robust model based and model assisted predictors of the finite population total the prediction approach to finite population inference has received considerable attention in recent years under this approach the finite population is assumed to be a realization from a superpopulation described by a known probability model usually a linear model the prediction approach is often criticized for its lack of robustness against model misspecification in this article we revisit this important issue and introduce a new robust prediction approach in which the superpopulation model is chosen adaptively from the well known box cox class of probability distributions the richness of the box cox class ensures robustness in our model based prediction approach we explain how our robust model based predictor can be adjusted to handle zero observations for the study variable and to achieve the design unbiasedness and benchmarking properties we demonstrate the robustness of our proposed predictors using a monte carlo simulation study and a real life example

interval censored data a note on the nonparametric maximum likelihood estimator of the distribution function summary gentleman geyer 1994 discuss the analysis of interval censored data and present results based on standard convex optimisation theory here this problem is viewed from the perspective of a mixing problem of indicator functions using an analogy with the problem of mixture distributions a variety of results are easily derived including a characterisation theorem for the maximum likelihood estimator and various reliably convergent algorithms software for the analysis of mixture distributions can be used to find the nonparametric estimate of the distribution function of the interval censored survival time examples are provided to demonstrate the theory

on multiple diagnostic procedures for the linear model abstract multiple diagnostic procedures entail a partition of the sample space into a set of critical regions when the procedure is designed in a piecemeal fashion these regions bear no particular relation to one another and the procedure as a whole can be logically inconsistent we use a simple example to illustrate these difficulties and also to suggest criteria that should be satisfied by any diagnostic procedure that is to meet the needs of the practitioner

unconditionally stable numerical method for a nonlinear partial integro differential equation the paper presents an unconditionally stable numerical scheme to solve a nonlinear integro differential equation which arises in mathematical modeling of the penetration of a magnetic field into a substance if the temperature is kept constant throughout the material numerical scheme comprises of the galerkin finite element method jangveladze and kiguradze 2011 for the spatial discretization followed by an implicit finite difference scheme for the time stepping we extended the results for stability estimates to a non homogeneous problem and derived optimal order error estimates for the semidiscretized and fully discretized equations using h 0 1 projection further to show the efficiency the proposed numerical method is demonstrated via numerical example

an algorithm for computing the nonparametric mle of a mixing distribution abstract a fast algorithm for calculating the nonparametric maximum likelihood estimate mle of a mixing distribution g in a mixture model is discussed the literature contains several methods for computing the nonparametric mle of g but these methods are slow in this article we develop an algorithm for maximizing the log likelihood l g over the family of all distribution functions that yields the nonparametric mle of g in some semiparametric problems a structural or fixed parameter is of interest and we are interested in computing profile likelihood sup gl g for a grid of values of the algorithm that we propose is fast enough for this purpose examples illustrate and compare the algorithms one taken from an article by laird the common mean problem and one taken from the literature on optimal experimental design it is also noted that routines from the literature on semi infinite programming may be used to compute the profile log likelihood

finite difference approximation of a nonlinear integro differential system finite difference approximation of the nonlinear integro differential system associated with the penetration of a magnetic field into a substance is studied the convergence of the finite difference scheme is proved the rate of convergence of the discrete scheme is given the decay of the numerical solution is compared with the analytical results proven earlier

linearly localized difference schemes for the nonlinear maxwell model of a magnetic field into a substance abstract a linearly localized difference scheme with the first order time approximation is proposed for solving a nonlinear maxwell model associated with the penetration of a magnetic field into a substance the new scheme is computationally efficient since the resulting algebra equations are linear and can be computed by the fast thomas algorithm without any newton type inner iterations it is also local in time that is only numerical solutions in one previous time level are necessary to update the current solutions such that it requires much less storage compared with the fully implicit method furthermore the exponential decaying behavior of difference solution which is analogous to that of the continuous solution is obtained to improve the time accuracy we apply the crank nicolson type time discretization to construct a second order linearly localized method numerical examples are presented to support our theoretical results

robust tests for heteroskedasticity in the one way error components model this paper constructs tests for heteroskedasticity in one way error components models in line with baltagi et al baltagi b h bresson g pirotte a 2006 joint lm test for homoskedasticity in a one way error component model journal of econometrics 134 401 417 our tests have two additional robustness properties first standard tests for heteroskedasticity in the individual component are shown to be negatively affected by heteroskedasticity in the remainder component we derive modified tests that are insensitive to heteroskedasticity in the component not being checked and hence help identify the source of heteroskedasticity second gaussian based lm tests are shown to reject too often in the presence of heavy tailed e g t student distributions by using a conditional moment framework we derive distribution free tests that are robust to non normalities our tests are computationally convenient since they are based on simple artificial regressions after pooled ols estimation

the analysis of transformed data abstract recently it was suggested bickel and doksum 1981 that when data are used to select a transformation the post transformation analysis of those data may need to be modified considerably from standard form so as to allow for the selection we argue that common sense and the work of box and cox 1964 point to a contrary conclusion our argument is based on considerations of parameter interpretation and subsequent bayesian analysis within the context of fitting normal error linear models numerical examples are used to illustrate the main points

an analysis of transformations revisited rebutted abstract in a paper written in 1964 box and cox described a method for estimating transformations and showed how in suitable cases valuable increases in simplicity and efficiency were possible since that time this technique has enjoyed wide practical use and considerable success however a recent theoretical paper by bickel and doksum 1981 seems to suggest that serious dangers are associated with the employment of this method and speaks of instability and cost of estimation of the transformation these difficulties seem to be associated with 1 examples which common sense would rule out namely situations where the effect of transformation on the data is almost linear so that it is a matter of indifference which transformation is used 2 the idea that it makes sense to state conclusions in terms of a number measured on an arbitrary scale 3 failure to take proper account of the jacobian of the transformation

finite element approximation of diffusion equations with convolution terms approximation of solutions to diffusion equations with memory represented by convolution integral terms is considered such problems arise from modeling of flows in fissured media convergence of the method is proved and results of numerical experiments confirming the theoretical results are presented the advantages of implementation of the algorithm in a multiprocessing environment are discussed

tests for the error component model in the presence of local misspecification it is well known that most of the standard specification tests are not valid when the alternative hypothesis is misspecified this is particularly true in the error component model when one tests for either random effects or serial correlation without taking account of the presence of the other effect in this paper we study the size and power of the standard rao s score tests analytically and by simulation when the data are contaminated by local misspecification these tests are adversely affected under misspecification we suggest simple procedures to test for random effects or serial correlation in the presence of local serial correlation or random effects and these tests require ordinary least squares residuals only our monte carlo results demonstrate that the suggested tests have good finite sample properties for local misspecification and in some cases even for far distant misspecification our tests are also capable of detecting the right direction of the departure from the null hypothesis we also provide some empirical illustrations to highlight the usefulness of our tests

best nonlinear three stage least squares estimation of certain econometric models a method is presented for estimating nonlinear simultaneous equations and transformation models in the presence of disturbance distribution of unknown form it asymptotically achieves the lower variance bound for instrumental variables estimates the author avoids smoothed nonparametric estimation his instruments averaging over the unsmoothed empirical distribution of preliminary residuals he allows for stationary serial dependence in various settings estimates are proposed and large sample inference rules justified these being unaffected if the optimal instruments use only an arbitrarily small vanishing fraction of the residuals the author investigates theoretically the effect of such computational savings on the goodness of the normal approximation copyright 1991 by the econometric society

interpretable inference on the mixed effect model with the box cox transformation we derived results for inference on parameters of the marginal model of the mixed effect model with the box cox transformation based on the asymptotic theory approach we also provided a robust variance estimator of the maximum likelihood estimator of the parameters of this model in consideration of the model misspecifications using these results we developed an inference procedure for the difference of the model median between treatment groups at the specified occasion in the context of mixed effects models for repeated measures analysis for randomized clinical trials which provided interpretable estimates of the treatment effect from simulation studies it was shown that our proposed method controlled type i error of the statistical test for the model median difference in almost all the situations and had moderate or high performance for power compared with the existing methods we illustrated our method with cluster of differentiation 4 cd4 data in an aids clinical trial where the interpretability of the analysis results based on our proposed method is demonstrated copyright 2017 john wiley sons ltd

a simple nonparametric approach to estimating the distribution of random coefficients in structural models abstract we explore least squares and likelihood nonparametric mixtures estimators of the joint distribution of random coefficients in structural models the estimators fix a grid of heterogeneous parameters and estimate only the weights on the grid points an approach that is computationally attractive compared to alternative nonparametric estimators we provide conditions under which the estimated distribution function converges to the true distribution in the weak topology on the space of distributions we verify most of the consistency conditions for three discrete choice models we also derive the convergence rates of the least squares nonparametric mixtures estimator under additional restrictions we perform a monte carlo study on a dynamic programming model

the geometry of mixture likelihoods a general theory in this paper certain fundamental properties of the maximum likelihood estimator of a mixing distribution are shown to be geometric properties of the likelihood set the existence support size likelihood equations and uniqueness of the estimator are revealed to be directly related to the properties of the convex hull of the likelihood set and the support hyperplanes of that hull it is shown using geometric techniques that the estimator exists under quite general conditions with a support size no larger than the number of distinct observations analysis of the convex dual of the likelihood set leads to a dual maximization problem a convergent algorithm is described the defining equations for the estimator are compared with the usual parametric likelihood equations for finite mixtures sufficient conditions for uniqueness are given part ii will deal with a special theory for exponential family mixtures

testing for heteroskedasticity in fixed effects models abstract we derive tests for heteroskedasticity after fixed effects estimation of linear panel models the asymptotic results are based on a large n fixed t framework where the incidental parameters problem is bypassed by utilizing a pseudo likelihood function conditional on the sufficient statistic for these parameters a simple studentization produces distribution free tests that can easily be implemented using an artificial regression based on residuals after fixed effects estimation a monte carlo exploration suggests that the tests perform well in small samples such as those encountered in practice

an algorithm for solving a nonlinear integro differential equation in this paper an algorithm based on adomian s decomposition method is developed to approximate the solution of the nonlinear integro differential equationu t x t email protected t 0a email protected email protected email protected u x x t email protected f x t 0

on fast computation of the non parametric maximum likelihood estimate of a mixing distribution summary a fast algorithm for computing the non parametric maximum likelihood estimate of a mixing distribution is presented at each iteration the algorithm adds new important points to the support set as guided by the gradient function updates all mixing proportions via a quadratically convergent method and discards redundant support points straightaway with its convergence being theoretically established numerical studies show that it is very fast and stable compared with several other algorithms that are available in the literature

large time behavior of solutions to a nonlinear integro differential system abstract asymptotic behavior of solutions as t to the nonlinear integro differential system associated with the penetration of a magnetic field into a substance is studied initial boundary value problems with two kinds of boundary data are considered the first with homogeneous conditions on whole boundary and the second with non homogeneous boundary data on one side of lateral boundary the rates of convergence are given too

nonparametric estimation of nonstationary spatial covariance structure abstract estimation of the covariance structure of spatial processes is a fundamental prerequisite for problems of spatial interpolation and the design of monitoring networks we introduce a nonparametric approach to global estimation of the spatial covariance structure of a random function z x t observed repeatedly at times ti i 1 t at a finite number of sampling stations xi i 1 2 n in the plane our analyses assume temporal stationarity but do not assume spatial stationarity or isotropy we analyze the spatial dispersions var z xi t z xj t as a natural metric for the spatial covariance structure and model these as a general smooth function of the geographic coordinates of station pairs xi xj the model is constructed in two steps first using nonmetric multidimensional scaling mds we compute a two dimensional representation of the sampling stations for which a monotone function of interpoint distances ij approximates the spatial dispersions mds transforms the problem

galerkin finite element method for one nonlinear integro differential model galerkin finite element method for the approximation of a nonlinear integro differential equation associated with the penetration of a magnetic field into a substance is studied first type initial boundary value problem is investigated the convergence of the finite element scheme is proved the rate of convergence is given too the decay of the numerical solution is compared with the analytical results

a geometric transversals approach to sensor motion planning for tracking maneuvering targets this paper presents a geometric transversals approach for representing the probability of track detection as an analytic function of time and target motion parameters by this approach the optimization of the detection probability subject to sensor kinodynamic constraints can be formulated as an optimal control problem using the proposed detection probability function the necessary conditions for optimality can be derived using calculus of variations and solved numerically using a variational iteration method vim the simulation results show that sensor state and control trajectories obtained by this approach bring about a significant increase in detection probability compared to existing strategies and require a computation that is significantly reduced compared to direct methods

asymptotic expansions of the information matrix test statistic the information matrix im test is shown to have a finite sample distribution which is poorly approximated by its asymptotic x 2 distribution in models and sample sizes commonly encountered in applied econometric research the quality of the x2 approximation depends upon the method chosen to compute the test failure to exploit restrictions on the covariance matrix of the test can lead to a test with appalling finite sample properties order o n 1 approximations to the exact distribution of an efficient form of the im test are reported these are developed from asymptotic expansions of the edgeworth and cornish fisher types they are compared with monte carlo estimates of the finite sample distribution of the test and are found to be superior to the usual x2 approximations in sample sizes of the magnitude found in applied micro econometric work the methods developed in the paper are applied to normal and exponential models and to normal regression models results are provided for the full im test and for heteroskedasticity and nonnormality diagnostic tests which are special cases of the im test in geieral the quality of alternative approximations is sensitive to covariate design however commonly used nonnormality tests are found to have distributions which to order o n 1 are invariant under changes in covariate design this leads to simple design and parameter invariant size corrections for nonnormality tests

an analysis of transformations for additive nonparametric regression abstract we consider a nonparametric regression model with a parametric family of dependent variable transformations one of which induces additive covariate effects we estimate the additive regression effects using the integration method and estimate the transformation parameter from a profiled instrumental variable and pseudolikelihood criterion the asymptotic distributions of the parameter and regression estimates are given the practical performance is investigated via an application

a note on studentizing a test for heteroscedasticity abstract breusch and pagan 1979 have recently proposed a convenient test for heteroscedasticity in general linear models this note derives the asymptotic distribution of their test under sequences of contiguous alternatives to the null hypothesis of homoscedasticity the test is shown to possess asymptotically incorrect size nominal significance level except in the case of strictly gaussian disturbances a slight modification of the test is proposed which corrects this defect

joint estimation and testing for functional form and heteroskedasticity abstract this paper develops the maximum likelihood procedure to estimate the appropriate functional form in regression models with heteroskedastic errors the analysis can then enable us to separate out the influence of non linearity in an estimate of the transformation parameter from the influence of stabilizing the error variance illustrative examples have been used to show that estimation and tests for functional form and heteroskedasticity can and should be jointly considered

on the application of robust regression based diagnostics to models of conditional means and conditional variances abstract a strategy is proposed for applying a class of robust regression based diagnostics to nonlinear models of conditional means and conditional variances for cross section or time series data the distinguishing feature of the current approach which builds on already popular residual based procedures is that no auxiliary assumptions are imposed at any testing stage consequently the statistics are guaranteed to have the correct asymptotic size under the relevant null hypothesis several new regression based conditional mean and conditional variance diagnostics are proposed the case of incompletely specified dynamics in time series models is explicitly covered

roc analysis for markers with mass at zero the receiver operating characteristic roc curve and in particular the area under the curve auc is commonly used to examine the discriminatory ability of diagnostic markers certain markers while basically continuous and non negative have a positive probability mass spike at the value zero we discuss a flexible modelling approach to such data and contrast it with the standard non parametric approach we show how the modelling approach can be extended to take account of the effect of explanatory variables we motivate this problem and illustrate the modelling approach using data on the coronary calcium score measured by electron beam tomography which is a marker for atherosclerosis

statistical tests based on transformed data abstract the problem of testing hypotheses in linear models when the original data have been transformed is considered it is assumed that the transformation involves an unknown parameter that has to be estimated from the data for certain important testing problems it is found that the asymptotic level and power is as if had been assumed known asymptotic efficiency results show that when the box cox transformation is used tests based on transformed data have good power properties simulation results for transformed two sample and linear regression testing problems show this to be true for moderate to small sample sizes as well in particular an trimmed t test based on averages of trimmed transformed variables performs very well in both light tailed and heavy tailed skew models when compared with the usual t test and rank tests

computing kernel smoothed conditional quantiles from many observations abstract quantiles of a variable y conditional on another variable x when plotted against x can be a useful descriptive tool these plots give a quick impression of the functional form of the relation between x and the location spread and shape of the conditional distribution of y if several y are observed for each x then sample quantiles could be calculated for each x the resulting quantile plot may be quite noisy however and smoothing across x may be desired this article presents an algorithm that calculates kernel smoothed conditional quantiles with a cross validation choice of bandwidth for x it is computationally feasible for large data sets when x assumes a small number of values since it requires only one pass through the full data set the cross validation does not require a pass through the data because of simplifications arising from the l 1 loss function being based on absolute values the technique is illustrated by plotting the conditional quantiles of the net wealth of a sample of

treatment effects in a logistic model involving the box cox transformation abstract we consider a logistic model for binary response data that allows the possibility of power transformation of x that is log p 1 p x i where x is a continuous variable x is the box cox transformation and i is a binary variable indicating treatment or group this model is applicable to observational studies or randomized trials when a treatment effect is investigated after controlling for a confounding variable x our focus is on inference concerning the treatment effect in the analysis a common approach might be to treat the estimated value of as fixed and ignore uncertainty associated with its estimation in inference about alternatively we might perform an unconditional analysis in which is regarded as a parameter we show that under the null hypothesis 0 these two approaches are asymptotically equivalent if the two groups have the same distribution of x and the same sample size this result also holds for the situation of multiple covariates each wit

a new family of power transformations to improve normality or symmetry summary we introduce a new power transformation family which is well defined on the whole real line and which is appropriate for reducing skewness and to approximate normality it has properties similar to those of the box cox transformation for positive variables the large sample properties of the transformation are investigated in the contect of a single random sample

transformations in stochastic dea models abstract a set of transformations based on the lp norm are used to generate alternative parametric and nonparametric formulations of production frontiers particular attention is paid to the cases p 1 least absolute value estimation and p chebyshev estimation a class of generalized transformations of inputs and outputs by using the box cox transformations is also explored and illustrated

some power considerations when deciding to use transformations conventional wisdom suggests that for small data sets having substantial skew one should attempt to determine the correct distributional form if possible and apply statistical methods appropriate for that distribution transformations such as the log or square root are often used if an appropriate distributional form cannot be determined a distribution free procedure such as a rank transformation or a randomization test procedure can be used to better appreciate the effect of such alternatives on both the type i error and power of detecting differences between treatment groups simulation studies were conducted for responses having specific gamma g r theta and log normal ln m v distributions the gamma and log normal distributions were selected so that they had the same first two moments a simple two group design was assumed the reference group always had an average disease level mu 3 0 mu r theta for gamma mu m for log normal and the treatment group always had means whose reductions ranged from 0 per cent to 50 per cent the effect of distributional type and the degree of skewness was investigated by varying the population parameter values six statistical test procedures were compared for the gamma distributions all test procedures were robust relative to the type i error the ump test based on a ratio of sample means produced the greatest power for all combinations of n r and rt the power losses associated with the randomization test the t test on original scale and the t test on the square root scale were very small 3 per cent to 6 per cent in absolute value for n 10 and 15 and less than 2 per cent for group sizes of 25 or more the power loss associated with the t test on the log scale was much larger ranging from 5 per cent to 10 per cent smaller power than the t test on original scale the wilcoxon rank test produced similar results to that of the log t test for small samples the power for the shifted log x c test increased monotonically to the asymptotic value of the orig t test the same five test procedures based on differences in sample means were then compared for the corresponding log normal distributions the ump test that is log x produced the highest power there was very little power lost for the sqrt t test the loss in power varied between 2 per cent and 5 per cent for the rank test abstract truncated at 400 words

model specification tests a simultaneous approach abstract in econometrics specification tests have been constructed to verify the validity of one specification at a time it is argued that most of these tests are not in general robust in the presence of other misspecifications so their application may result in misleading conclusions using the lagrange multiplier principle we develop efficient test procedures that are capable of testing a number of specifications simultaneously these tests will confirm the validity or invalidity of a general model requiring the estimates of the restricted model only through an extensive monte carlo experiment we study the performance of these tests and some commonly used one directional tests we also suggest a multiple comparison procedure to identify different sources of errors this we hope will lead to a better specification of econometric models

recent developments in computer assisted analysis of mixtures this paper reviews recent developments in the area of computer assisted analysis of mixture distributions c a man given a biometric situation of interest in which under homogeneity assumptions a certain parametric density occurs such as the poisson the binomial the geometric the normal and so forth then it is argued that this situation can easily be enlarged to allow a variation of the scalar parameter in the population this situation is called unobserved heterogeneity this naturally leads to a specific form of nonparametric mixture distribution that can then be assumed to be the standard model in the biometric application of interest since it also incorporates the homogeneous situations as a special case besides developments in theory and algorithms the work focuses on developments in biometric applications such as meta analysis fertility studies estimation of prevalence under clustering and estimation of the distribution function of survival time under interval censoring the approach is nonparametric for the mixing distribution including leaving the number of components subpopulations of the mixing distribution unknown

finite differences versus finite elements for solving nonlinear integro differential equations consider the nonlinear integro differential equation ut x t 0t a t x ux x d f x t 0 x 0 t t with appropriate initial and boundary conditions this problem serves as a model for one dimensional heat flow in materials with memory the numerical solution via finite elements was discussed in b neta j math anal appl 89 1982 598 611 in this paper we compare the results obtained there with finite difference approximation from the point of view of accuracy and computer storage it turns out that the finite difference method yields comparable results for the same mesh spacing using less computer storage

tests following transformations chen and loh showed that the box cox transformed two sample t test is more powerful than the ordinary t test under pitman alternatives where the location shifts appear in the untransformed scale in this article we prove that chen and loh s result also holds for a general family of transformations an upper bound on the asymptotic relative efficiency are is obtained in addition we investigate bounds on the are under pitman location shift alternatives in the transformed scale we find that when the estimate for a is consistent a lower bound on the are is the reciprocal of fisher information of the standard transformed distribution this lower bound is close to 1 for commonly used symmetric distributions

large time behavior of solutions and finite difference scheme to a nonlinear integro differential equation the large time behavior of solutions and finite difference approximations of the nonlinear integro differential equation associated with the penetration of a magnetic field into a substance are studied asymptotic properties of solutions for the initial boundary value problem with homogeneous dirichlet boundary conditions is considered the rates of convergence are given too the convergence of the semidiscrete and the finite difference schemes are also proved

collocation approximation methods for nonlinear singular integrodifferential equations in banach spaces abstract a new approximation method is proposed for the numerical evaluation of the nonlinear singular integrodifferential equations defined in banach spaces the collocation approximation method is therefore applied to the numerical solution of such type of nonlinear equations by using a system of chebyshev functions through the application of the collocation method is investigated the existence of solutions of the system of non linear equations used for the approximation of the nonlinear singular integrodifferential equations which are defined in a complete normed space i e a banach space

numerical solution of a nonlinear integro differential equation abstract galerkin s method with appropriate discretization in time is considered for approximating the solution of the nonlinear integro differential equation u t x t 0 t a t x u x x d f x t 0 an error estimate in a suitable norm will be derived for the difference u uh between the exact solution u and the approximant uh it turns out that the rate of convergence of uh to u as h 0 is optimal this result was confirmed by the numerical experiments

equivalence of truncated count mixture distributions and mixtures of truncated count distributions summary this article is about modeling count data with zero truncation a parametric count density family is considered the truncated mixture of densities from this family is different from the mixture of truncated densities from the same family whereas the former model is more natural to formulate and to interpret the latter model is theoretically easier to treat it is shown that for any mixing distribution leading to a truncated mixture a usually different mixing distribution can be found so that the associated mixture of truncated densities equals the truncated mixture and vice versa this implies that the likelihood surfaces for both situations agree and in this sense both models are equivalent zero truncated count data models are used frequently in the capture recapture setting to estimate population size and it can be shown that the two horvitz thompson estimators associated with the two models agree in particular it is possible to achieve strong results for mixtures of truncated poisson densities including reliable global construction of the unique npmle nonparametric maximum likelihood estimator of the mixing distribution implying a unique estimator for the population size the benefit of these results lies in the fact that it is valid to work with the mixture of truncated count densities which is less appealing for the practitioner but theoretically easier mixtures of truncated count densities form a convex linear model for which a developed theory exists including global maximum likelihood theory as well as algorithmic approaches once the problem has been solved in this class it might readily be transformed back to the original problem by means of an explicitly given mapping applications of these ideas are given particularly in the case of the truncated poisson family

testing for structural stability in the whole sample the paper examines a lagrange multiplier type test for the constancy of the parameter in general models with dependent data without imposing any artificial choice of the possible location of the break in order to prove the asymptotic behaviour of the test we extend a strong approximation result for partial sums of a sequence of random variables we also present a monte carlo experiment to examine the finite sample performance of the test and how it compares with tests which assume some knowledge of the possible location of the break

alternative transformations to handle extreme values of the dependent variable abstract transformations that could be used to reduce the influence of extreme observations of dependent variables which can assume either sign on regression coefficient estimates are studied in this article two that seem reasonable on a priori grounds the extended box cox bc and the inverse hyperbolic sine ihs are evaluated in detail one feature is that the log likelihood function for ihs is defined for zero values of the dependent variable which is not true of bc the double length regression technique davidson and mackinnon 1984 is used to perform hypothesis tests of one transformation against the other using canadian data on household net worth these tests support the use of ihs instead of bc for this data set empirical investigators in economics often work with a logged dependent variable taking the natural logarithm of a data series is of course a special case of bc to reduce the weight their particular estimation procedure might otherwise attach to extreme values of the dependent v

the effects of transformations and preliminary tests for non linearity in regression non linear relationships between two variables are often detected as a result of a preliminary statistical test for linearity common approaches to dealing with non linearity are to a make a linearizing transformation in the independent variable or b fit a relationship that is non linear in the independent variable such as including a quadratic term with either approach the resulting test for association between the two variables can have an inflated type i error we consider testing the significance of the quadratic term in a quadratic model as a preliminary test for non linearity using simulation experiments and asymptotic arguments we quantify the type i error inflation and suggest simple modifications of standard practice to protect the size of the type i error in the case of quadratic regression the type i error will be increased by roughly 50 per cent the simple strategy of appropriately correcting the alpha level is shown to have minimal loss of power if the relationship is truly linear in the case of a linearizing transformation the impact on the type i error will depend on the values of the independent variable and on the set of potential linearizing transformations considered simulation results suggest that a procedure which adjusts the test statistic according to the results of the preliminary test may offer adequate protection

testing strategies for model specification a crucial element in the development of econometric methodology during the past decade has been the concern with testing as opposed to estimating econometric models in this paper we discuss especially for the econometric analysis of time series the main types of test procedures and we also investigate the opportunities to uphold the neyman pearson theory in the context of thorough model specification testing in applied work it is quite usual to carry out several tests on the same set of sample data we consider an extension of the neyman pearson framework to the case of such repeated testing and examine situations where the various hypotheses under test have a particular nesting structure for the case where a sequence of superposed alternatives is tested by so called marginal tests we prove that the various test statistics are asymptotically independent under a common null hypothesis if the statistics are based on either the likelihood ratio or the wald or the lagrange multiplier approach testing a particular null hypothesis against a series of juxtaposed alternatives appears to lead to independent test statistics only in specific circumstances it is shown how independence of test statistics enables the control over the overall type i error probability which is an essential element in the neyman pearson theory using the notions of constructive hypotheses and auxiliary hypotheses we can draw a clear distinction between specification tests and misspecification tests next an overview is given of approaches to and examples of specification and misspecification testing with respect to the former attention is paid to the problem determining the order of dynamics and discriminating between system dynamics and error dynamics the misspecification testing is reviewed for specification error nonconstancy of coefficients heteroscedasticity serial dependence and nonnormality of disturbances also the problem of testing for several misspecifications jointly or sequentially is considered finally we discuss the options and associated difficulties in implementing the various tests in an overall testing strategy