales.

Reconciling Conflicting Evidence on the Performance of Propensity-Score Matching Methods

There is a long-standing debate in the literature over whether social programs can be reliably evaluated without a randomized experiment. This paper summarizes results from a larger paper (Smith and Todd, 2001) that uses experimental data combined with nonexperimental data to evaluate the performance of alternative nonexperimental estimators. The impact estimates based on experimental data provide a benchmark against which to judge the performance of nonexperimental estimators. Our experimental data come from the National Supported Work (NSW) Demonstration and the nonexperimental data from the Current Population Survey (CPS) and the Panel Study of Income Dynamics (PSID). These same data were used in influential papers by Robert LaLonde (1986), James Heckman and Joseph Hotz (1989), and Rajeev Dehejia and Sadek Wahba (1998, 1999). We focus on a class of estimators called propensity-score matching estimators, which were introduced in the statistics literature by Paul Rosenbaum and Donald Rubin (1983). Traditional propensity-score matching methods pair each program participant with a single nonparticipant, where pairs are chosen based on the degree of similarity in the estimated probabilities of participating in the program (the propensity scores). More recently developed nonparametric matching estimators described in Heckman et al. (1997, 1998a, b) use weighted averages over multiple observations to construct matches. We apply both kinds of estimators in this paper. Heckman et al. (1997, 1998a, b) evaluate the performance of matching estimators using experimental data from the U.S. National Job Training Partnership Act (JTPA) Study combined with comparison group samples drawn from three sources. They show that data quality is a crucial ingredient to any reliable estimation strategy. Specifically, the estimators they examine are only found to perform well in replicating the results of the experiment when they are applied to comparison group data satisfying the following criteria: (i) the same data sources (i.e., the same surveys or the same type of administrative data or both) are used for participants and nonparticipants, so that earnings and other characteristics are measured in an analogous way, (ii) participants and nonparticipants reside in the same local labor markets, and (iii) the data contain a rich set of variables relevant to modeling the program-participation decision. If the comparison group data fails to satisfy these criteria, the performance of the estimators diminishes greatly. More recently, Dehejia and Wahba (1998, 1999) have used the NSW data (also used by LaLonde) to evaluate the performance of propensity-score matching methods, including pairwise matching and caliper matching. They find that these simple matching estimators succeed in closely replicating the experimental NSW results, even though the comparison group data do not satisfy any of the criteria found to be important in Heckman et al. (1997, 1998a). From this evidence, they conclude that matching approaches are generally more reliable than traditional econometric estimators. In this paper, we reanalyze the NSW data in an attempt to reconcile the conflicting findings * Smith: Department of Economics, University of Western Ontario, Social Science Centre, London, ON, N6A 5C2, Canada, and NBER; Todd: Department of Economics, University of Pennsylvania, 3718 Locust Walk, Philadelphia, PA 19104, and NBER. Versions of the paper that is the source for this paper have been presented at a 2000 meeting of the Institute for Research on Poverty in Madison, Wisconsin, at the Western Research Network on Employment and Training summer workshop (August 2000), at the Canadian International Labour Network meetings (September 2000), and at the University of North Carolina. We thank James Heckman for comments on this paper, and we thank Robert LaLonde for comments and for providing us with the data from his 1986 study. We thank Rajeev Dehejia for providing us with information helpful in reconstructing the samples used in the Dehejia and Wahba (1998, 1999) studies. Jingjing Hsee and Miana Plesca provided excellent research assistance.

Strong uniform convergence for the estimator of the regression function under φ-mixing conditions

Suppose the observations (Xi,Yi), i=1,…, n, are ϕ-mixing. The strong uniform convergence and convergence rate for the estimator of the regression function was studied by serveral authors, e.g. G. Collomb (1984), L. Gyorfi et al. (1989). But the optimal convergence rates are not reached unless the Yi are bounded or the E exp (a|Yi|) are bounded for some a>0. Compared with the i.i.d. case the convergence of the Nadaraya-Watson estimator under ϕ-mixing variables needs strong moment conditions. In this paper we study the strong uniform convergence and convergence rate for the improved kernel estimator of the regression function which has been suggested by Cheng P. (1983). Compared with Theorem A in Y. P. Mack and B. Silverman (1982) or Theorem 3.3.1 in L. Gyorfi et al. (1989), we prove the convergence for this kind of estimators under weaker moment conditions. The optimal convergence rate for the improved kernel estimator is attained under almost the same conditions of Theorem 3.3.2 in L. Gyorfi et al. (1989).

ON THE STUDY OF VLSI DERIVATION FOR OPTICAL FLOW ESTIMATION

In this paper we propose studying several ways to implement a realistic and efficient VLSI design for a gradient-based dense motion estimator. The kind of estimator we focus on belongs to the class of differential methods. It is classically based on the optical flow constraint equation in association with a smoothness regularization term and also incorporates robust cost functions to alleviate the influence of large residuals. This estimator is expressed as the minimization of a global energy function defined within the framework of an incremental formulation associated with a multiresolution setup. In order to make possible the conception of efficient hardware, we consider a modified minimization strategy. This new minimization strategy is not only well suited to VLSI derivation, it is also very efficient in terms of quality of the result. The complete VLSI derivation is realized using high-level specifications.

Linear system identification using the TLS EXIN neuron

The paper presents a neural approach for the parameter estimation of adaptive IIR filters for linear system identification. It is based on a novel neuron, the TLS EXIN neuron, capable of resolving the TLS problem present in this kind of estimation, where noisy errors affect not only the observation vector but also the data matrix. After a survey of other techniques for solving such parameters estimations, the TLS EXIN neuron is compared both theoretically and numerically with the former techniques, resulting in improved performance. Moreover, it is also proved that the TLS EXIN neuron permits some powerful acceleration techniques, unlike the other approaches. These results are also shown numerically.

Sacrifice Ratios and the Conduct of Monetary Policy in Conditions of Low Inflation

The focus of monetary policy has shifted markedly over the past 15 years away from attempts to fine tune the economy towards the longer-run goal of attaining price stability and creating the necessary conditions for sustainable economic growth. In an attempt to minimise the costs of such a transition, central banks have become more independent and monetary policy more transparent, changes intended to increase the credibility of monetary policy and to reduce short-run sacrifice ratios. However, concerns have been expressed that an environment of price stability and independent central banks may instead lead to higher sacrifice ratios and, perhaps, even higher rates of structural unemployment, because of the increased importance of nominal and real rigidities at low rates of inflation. The purpose of this paper is to analyse whether there are any grounds for such concerns. We do so by estimating sacrifice ratios for 19 industrialised countries, using three alternative approaches: (1) estimating aggregate supply curves; (2) estimating structural price and wage equations; and (3) comparing actual changes in inflation with changes in standard measures of output and labour market slack. The empirical evidence shows that, as the average rate of inflation for the 19 countries in our sample has fallen from 8% to 3½%, the average sacrifice ratio has increased from around 1.5 to about 2.5. Although sacrifice ratios appear to have risen in virtually all countries, the increases tend to be smallest in those that have adopted measures to deregulate labour and product markets and in countries where the central bank has adopted explicit inflation targets. However, the empirical evidence also reveals that point estimates of the sacrifice ratios for individual countries are quite sensitive to the econometric method adopted. This last result suggests that identification of the sources of higher sacrifice ratios remains elusive and thus that one should be cautious about drawing strong implications for monetary policy from these kinds of estimates.

On the Persistence of Lower Dimensional Invariant Tori under Quasi-Periodic Perturbations

The paper also contains estimates on the amount of surviving tori. The worst situation happens when the initial tori are normally elliptic. In this case, a torus (identified by the vector of intrinsic frequencies) can be continued with respect to a perturbative parameter $\varepsilon\in[0,\varepsilon_0]$ , except for a set of ɛ of measure exponentially small with ɛ 0 . In the case that ɛ is fixed (and sufficiently small), we prove the existence of invariant tori for every vector of frequencies close to the one of the initial torus, except for a set of frequencies of measure exponentially small with the distance to the unperturbed torus. As a particular case, if the perturbation is autonomous, these results also give the same kind of estimates on the measure of destroyed tori. Finally, these results are applied to some problems of celestial mechanics, in order to help in the description of the phase space of some concrete models.

Method of Ranking of Statistical Alternatives (RSA) on the Basis of Preliminary Made Expert Judgements: Mathematical Principles

This paper considers conceptual mathematical issues related to comparing the estimation of the effectiveness of countermeasures to be applied at different stages of a radiation incident. The countermeasures are described by a vector of attributes whose coordinates are random values. They are compared by integration of a combined distribution function, the core being a value function (VF). This function is reconstructed at a preliminary stage of registering expert preferences which are relative attribute weights specified for some points. At the same stage the collective compatibility of preferences and their extension to whole space of possible attributes is tested. The result of comparison of strategies is not just an evaluation 'better-worse', but also saying 'to what extent' and uncertainty of this estimate. Two kinds of estimate can be made: dimensionless estimates allowing for a contour surface of VF, and those having the dimension of any attribute providing for the values of VF.

Remote sensing and agricultural statistics: Crop area estimation in north-eastern Spain through diachronic Landsat TM and ground sample data

Landsat Thematic Maper (TM) imagery was used to estimate crop area using the regression method. Two different kind of estimates have been made; one using a Landsat TM image of the same year as the ground sample and the other using an image taken the year before. The results show that if the rate of land cover change is not great the use of an image of the year previous to the ground survey is a way of reducing the costs of the images acquisition without a great loss in the accuracy of the area estimation of the main crops compared to the conventional regression method.

Finite Time Self-Tuning Control by Minimax Estimators and an Uncertainty Principle

The first aim of this paper is to investigate finite-time guaranteed self-tuning control. A second aim is to prove a property of minimax estimators that a direct functional relationship can be established between the unknown "true" bounds of equation-errors and the level of control performance achieved. It is also shown that performance of a pole placement controller, based on any kind of estimator, is limited. This is called the "uncertainty principle". Finally it is shown that, under minimal á priori knowledge of the parameters of a second order plant, the "tuning" a pole-placement controller can be guaranteed to take place within eight sampling periods.

Hile-yeh estimates of eigenvalues of polyharmonic operators

The new bounds of eigenvalues of polyharmonic operators are deduced. This work is a generalization of some kind of estimates of the biharmonic operator.

Experiment on validity of skin resistance level as an index of arousal level

It is important in establishing and improving work management and work planning to estimate the arousal level of workers during operation and monitoring tasks. This paper proposes a technique based on experimental results to estimate the arousal level during job execution. In this experiment, both a monotonous low workload task which degrades the arousal level and a high workload task which has an awakening action were alternately applied to five subjects for three hours. Skin resistance level (SRL) as an index of arousal level of the autonous nervous system was measured with subjective drowsiness and task performance, that is, signal omission probability for low workload task and both reaction time and error probability for high workload task, as indexes of arousal level of the central nervous system. The following results were obtained. (1) The results suggested that SRL as an index of arousal level of the autonous nervous system is significantly related and correlated with subjective drowsiness and signal omission probability as indexes of arousal level of the central nervous system. (2) The average reaction time and the error probability tended to increase by the application of high workload when the arousal level was degraded. The influence of degraded arousal continued for a short time and showed an unfavorable effect on task execution. The degree of this influence, however, differed between subjects. (3) SRL can be used as an index of arousal level of the autonous nervous system because the measurement is comparatively easy and is little influenced by artifacts due to body movements. (4) Using SRL at initial high workload period as the standard value, it is possible to quantify the SRL value at arbitrary time by estimating how many times the standard value goes into the SRL value. Based on this quantified value as an index of arousal level, comparison with task performance can be made. The proposed index of arousal level of the autonous nervous system showed a significant correlation with indexes of the central nervous system. This technique can be applied to various kinds of estimation on human characteristics accompanied with changes in arousal level.

EFFECTIVE POPULATION SIZE AND GENETIC DRIFT IN TRISTYLOUS EICHHORNIA PANICULATA (PONTEDERIACEAE).

Populations of the tristylous, annual Eichhornia paniculata are markedly differentiated with respect to frequency of mating types. This variation is associated with evolutionary changes in mating system, from predominant outcrossing to high self-fertilization. To assess the potential influence of genetic drift acting on this variation, we estimated effective population size in 10 populations from northeastern Brazil using genetic and demographic methods. Effective size (Ne ) was inferred from temporal changes in allele frequency at two to eight isozyme loci and also calculated using five demographic variables: 1) the number of flowering individuals (N); 2) temporal fluctuations in N; 3) variance in flower number; 4) frequency of mating types; and 5) selfing rate. Average Ne based on isozyme data was 15.8, range 3.4-70.6, and represented a fraction (mean Ne /N = 0.106) of the census number of individuals (mean N = 762.8; range: 30.5-5,040). Temporal variation in N and variance in flower number each reduced Ne to about a half of N whereas mating type frequencies and selfing rate caused only small reductions in Ne relative to N. All estimates of Ne based on demographic variables were considerably larger than those obtained from genetic data. The two kinds of estimates were in general agreement, however, when all demographic variables were combined into a single measure. Monte Carlo simulations indicated that effective size must be fewer than about 40 for drift to overcome the frequency-dependent selection that maintains the polymorphism for mating type. Applying the average Ne /N value to 167 populations censused in northeastern Brazil indicated that 72% had effective sizes below this number. This suggests that genetic drift is likely to play a dominant role in natural populations of E. paniculata.

Estimates of solutions to linear elliptic systems and equations

Whenever nonlinear problems have to be solved through approximation methods by solving related linear problems a priori estimates are very useful. In the following this kind of estimates are presented for a variety of equations related to generalized firs

Positive solutions of systems of nonlinear eigenvalue problems

the real-valued functions a:’ = a$), a$, rz,) 2 0, 1 5 i, j 5 N, 1 I k 5 r are Lipschitz continuous on 0 and the matrix (a?‘), 1 I k 5 r, is positive definite on a. The operators Lk are uniformly elliptic. In the case of a single equation, r = 1, Ambrosetti and Hess, [2], have proved that the bifurcation from infinity occurs when the nonlinearity, f, is asymptotically linear and its asymptotic derivative positive. Peitgen and Schmitt, [8, 91, have obtained similar results for nonlinearities that satisfy more general asymptotic boundedness conditions. We extend these results to the system (1. l), r L 1. In Section 3 we prove that the bifurcation from infinity occurs at some A*, when f is asymptotically linear and its asymptotic derivative, M(x) = (m,(X)), satisfies the following conditions: mij 2 0, i # j, and for at least one i E [ 1, . . . , r), rn: # 0. (If we look at the linearized system (at co), these are the conditions that guarantee the existence of a positive eigenvalue with a positive eigenfunction, a result due to Hess, [5].) Our result is analogous to that of Hess, [5, theorem 21, treating the case of bifurcation from the trivial solution, and we obtain the same kind of estimates for A *. We use global perturbation techniques, employed by Peitgen and Schmitt, [8, 91, for the case of a single equation. This method enables us to also trace these bifurcations via global continua of solutions of a perturbed problem.

Accuracy in material budget estimates with regard to temporal and spatial resolution of monitored factors

The flushing of a continuously supplied conservative tracer in a multibasin estuary was studied using a hydrodynamical distribution model, vertically subdivided into two layers for mixing parameterization. The model has a sufficient number of grid cells to permit a spatial resolution of the tracer plume. The water exchange between different modelled basins was provided by previous simulation results from a circulation model with a temporal resolution of 1 h. The tracer turnover has been statistically analysed with regard to the content of the inner basin estimated from profile sampling and the transport across its adjacent sounds, respectively. Both of these methods of assessing the turnover of material have been employed in the ongoing biological field program in the actual estuary. The primary goal of the present paper has been to evaluate the trade-off between sampling resolution (in time and space) vs. the relative deviation of the estimates from the values corresponding to the highest resolution. It is concluded that the accuracy of these two different kinds of estimates will be determined by both a systematic and a nonsystematic deviation. The systematic deviation for content estimates seems possible to compensate for, since it is mainly determined by the position of the samples in the vertical and horizontal gradients. For transport estimates the systematic error is zero only when corresponding flow and concentration data are sampled simultaneously. At different sampling frequencies the expected accuracy is not likely to be improved by using more sophisticated methods than linear interpolation for missing data.

A soft decision viterbi decoding method using received carrier level in fading channel

AbstractTransmission channels in mobile communication are extremely unstable due to the effect of multipath fading. Therefore the realization of high‐reliability communication necessitates the introduction of error control in the form of error‐correction coding.This paper considers the decoding of error‐correcting codes that are adapted to digital mobile communication operating under Rayleigh fading conditions. A soft decision Viterbi decoding using the received carrier level is studied for the case of convolutional codes. This soft decision method is based on the level of the received carrier by adaptively determining the metric used in the decoding. In this way a metric is obtained for digital mobile communication.This paper also presents an estimation method using error exponent which provides effective means to realize such a soft decision method. If the channel can be considered memoryless due for example to interleaving, then this method provides an easy way to estimate: (1) the figure of merit for quantizing thresholds, and (2) the gains of the soft decision.First, it is shown that using this kind of estimation in the case of channels which can be considered sufficiently memoryless due to interleaving, extremely large gain is obtained by the soft decision method discussed in this paper.Next, simulations are performed and the efficiency of the estimation method is demonstrated. Finally, the bit error rate characteristics are shown for the case when the channel is not made sufficiently memoryless by interleaving.

Comparative studies of non-iterative estimators based on ihara and kano's method in exploratory factor analysis

In a factor analysis model, the asymptotic variance of the non-iterative estimator of Ihara and Kano (1986) is first provided, and five kinds of estimators, based on Ihara and Kano's method are constructed by using the asymptotic result. These estimators and that based on the maximum likelihoodare compared both theoretically and experimentally. In conclusion, the arithmetic mean of some Ihara and Kano estimators is recommended as a uniqueness estimator at least for small and medium sample sizes.