a large sample study of cox s regression model strong consistency and asymptotic normality are established for the maximum partial likelihood estimate of the regression parameter in cox s regression model estimates are also derived for the underlying cumulative hazard function and survival distribution we establish the asymptotic normality of these estimates and calculate the limiting variances

mitigation of loopback self interference in full duplex mimo relays full duplex relaying is more spectrally efficient than half duplex relaying as only one channel use is needed per two hops however it is crucial to minimize relay self interference to render full duplex feasible for this purpose we analyze a broad range of multiple input multiple output mimo mitigation schemes natural isolation time domain cancellation and spatial suppression cancellation subtracts replicated interference signal from the relay input while suppression reserves spatial dimensions for receive and transmit filtering spatial suppression can be achieved by antenna subset selection null space projection i e receiving and transmitting in orthogonal subspaces or joint transmit and receive beam selection to support more spatial streams by choosing the minimum eigenmodes for overlapping subspaces in addition minimum mean square error mmse filtering can be employed to maintain the desired signal quality which is inherent for cancellation and the combination of time and spatial domain processing may be better than either alone targeting at minimal interference power we solve optimal filters for each scheme in the cases of joint separate and independent design the performance of mitigation schemes is evaluated and compared by simulations the results confirm that self interference can be mitigated effectively also in the presence of imperfect side information

empirical likelihood ratio confidence regions than are those based on student s t statistic an effective method is presented for computing empirical profile likelihoods for the mean of a vector random variable the method is a reduction by convex duality to an unconstrained minimization of a convex function on a low dimensional domain algorithms exist for finding the unique global minimum at a superlinear rate of convergence a byproduct is a noncombinatorial algorithm for determining whether a given point lies within the convex hull of a finite set of points the multivariate empirical likelihood regions are justified for functions of several means such as variances correlations and regression parameters and for statistics with linear estimating equations an algorithm is given for computing profile empirical likelihoods for these statistics

empirical likelihood ratio confidence intervals for a single functional summary the empirical distribution function based on a sample is well known to be the maximum likelihood estimate of the distribution from which the sample was taken in this paper the likelihood function for distributions is used to define a likelihood ratio function for distributions it is shown that this empirical likelihood ratio function can be used to construct confidence intervals for the sample mean for a class of m estimates that includes quantiles and for differentiable statistical functionals the results are nonparametric extensions of wilks s 1938 theorem for parametric likelihood ratios the intervals are illustrated on some real data and compared in a simulation to some bootstrap confidence intervals and to intervals based on student s t statistic a hybrid method that uses the bootstrap to determine critical values of the likelihood ratio is introduced

a discrete uniformization theorem for polyhedral surfaces a notion of discrete conformality for hyperbolic polyhedral surfaces is introduced in this paper this discrete conformality is shown to be computable it is proved that each hyperbolic polyhedral metric on a closed surface is discrete conformal to a unique hyperbolic polyhedral metric with a given discrete curvature satisfying gauss bonnet formula furthermore the hyperbolic polyhedral metric with given curvature can be obtained using a discrete yamabe flow with surgery in particular each hyperbolic polyhedral metric on a closed surface with negative euler characteristic is discrete conformal to a unique hyperbolic metric

asymptotic optimality of empirical likelihood for testing moment restrictions we show by example that empirical likelihood and other commonly used tests for moment restrictions are unable to control the exponential rate at which the probability of a type i error tends to zero unless the possible distributions for the observed data are restricted appropriately from this it follows that for the optimality claim for empirical likelihood in kitamura 2001 to hold additional assumptions and qualifications are required under stronger assumptions than those in kitamura 2001 we establish the following optimality result i empirical likelihood controls the rate at which the probability of a type i error tends to zero and ii among all procedures for which the probability of a type i error tends to zero at least as fast empirical likelihood maximizes the rate at which the probability of a type ii error tends to zero for most alternatives this result further implies that empirical likelihood maximizes the rate at which the probability of a type ii error tends to zero for all alternatives among a class of tests that satisfy a weaker criterion for their type i error probabilities

empirical likelihood based inference in conditional moment restriction models this paper proposes an asymptotically efficient method for estimating models with conditional moment restrictions our estimator generalizes the maximum empirical likelihood estimator mele of qin and lawless 1994 using a kernel smoothing method we efficiently incorporate the information implied by the conditional moment restrictions into our empirical likelihood based procedure this yields a one step estimator which avoids estimating optimal instruments our likelihood ratio type statistic for parametric restrictions does not require the estimation of variance and achieves asymptotic pivotalness implicitly the estimation and testing procedures we propose are normalization invariant simulation results suggest that our new estimator works remarkably well in finite samples

an empirical likelihood goodness of fit test for time series summary standard goodness of fit tests for a parametric regression model against a series of nonparametric alternatives are based on residuals arising from a fitted model when a parametric regression model is compared with a nonparametric model goodness of fit testing can be naturally approached by evaluating the likelihood of the parametric model within a nonparametric framework we employ the empirical likelihood for an mixing process to formulate a test statistic that measures the goodness of fit of a parametric regression model the technique is based on a comparison with kernel smoothing estimators the empirical likelihood formulation of the test has two attractive features one is its automatic consideration of the variation that is associated with the nonparametric fit due to empirical likelihood s ability to studentize internally the other is that the asymptotic distribution of the test statistic is free of unknown parameters avoiding plug in estimation we apply the test to a discretized diffusion model which has recently been considered in financial market analysis

the conditional permutation test for independence while controlling for confounders we propose a general new method the conditional permutation test for testing the conditional independence of variables x and y given a potentially high dimensional random vector z that may contain confounding factors the test permutes entries of x non uniformly to respect the existing dependence between x and z and thus to account for the presence of these confounders like the conditional randomization test of candes and co workers in 2018 our test relies on the availability of an approximation to the distribution of x z whereas their test uses this estimate to draw new x values for our test we use this approximation to design an appropriate non uniform distribution on permutations of the x values already seen in the true data we provide an efficient markov chain monte carlo sampler for the implementation of our method and establish bounds on the type i error in terms of the error in the approximation of the conditional distribution of x z finding that for the worst case test statistic the inflation in type i error of the conditional permutation test is no larger than that of the conditional randomization test we validate these theoretical results with experiments on simulated data and on the capital bikeshare data set

testing conditional independence using maximal nonlinear conditional correlation in this paper the maximal nonlinear conditional correlation of two random vectors x and y given another random vector z denoted by 1 x y z is defined as a measure of conditional association which satisfies certain desirable properties when z is continuous a test for testing the conditional independence of x and y given z is constructed based on the estimator of a weighted average of the form nz k 1 f z z k 2 1 x y z z k where f z is the probability density function of z and the z k s are some points in the range of z under some conditions it is shown that the test statistic is asymptotically normal under conditional independence and the test is consistent

a consistent characteristic function based test for conditional independence abstract y is conditionally independent of z given x if pr f y x z f y x 1 for all y on its support where f denotes the conditional density of y given x z or x this paper proposes a nonparametric test of conditional independence based on the notion that two conditional distributions are equal if and only if the corresponding conditional characteristic functions are equal we extend the test of su and white 2005 a hellinger metric nonparametric test for conditional independence discussion paper department of economics ucsd in two directions 1 our test is less sensitive to the choice of bandwidth sequences 2 our test has power against deviations on the full support of the density of x y z we establish asymptotic normality for our test statistic under weak data dependence conditions simulation results suggest that the test is well behaved in finite samples applications to stock market data indicate that our test can reveal some interesting nonlinear dependence that a traditional linear granger causality test fails to detect

consistent model specification tests for time series econometric models in this paper we consider general hypothesis testing problems for nonparametric and semiparametric time series econometric models we apply the general methodology to construct a consistent test for omitted variables and a consistent test for a partially linear model the proposed tests are shown to have asymptotic normal distributions under their respective null hypotheses we also discuss the problems of testing portfolio conditional mean variance efficiency and testing a semiparametric single index model monte carlo simulations are conducted to examine the finite sample performances of the nonparametric omitted variable test and the test for a partially linear specification

a unified approach for calculating error rates of linearly modulated signals over generalized fading channels we present a unified analytical framework to determine the exact average symbol error rate ser of linearly modulated signals over generalized fading channels the results are applicable to systems employing coherent demodulation with maximal ratio combining multichannel reception the analyses assume independent fading paths which are not necessarily identically distributed in all cases the proposed approach leads to an expression of the average ser involving a single finite range integral which can be easily computed numerically in addition as special cases ser expressions for single channel reception are obtained these expressions reduce to well known solutions give alternative often simpler expressions for previous results or provide new formulas that are either closed form expressions or simple to compute numerically

optimal tests when a nuisance parameter is present only under the alternative this paper derives asymptotically optimal tests for testing problems in which a nuisance parameter exists under the alternative hypothesis but not under the null for example the results apply to tests of structural change with unknown changepoint the testing problem considered is nonstandard and the classical asymptotic optimality results for the lagrange multiplier wald and likelihood ratio do not apply a weighted average power criterion is used here to generate optimal tests this criterion is similar to that used by a wald 1943 to obtain the classical asymptotic optimality properties of wald tests in regular testing problems copyright 1994 by the econometric society

testing conditional independence via empirical likelihood we construct two classes of smoothed empirical likelihood ratio tests for the conditional independence hypothesis by writing the null hypothesis as an infinite collection of conditional moment restrictions indexed by a nuisance parameter one class is based on the cdf another is based on smoother functions we show that the test statistics are asymptotically normal under the null hypothesis and a sequence of pitman local alternatives we also show that the tests possess an asymptotic optimality property in terms of average power simulations suggest that the tests are well behaved in finite samples applications to some economic and financial time series indicate that our tests reveal some interesting nonlinear causal relations which the traditional linear granger causality test fails to detect

a test for volatility spillover with application to exchange rates abstract this paper proposes a class of asymptotic n 0 1 tests for volatility spillover between two time series that exhibit conditional heteroskedasticity and may have infinite unconditional variances the tests are based on a weighted sum of squared sample cross correlations between two squared standardized residuals we allow to use all the sample cross correlations and introduce a flexible weighting scheme for the sample cross correlation at each lag cheung and ng 1996 test and granger 1969 type regression based test can be viewed as uniform weighting because they give equal weighting to each lag non uniform weighting often gives better power than uniform weighting as is illustrated in a simulation study we apply the new tests to study granger causalities between two weekly nominal u s dollar exchange rates deutschemark and japanese yen it is found that for causality in mean there exists only simultaneous interaction between the two exchange rates for causality in variance there also exists strong simultaneous interaction between them moreover a change in past deutschemark volatility granger causes a change in current japanese yen volatility but a change in past japanese yen volatility does not granger cause a change in current deutschemark volatility

conditional distance correlation statistical inference on conditional dependence is essential in many fields including genetic association studies and graphical models the classic measures focus on linear conditional correlations and are incapable of characterizing nonlinear conditional relationship including nonmonotonic relationship to overcome this limitation we introduce a nonparametric measure of conditional dependence for multivariate random variables with arbitrary dimensions our measure possesses the necessary and intuitive properties as a correlation index briefly it is zero almost surely if and only if two multivariate random variables are conditionally independent given a third random variable more importantly the sample version of this measure can be expressed elegantly as the root of a v or u process with random kernels and has desirable theoretical properties based on the sample version we propose a test for conditional independence which is proven to be more powerful than some recently developed tests through ou

the bayesian bootstrap the bayesian bootstrap is the bayesian analogue of the bootstrap instead of simulating the sampling distribution of a statistic estimating a parameter the bayesian bootstrap simulates the posterior distribution of the parameter operationally and inferentially the methods are quite similar because both methods of drawing inferences are based on somewhat peculiar model assumptions and the resulting inferences are generally sensitive to these assumptions neither method should be applied without some consideration of the reasonableness of these model assumptions in this sense neither method is a true bootstrap procedure yielding inferences unaided by external assumptions

testing for monotonicity in unobservables under unconfoundedness monotonicity in a scalar unobservable is a common assumption when modeling heterogeneity in structural models among other things it allows one to recover the underlying structural function from certain conditional quantiles of observables nevertheless monotonicity is a strong assumption and in some economic applications unlikely to hold e g random coefficient models its failure can have substantive adverse consequences in particular inconsistency of any estimator that is based on it having a test for this hypothesis is hence desirable this paper provides such a test for cross section data we show how to exploit an exclusion restriction together with a conditional independence assumption which in the binary treatment literature is commonly called unconfoundedness to construct a test our statistic is asymptotically normal under local alternatives and consistent against global alternatives monte carlo experiments show that a suitable bootstrap procedure yields tests with reasonable level behavior and useful power we apply our test to study the role of unobserved ability in determining black white wage differences and to study whether engel curves are monotonically driven by a scalar unobservable

interval estimation of value at risk based on garch models with heavy tailed innovations arch and garch models are widely used to model financial market volatilities in risk management applications considering a garch model with heavy tailed innovations we characterize the limiting distribution of an estimator of the conditional value at risk var which corresponds to the extremal quantile of the conditional distribution of the garch process we propose two methods the normal approximation method and the data tilting method for constructing confidence intervals for the conditional var estimator and assess their accuracies by simulation studies finally we apply the proposed approach to an energy market data set

testing the conditional independence and monotonicity assumptions of item response theory when item characteristic curves are nondecreasing functions of a latent variable the conditional or local independence of item responses given the latent variable implies nonnegative conditional covariances between all monotone increasing functions of a set of item responses given any function of the remaining item responses this general result provides a basis for testing the conditional independence assumption without first specifying a parametric form for the nondecreasing item characteristic curves the proposed tests are simple have known asymptotic null distributions and possess certain optimal properties in an example the conditional independence hypothesis is rejected for all possible forms of monotone item characteristic curves

nonparametric transition based tests for jump diffusions we develop a specification test for the transition density of a discretely sampled continuous time jump diffusion process based on a comparison of a nonparametric estimate of the transition density or distribution function with their corresponding parametric counterparts assumed by the null hypothesis as a special case our method applies to pure diffusions we provide a direct comparison of the two densities for an arbitrary specification of the null parametric model using three different discrepancy measures between the null and alternative transition density and distribution functions we establish the asymptotic null distributions of proposed test statistics and compute their power functions we investigate the finite sample properties through simulations and compare them with those of other tests this article has supplementary material online

empirical likelihood for linear models empirical likelihood is a nonparametric method of inference it has sampling properties similar to the bootstrap but where the bootstrap uses resampling it profiles a multinomial likelihood supported on the sample its properties in i i d settings have been investigated in works by owen by hall and by diciccio hall and romano this article extends the method to regression problems fixed and random regressors are considered as are robust and heteroscedastic regressions to make the extension three variations on the original idea are considered it is shown that when some functionals of the distribution of the data are known one can get sharper inferences on other functionals by imposing the known values as constraints on the optimization the result is first order equivalent to conditioning on a sample value of the known functional the use of a euclidean alternative to the likelihood function is investigated a triangular array version of the empirical likelihood theorem is given the one way anova and heteroscedastic regression models are considered in detail an example is given in which inferences are drawn on the parameters of both the regression function and the conditional variance model

a regularization approach to the many instruments problem abstract this paper focuses on the estimation of a finite dimensional parameter in a linear model where the number of instruments is very large or infinite in order to improve the small sample properties of standard instrumental variable iv estimators we propose three modified iv estimators based on three different ways of inverting the covariance matrix of the instruments these inverses involve a regularization or smoothing parameter it should be stressed that no restriction on the number of instruments is needed and that all the instruments are used in the estimation we show that the three estimators are asymptotically normal and attain the semiparametric efficiency bound higher order analysis of the mse reveals that the bias of the modified estimators does not depend on the number of instruments finally we suggest a data driven method for selecting the regularization parameter interestingly our regularization techniques lead to a consistent nonparametric estimation of the optimal instrument

the virtual cohomological dimension of the mapping class group of an orientable surface let f f r be the mapping class group of a surface f of genus g with s punctures and r boundary components the purpose of this paper is to establish cohomology properties of f parallel to those of the arithmetic groups if g is a linear algebraic group defined over q x is the symmetric space associated to g and a is an arithmetic subgroup of g then a is virtually torsion free and acts properly discontinuously on x the rational homology of a is the same as that of x a furthermore there is a bordification of x bs to a manifold with corners 3 and an extension of the action of a to a properly discontinuous action on jf so that the quotient x a is compact the boundary of jf is homotopy equivalent to a wedge of spheres say of dimension d and the virtual cohomological dimension of a is n d 1 where n is the dimension of x in the case of the mapping class group there is no analog for g ivanov unpublished has proven that f is not arithmetic nevertheless f acts properly discontinuously on teichmiiller space r which is homeomorphic to euclidean space of dimension 6 g 6 2 s 3 will play the role of the symmetric space the quotient of 9by f is the moduli space of curves whose rational homology is then identified with that of e harvey har has constructed a borel serre bordification j of 3 by analytic methods in the case where f has punctures we will build g by a different combinatorial method in addition we will explicitly describe inside y a cell complex y of dimension 4 g 4 s onto which j may be f equivariantly retracted thus establishing an analog of the constructions for sl n by serre soul6 sol and ash a this complex will be of the lowest possible dimension because we will use j to prove our main result

testing for separability in structural equations abstract separability is an important feature of structural equations as it implies the absence of unobservable heterogeneity of effects and has significant implications for identification and efficiency of estimation this paper provides a nonparametric test for separability in structural equations the test is based on a conditional independence test recently developed by huang et al 2013 building on consistent procedures of bierens 1982 1990 and stinchcombe and white 1998 the test is easy to implement and achieves n local power we apply our test to study interest rate elasticities of loan demand in microfinance and the impact of education on wages

tiling the projective foliation space of a punctured surface there is a natural way to associate7 to each ideal triangulation of a punctured surface a cell decomposition of the projective foliation space of the punctured surface a recent theme in the topology of surfaces has been the special role played by punctured surfaces both in the study of geometric structures and in the study of measured foliations for example one important result has been the construction of an equivariant ideal cell decomposition of the teichmriller space of a punctured surface a result due to many people including harer strebel mumford epstein and bowditch and penner see for example har eb and p in all of these proofs an important construct has been an ideal cell division of the punctured surface indeed the cells of teichmuller space are in 1 1 correspondence with isotopy classes of ideal cell dirisions of the punctured surface in m1 and m2 ideal cell divisions were used in the study of measured foliations on a punctured surface in order to define conjugacy invariants of certain elements of the mapping class group of a punctured surface and to present an algorithm for computing these invariants it is the purpose of this work to provide a deeper foundation for the algorithm described in m1 in particular we shall develop the theory of measured foliations on a punctured surface from the ground up using the plan and several technical tools from flp but utilizing ideal triangulations in place of pairs of pants decompositions for actually constructing measured foliations our main result here is that to each isotopy class of ideal triangulations there is a naturally associated cell decompositiosn of b s thurston s space of projective measured foliations this result parallels the result of harer and penner that on any surface punctured or not to each choice of a pair of pants decomposition plus an additional choice of data sufficient to determine a marking of the surface there is a naturally associated cell decomposition of bs many of the techniques of proof used here are not new being adaptations and reorganizations of the techniques of flp the notable exception occurs in the use of elementary moves on ideal triangulations to understand the overlap maps of different parameterizations of xs rec eived by the editors may 25 1985 and in revised form april 3

nonparametric estimation of convex models via mixtures we present a general approach to estimating probability measures constrained to lie in a convex set we represent constrained measures as mixtures of simple known extreme measures and so the problem of estimating a constrained measure becomes one of estimating an unconstrained mixing measure convex constraints arise in many modeling situations such as estimation of the mean and estimation under stochastic ordering constraints we describe mixture representation techniques for these and other situations and discuss applications to maximum likelihood and bayesian estimation

testing the markov property with high frequency data this paper develops a framework to nonparametrically test whether discrete valued irregularly spaced financial transactions data follow a markov process for that purpose we consider a specific optional sampling in which a continuous time markov process is observed only when it crosses some discrete level this framework is convenient for it accommodates the irregular spacing that characterizes transactions data under such an observation rule the current price duration is independent of a previous price duration given the previous price realization a simple nonparametric test then follows by examining whether this conditional independence property holds monte carlo simulations suggest that the asymptotic test has huge size distortions though a bootstrap based variant entails reasonable size and power properties in finite samples as for an empirical illustration we investigate whether bid ask spreads follow markov processes using transactions data from the new york stock exchange the motivation lies on the fact that asymmetric information models of market microstructures predict that the markov property does not hold for the bid ask spread we robustly reject the markov assumption for two out of the five stocks under scrutiny finally it is reassuring that our results are consistent with two alternative measures of asymmetric information

on the performance of full duplex two way relay channels with spatial modulation in this paper the spatial modulation sm technique is employed at the source and relay nodes in a full duplex two way relay channel fd twrc to support spectral efficient bi directional communications while guaranteeing a low cost implementation maximum likelihood detectors are employed at each node that is subject to an intrinsic self loop interference we first propose a tight upper bound on the average bit error probability abep then based on the abep upper bound an asymptotic abep expression is derived in the high signal to noise ratio snr regime exploiting the asymptotic abep an exact snr threshold for the selection between fd twrc sm and half duplex hd twrc sm is derived in a closed form which sheds light on when it is beneficial to select the fd or hd mode in addition the power allocation pa among sources and relay is investigated through which an optimal pa factor in terms of abep is obtained all analytical results derived in this paper are verified by monte carlo simulations from which some new insights are obtained on the performance of fd twrc sm

bootstrap methods for markov processes the block bootstrap is the best known bootstrap method for time series data when the analyst does not have a parametric model that reduces the data generation process to simple random sampling however the errors made by the block bootstrap converge to zero only slightly faster than those made by first order asymptotic approximations this paper describes a bootstrap procedure for data that are generated by a markov process or a process that can be approximated by a markov process with sufficient accuracy the procedure is based on estimating the markov transition density nonparametrically bootstrap samples are obtained by sampling the process implied by the estimated transition density conditions are given under which the errors made by the markov bootstrap converge to zero more rapidly than those made by the block bootstrap

testing conditional independence via rosenblatt transforms this paper proposes new tests of conditional independence of two random variables given a single index involving an unknown finite dimensional parameter the tests employ rosenblatt transforms and are shown to be distribution free while retaining computational convenience some results from monte carlo simulations are presented and discussed

an exact analysis of conditional independence in several 2 x 2 contingency tables summary this paper proposes an exact test of conditional independence and an efficient algorithm for several 2 x 2 contingency tables simulations compare it with a commonly used exact test for null interaction and common odds ratio

asymptotic equivalence between the cox estimator and the general ml estimators of regression and survival parameters in the cox model the usual approach to estimating regression parameters in the cox regression model uses the partial likelihood if the covariates are not time dependent the model can be stated in terms of the survival function which allows one to derive a generalized likelihood containing both regression and survival curve parameters it is shown that in the absence of ties an estimator results which is asymptotically equivalent to the partial likelihood estimator a joint information matrix leads simply to standard errors for both regression and survival curve parameters which are asymptotically correct

expected conditional characteristic function based measures for testing independence we propose a novel class of independence measures for testing independence between two random vectors based on the discrepancy between the conditional and the marginal characteristic functions the

a test for model specification of diffusion processes we propose a test for model specification of a parametric diffusion process based on a kernel estimation of the transitional density of the process the empirical likelihood is used to formulate a statistic for each kernel smoothing bandwidth which is effectively a studentized l2 distance between the kernel transitional density estimator and the parametric transitional density implied by the parametric process to reduce the sensitivity of the test on smoothing bandwidth choice the final test statistic is constructed by combining the empirical likelihood statistics over a set of smoothing bandwidths to better capture the finite sample distribution of the test statistic and data dependence the critical value of the test is obtained by a parametric bootstrap procedure properties of the test are evaluated asymptotically and numerically by simulation and by a real data example

the euler characteristic of the moduli space of curves let fg 1 g 1 be the mapping class group consisting of all isotopy classes of base point and orientation preserving homeomorphisms of a closed oriented surface f of genus g let 1 be its euler characteristic in the sense of wall that is z f i fgl f l z e f where f is any torsion free subgroup of finite index in f 1 and e is a contractible space on which f acts freely and properly discontinuously an example of such a space is the teichmiiller space 1 and g f can be interpreted as the orbifold euler characteristic of f i join the moduli space of curves of genus g with base point the purpose of this paper is to prove the following formula for f i

performance and distance spectrum of space time codes in fast rayleigh fading channels in this paper we analyze the performance of spacetime codes and propose a distance spectrum computation method in fast rayleigh fading channels we first derive a new fer upper bound using the union bound and the pep upper bound in the fast fading environment the derived fer upper bound is very accurate requires only the distance spectrum of the spacetime code and takes a closed form expression then we propose a distance spectrum computation method of space time codes in fast fading channels which exploits the symmetric property of the error state diagram in space time trellis coded mpsk modulation to reduce the computation complexity numerical results illustrate that the derived fer bound is tight enough to estimate the performance of space time codes in fast fading channels with sufficient accuracy

testing conditional moment restrictions let x z be a pair of observable random vectors we construct a new smoothed empirical likelihood based test for the hypothesis e g z x 0 w p 1 where g is a vector of known functions and an unknown finite dimensional parameter we show that the test statistic is asymptotically normal under the null hypothesis and derive its asymptotic distribution under a sequence of local alternatives furthermore the test is shown to possess an optimality property in large samples simulation evidence suggests that it also behaves well in small samples

significance testing in nonparametric regression based on the bootstrap this paper proposes a test for selecting explanatory variables in nonparametric regression the test does not need to estimate the conditional expectation function given all the variables but only those which are significant under the null hypothesis this feature is computationally convenient and solves in part the problem of the curse of dimensionality when selecting regressors in a nonparametric context the proposed test statistic is based on functionals of a u process contiguous alternatives converging to the null at a rate n 1 2 can be detected the asymptotic null distribution of the statistic depends on certain features of the data generating process and asymptotic tests are difficult to implement except in rare circumstances we justify the consistency of two easy to implement bootstrap tests which exhibit good level accuracy for fairly small samples according to the reported monte carlo simulations these results are also applicable to test other interesting restrictions on nonparametric curves like partial linearity and conditional independence

on the bootstrap and likelihood based confidence regions summary we describe a method for constructing likelihood based confidence regions for a vector parameter using the bootstrap and nonparametric density estimation the technique is illustrated by application to a numerical example and its theoretical properties are elucidated it is argued that likelihood based regions should not be approximated by ellipses if we are to have any hope of capturing first order departures from normality bootstrap algorithms for constructing simultaneous confidence intervals for the components of a vector parameter are also presented advantages of the percentile t method over the ordinary percentile method are demonstrated in a multivariate setting

integrated square error properties of kernel estimators of regression functions weak laws of large numbers and central limit theorems are proyed for integrated square error of kernel estimators of regression functions the regressor is assumed to take values in rp and the regressand x to be real valued it is shown that in many cases integrated square error is asymptotically normally distributed and independent of the x sample as an application a test for the regression function such as that proposed by konakov is seen to be asymptotically independent of an arbitrary test based on the xsample the proofs involve martingale methods