the calculation of thermoacoustic oscillations thermoacoustic oscillations occur in a wide variety of practical applications in which heat is supplied to an acoustic resonator a simple geometry is investigated systematically to determine the importance of various flow parameters on the frequency of the oscillations detailed consideration of elementary examples shows that the form of the coupling between the heat input and the unsteady flow has a crucial effect on the frequency of oscillation the same elementary examples are used to compare how well if at all different calculation methods in the literature account for this influence a mean flow and a distributed region of heat input significantly complicate the analysis of thermoacoustic oscillations and are often neglected model problems are used to illustrate that mean flow effects can become significant even at modest inlet mach numbers and to indicate circumstances under which a distributed heat input may be treated as concentrated

a constrained risk inequality with applications to nonparametric functional estimation a general constrained minimum risk inequality is derived given two densities f and f 0 we find a lower bound for the risk at the point given an upper bound for the risk at the point 0 the inequality sheds new light on superefficient estimators in the normal location problem and also on an adaptive estimation problem arising in nonparametric functional estimation

empirical bayes selection of wavelet thresholds this paper explores a class of empirical bayes methods for level dependent threshold selection in wavelet shrinkage the prior considered for each wavelet coefficient is a mixture of an atom of probability at zero and a heavy tailed density the mixing weight or sparsity parameter for each level of the transform is chosen by marginal maximum likelihood if estimation is carried out using the posterior median this is a random thresholding procedure the estimation can also be carried out using other thresholding rules with the same threshold details of the calculations needed for implementing the procedure are included in practice the estimates are quick to compute and there is software available simulations on the standard model functions show excellent performance and applications to data drawn from various fields of application are used to explore the practical performance of the approach by using a general result on the risk of the corresponding marginal maximum likelihood approach for a single sequence overall bounds on the risk of the method are found subject to membership of the unknown function in one of a wide range of besov classes covering also the case of f of bounded variation the rates obtained are optimal for any value of the parameter p in 0 simultaneously for a wide range of loss functions each dominating the lq norm of the th derivative with 0 and 0 q 2 attention is paid to the distinction between sampling the unknown function within white noise and sampling at discrete points and between placing constraints on the function itself and on the discrete wavelet transform of its sequence of values at the observation points results for all relevant combinations of these scenarios are obtained in some cases a key feature of the theory is a particular boundary corrected wavelet basis details of which are discussed overall the approach described seems so far unique in combining the properties of fast computation good theoretical properties and good performance in simulations and in practice a key feature appears to be that the estimate of sparsity adapts to three different zones of estimation first where the signal is not sparse enough for thresholding to be of benefit second where an appropriately chosen threshold results in substantially improved estimation and third where the signal is so sparse that the zero estimate gives the optimum accuracy rate

equivalence theory for density estimation poisson processes and gaussian white noise with drift this paper establishes the global asymptotic equivalence between a poisson process with variable intensity and white noise with drift under sharp smoothness conditions on the unknown function this equivalence is also extended to density estimation models by poissonization the asymptotic equivalences are established by constructing explicit equivalence mappings the impact of such asymptotic equivalence results is that an investigation in one of these nonparametric models automatically yields asymptotically analogous results in the other models

new goodness of fit tests and their application to nonparametric confidence sets suppose one observes a process v on the unit interval where dv f 0 dw with an unknown parameter f 0 l 1 0 1 and standard brownian motion w we propose a particular test of one point hypotheses about f 0 which is based on suitably standardized increments of v this test is shown to have desirable consistency properties if for instance f 0 is restricted to various holder classes of functions the test is mimicked in the context of nonparametric density estimation nonparametric regression and interval censored data under shape restrictions on the parameter such as monotonicity or convexity we obtain confidence sets for f 0 adapting to its unknown smoothness

a bayesian view of doubly robust causal inference in causal inference the effect of confounding may be controlled using regression adjustment in an outcome model propensity score adjustment inverse probability of treatment weighting or a combination of these approaches based on modelling the treatment assignment mechanism along with their doubly robust extensions have been difficult to motivate using formal likelihood based or bayesian arguments as the treatment assignment model plays no part in inferences concerning the expected outcomes on the other hand forcing dependency between the outcome and treatment assignment models by allowing the former to be misspecified results in loss of the balancing property of the propensity scores and the loss of any double robustness in this paper we explain in the framework of misspecified models why doubly robust inferences cannot arise from purely likelihood based arguments as an alternative to bayesian propensity score analysis we propose a bayesian posterior predictive method for constructing doubly robust estimation procedures by incorporating the inverse treatment assignment probabilities as importance sampling weights in monte carlo integration

gmm redundancy results for general missing data problems we consider questions of efficiency and redundancy in the gmm estimation problem in which we have two sets of moment conditions where two sets of parameters enter into one set of moment conditions while only one set of parameters enters into the other we then apply these results to a selectivity problem in which the first set of moment conditions is for the model of interest and the second set of moment conditions is for the selection process we use these results to explain the counterintuitive result in the literature that under an ignorability assumption that justifies gmm with weighted moment conditions weighting using estimated probabilities of selection is better than weighting using the true probabilities we also consider estimation under an exogeneity of selection assumption such that both the unweighted and the weighted moment conditions are valid and we show that when weighting is not needed for consistency it is also not useful for efficiency

feedback control of combustion instabilities from within limit cycle oscillations using h loop shaping and the ν gap metric combustion instabilities arise owing to a two way coupling between acoustic waves and unsteady heat release oscillation amplitudes successively grow until nonlinear effects cause saturation into limit cycle oscillations feedback control in which an actuator modifies some combustor input in response to a sensor measurement can suppress combustion instabilities linear feedback controllers are typically designed using linear combustor models however when activated from within limit cycle the linear model is invalid and such controllers are not guaranteed to stabilize this work develops a feedback control strategy guaranteed to stabilize from within limit cycle oscillations a low order model of a simple combustor exhibiting the essential features of more complex systems is presented linear plane acoustic wave modelling is combined with a weakly nonlinear describing function for the flame the latter is determined numerically using a level set approach its implication is that the open loop transfer function oltf needed for controller design varies with oscillation level the difference between the mean and the rest of the oltfs is characterized using the gap metric providing the minimum required robustness margin for an formula see text loop shaping controller such controllers are designed and achieve stability both for linear fluctuations and from within limit cycle oscillations

adaptive estimation of a quadratic functional by model selection we consider the problem of estimating s 2 when s belongs to some separable hilbert space and one observes the gaussian process y t langles t rangle sigmal t for all t epsilon mathbb h where l is some gaussian isonormal process this framework allows us in particular to consider the classical gaussian sequence model for which mathbb h l 2 mathbb n and l t sum lambda geq1 t lambda varepsilon lambda where varepsilon lambda lambda geq1 is a sequence of i i d standard normal variables our approach consists in considering some at most countable families of finite dimensional linear subspaces of mathbb h the models and then using model selection via some conveniently penalized least squares criterion to build new estimators of s 2 we prove a general nonasymptotic risk bound which allows us to show that such penalized estimators are adaptive on a variety of collections of sets for the parameter s depending on the family of models from which they are built in particular in the context of the gaussian sequence model a convenient choice of the family of models allows defining estimators which are adaptive over collections of hyperrectangles ellipsoids l p bodies or besov bodies we take special care to describe the conditions under which the penalized estimator is efficient when the level of noise sigma tends to zero our construction is an alternative to the one by efroimovich and low for hyperrectangles and provides new results otherwise

estimating exposure effects by modelling the expectation of exposure conditional on confounders in order to estimate the causal effects of one or more exposures or treatments on an outcome of interest one has to account for the effect of confounding factors which both covary with the exposures or treatments and are independent predictors of the outcome in this paper we present regression methods which in contrast to standard methods adjust for the confounding effect of multiple continuous or discrete covariates by modelling the conditional expectation of the exposures or treatments given the confounders in the special case of a univariate dichotomous exposure or treatment this conditional expectation is identical to what rosenbaum and rubin have called the propensity score they have also proposed methods to estimate causal effects by modelling the propensity score our methods generalize those of rosenbaum and rubin in several ways first our approach straightforwardly allows for multivariate exposures or treatments each of which may be continuous ordinal or discrete second even in the case of a single dichotomous exposure our approach does not require subclassification or matching on the propensity score so that the potential for residual confounding i e bias due to incomplete matching is avoided third our approach allows a rather general formalization of the idea that it is better to use the estimated propensity score than the true propensity score even when the true score is known the additional power of our approach derives from the fact that we assume the causal effects of the exposures or treatments can be described by the parametric component of a semiparametric regression model to illustrate our methods we reanalyze the effect of current cigarette smoking on the level of forced expiratory volume in one second in a cohort of 2 713 adult white males we compare the results with those obtained using standard methods

identification of heat transfer dynamics for non modal analysis of thermoacoustic stability a systematic approach for non modal stability analysis of thermoacoustic systems with a localized heat source is proposed the response of the heat source to flow perturbations is obtained from unsteady computational fluid dynamics combined with correlation based linear system identification a model for the complete thermoacoustic system is formulated with a galerkin expansion technique where the heat source is included as an acoustically compact element the eigenvalues of the resulting system are obtained from discretization of the solution operator the maximum growth factor is estimated from the pseudospectra using kreiss theorem the approach is illustrated with a simple rijke tube configuration results obtained with a simple baseline model for the heat source dynamics based on king s law widely used in hot wire anemometry are compared against the more advanced treatment developed here analysis of pseudospectra diagrams shows that the choice of the heat source model does influence the sensitivity of eigenvalues to perturbations and hence the non normal behavior the maximum growth factor for the system with the heat source model based on king s law is more sensitive to changes in the heat source location than the cfd based heat source model

efficiency loss caused by linearity condition in dimension reduction linearity sometimes jointly with constant variance is routinely assumed in the context of sufficient dimension reduction it is well understood that when these conditions do not hold blindly using them may lead to inconsistency in estimating the central subspace and the central mean subspace surprisingly we discover that even if these conditions do hold using them will bring efficiency loss this paradoxical phenomenon is illustrated through sliced inverse regression and principal hessian directions the efficiency loss also applies to other dimension reduction procedures we explain this empirical discovery by theoretical investigation

adaptive hypothesis testing using wavelets let a function f be observed with a noise we wish to test the null hypothesis that the function is identically zero against a composite nonparametric alternative functions from the alternative set are separated away from zero in an integral e g l 2 norm and also possess some smoothness properties the minimax rate of testing for this problem was evaluated in earlier papers by ingster and by lepski and spokoiny under different kinds of smoothness assumptions it was shown that both the optimal rate of testing and the structure of optimal in rate tests depend on smoothness parameters which are usually unknown in practical applications in this paper the problem of adaptive assumption free testing is considered it is shown that adaptive testing without loss of efficiency is impossible an extra log log factor is inessential but unavoidable payment for the adaptation a simple adaptive test based on wavelet technique is constructed which is nearly minimax for a wide range of besov classes

perturbation theory of nonlinear non self adjoint eigenvalue problems simple eigenvalues abstract the study of the vibrational modes and stability of a given physical system is strongly tied to the efficient numerical evaluation of its eigenvalues the operators governing the eigenproblem are in general nonlinear in the eigenvalue and non self adjoint which makes the repeated solution of the eigenvalue problem necessary for example when the effect of several parameter values on the system needs to be assessed expensive this study reviews the adjoint based incremental procedure for calculating the coefficients of power series expansions of simple non degenerate eigenvalues and their eigenvectors these expansions approximate the eigenvalues to any desired order in a finite region an efficient numerical implementation of the theory is proposed and it is shown how high order power series approximations of the eigenvalues give very accurate results within the radius of convergence of the power series which is finite and generally not small furthermore the domain of convergence of the power series might be extended by considering pade expansions of the eigenvalues examples involving the stability of the orr sommerfeld equation the biharmonic equation for the vibrational modes of a membrane and the emission of sound from a rijke tube associated with thermoacoustic feedback are used to assess and validate the theory

on bayesian estimation of marginal structural models summary the purpose of inverse probability of treatment ipt weighting in estimation of marginal treatment effects is to construct a pseudo population without imbalances in measured covariates thus removing the effects of confounding and informative censoring when performing inference in this article we formalize the notion of such a pseudo population as a data generating mechanism with particular characteristics and show that this leads to a natural bayesian interpretation of ipt weighted estimation using this interpretation we are able to propose the first fully bayesian procedure for estimating parameters of marginal structural models using an ipt weighting our approach suggests that the weights should be derived from the posterior predictive treatment assignment and censoring probabilities answering the question of whether and how the uncertainty in the estimation of the weights should be incorporated in bayesian inference of marginal treatment effects the proposed approach is compared to existing methods in simulated data and applied to an analysis of the canadian co infection cohort

the central role of the propensity score in observational studies for causal effects abstract the results of observational studies are often disputed because of nonrandom treatment assignment for example patients at greater risk may be overrepresented in some treatment group this paper discusses the central role of propensity scores and balancing scores in the analysis of observational studies the propensity score is the estimated conditional probability of assignment to a particular treatment given a vector of observed covariates both large and small sample theory show that adjustment for the scalar propensity score is sufficient to remove bias due to all observed covariates applications include matched sampling on the univariate propensity score which is equal percent bias reducing under more general conditions than required for discriminant matching multivariate adjustment by subclassification on balancing scores where the same subclasses are used to estimate treatment effects for all outcome variables and in all subpopulations and visual representation of multivariate adjustment by a two dimensional plot author

semiparametric methods for response selective and missing data problems in regression summary suppose that data are generated according to the model f ylx 0 g x where y is a response and x are covariates we derive and compare semiparametric likelihood and pseudolikelihood methods for estimating 0 for situations in which units generated are not fully observed and in which it is impossible or undesirable to model the covariate distribution the probability that a unit is fully observed may depend on y and there may be a subset of covariates which is observed only for a subsample of individuals our key assumptions are that the probability that a unit has missing data depends only on which of a finite number of strata that y x belongs to and that the stratum membership is observed for every unit applications include case control studies in epidemiology field reliability studies and broad classes of missing data and measurement error problems our results make fully efficient estimation of 0 feasible and they generalize and provide insight into a variety of methods that have been proposed for specific problems

adaptive wavelet estimation a block thresholding and oracle inequality approach we study wavelet function estimation via the approach of block thresh olding and ideal adaptation with oracle oracle inequalities are derived and serve as guides for the selection of smoothing parameters based on an oracle inequality and motivated by the data compression and localization properties of wavelets an adaptive wavelet estimator for nonparametric re gression is proposed and the optimality of the procedure is investigated we show that the estimator achieves simultaneously three objectives adaptiv ity spatial adaptivity and computational efficiency specifically it is proved that the estimator attains the exact optimal rates of convergence over a range of besov classes and the estimator achieves adaptive local minimax rate for estimating functions at a point the estimator is easy to imple ment at the computational cost of on simulation shows that the es timator has excellent numerical performance relative to more traditional wavelet estimators 1 introduction wavelet methods have demonstrated considerable suc cess in nonparametric function estimation in terms of spatial adaptivity com putational efficiency and asymptotic optimality in contrast to the traditional linear procedures wavelet methods achieve near optimal convergence rates over large function classes such as besov classes and enjoy excellent mean squared error properties when used to estimate functions that are spatially inhomogeneous for example as shown by donoho and johnstone 1998 wavelet methods can outperform optimal linear methods even at the level of convergence rate over certain besov classes standard wavelet methods achieve adaptivity through term by term thresholding of the empirical wavelet coefficients there each individual empirical wavelet coefficient is compared with a predetermined threshold a wavelet coefficient is retained if its magnitude is above the threshold level and is discarded otherwise a well known example of term by term thresholding is donoho and johnstone s visushrink donoho and johnstone 1994 visushrink is spatially adaptive and the estimator is within a log arithmic factor of the optimal convergence rate over a wide range of besov classes visushrink achieves a degree of tradeoff between variance and bias contributions to the mean squared error however the tradeoff is not optimal visushrink reconstruction is often over smoothed hall kerkyacharian and picard 1999 considered block thresholding for wavelet function estimation which thresholds empirical wavelet coefficients in

semiparametric regression estimation in the presence of dependent censoring summary we propose a semiparametric estimation procedure for estimating the regression of an outcome y measured at the end of a fixed follow up period on baseline explanatory variables x measured prior to start of follow up in the presence of dependent censoring given x the proposed estimators are consistent when the data are missing at random but not missing completely at random rubin 1976 and do not require full specification of the complete data likelihood specifically we assume that the probability of censoring at time t is independent of the outcome y conditional on the recorded history up to t of a vector of time dependent covariates that are correlated with y our estimators can be used to adjust for dependent censoring and nonrandom noncompliance in randomised trials studying the effect of a treatment on the mean of a response variable of interest even with independent censoring our methods allow the investigator to increase efficiency by exploiting the correlation of the outcome with a vector of time dependent covariates

using a monotone single index model to stabilize the propensity score in missing data problems and causal inference the augmented inverse weighting method is one of the most popular methods for estimating the mean of the response in causal inference and missing data problems an important component of this method is the propensity score popular parametric models for the propensity score include the logistic probit and complementary log log models a common feature of these models is that the propensity score is a monotonic function of a linear combination of the explanatory variables to avoid the need to choose a model we model the propensity score via a semiparametric single index model in which the score is an unknown monotonic nondecreasing function of the given single index under this new model the augmented inverse weighting estimator aiwe of the mean of the response is asymptotically linear semiparametrically efficient and more robust than existing estimators moreover we have made a surprising observation the inverse probability weighting and aiwes based on a correctly specified parametric model may have worse performance than their counterparts based on a nonparametric model a heuristic explanation of this phenomenon is provided a real data example is used to illustrate the proposed methods

a paradox concerning nuisance parameters and projected estimating functions summary this paper is concerned with a paradox associated with parameter estimation in the presence of nuisance parameters in a statistical model with unknown nuisance parameters the efficiency of an estimator of a parameter usually increases when the nuisance para meters are known however the opposite phenomenon can sometimes occur in this paper we elucidate the occurrence of this paradox by examining estimating functions in particular we focus on the projected estimating function which is defined by the projection of the score function on to a given estimating function a sufficient condition for the paradox to occur is the orthogonality of the two components of the projected estimating functions corresponding to parameters of interest and nuisance parameters in addition a numerical assessment is conducted in the context of a simple model to investigate the improvement of the asymptotic efficiency of estimators

estimation of the effect of interventions that modify the received treatment motivated by a study of surgical operating time and post operative outcomes for lung cancer we consider the estimation of causal effects of continuous point exposure treatments to investigate causality the standard paradigm postulates a series of treatment specific counterfactual outcomes and establishes conditions under which we may learn about them from observational study data while many choices are possible causal effects are typically defined in terms of variation of the mean of counterfactual outcomes in hypothetical worlds in which specific treatment strategies are applied to all individuals for example one might compare two worlds one where each individual receives some specific dose and a second where each individual receives some other dose for our motivating study defining causal effects in this way corresponds to hypothetical interventions that could not conceivably be implemented in the real world in this work we consider an alternative complimentary framework that investigates variation in the mean of counterfactual outcomes under hypothetical treatment strategies where each individual receives a treatment dose corresponding to that actually received but modified in some pre specified way quantification of this variation is defined in terms of contrasts for specific interventions as well as in terms of the parameters of a new class of marginal structural mean models within this framework we propose three estimators an outcome regression estimator an inverse probability of treatment weighted estimator and a doubly robust estimator we illustrate the methods with an analysis of the motivating data copyright 2013 john wiley sons ltd

accounting for convective effects in zero mach number thermoacoustic models this paper presents a methodology to account for some mean flow effects on thermo acoustic instabilities when using the zero mach number assumption it is shown that when a computational domain is represented under the m 0 assumption a nonzero mach number element can simply be taken into account by imposing a proper acoustic impedance at the boundaries so as to mimic the mean flow effects in the outer not computed flow domain a model that accounts for the coupling between acoustic and entropy waves is presented it relies on a delayed entropy coupled boundary condition decbc for the helmholtz equation satisfied by the acoustic pressure the model proves able to capture low frequency entropic modes even without mean flow terms in the fluctuating pressure equation

a c_p criterion for semiparametric causal inference for marginal structural models which recently play an important role in causal inference we consider a model selection problem in the framework of a semiparametric approach using inverse probability weighted estimation or doubly robust estimation in this framework the modeling target is a potential outcome which may be a missing value and so we cannot apply the aic nor its extended version to this problem in other words there is no analytical information criterion obtained according to its classical derivation for this problem hence we define a mean squared error appropriate for treating the potential outcome and then we derive its asymptotic unbiased estimator as a c p criterion from an asymptotics for the semiparametric approach and using an ignorable treatment assignment condition in simulation study it is shown that the proposed criterion exceeds a conventionally derived existing criterion in the squared error and model selection frequency specifically in all simulation settings the proposed criterion provides clearly smaller squared errors and higher frequencies selecting the true or nearly true model moreover in real data analysis we check that there is a clear difference between the selections by the two criteria

importance sampling via the estimated sampler monte carlo importance sampling for evaluating numerical integration is discussed we consider a parametric family of sampling distributions and propose the use of the sampling distribution estimated by maximum likelihood the proposed method of importance sampling using the estimated sampling distribution is shown to improve the asymptotic variance of the ordinary method using the true sampling distribution the argument is closely related to the discussion of the paradox in henmi eguchi 2004 we focus on a condition under which the estimated integration value obtained by the proposed method has asymptotic zero variance

parameter orthogonality and approximate conditional inference on propose une statistique du rapport de vraisemblance construite a partir de la distribution conditionnelle des observations etant donne les estimateurs du maximum de vraisemblance pour les parametres de nuisance

variance estimation in inverse probability weighted cox models inverse probability weighted cox models can be used to estimate marginal hazard ratios under different point treatments in observational studies to obtain variance estimates the robust sandwich variance estimator is often recommended to account for the induced correlation among weighted observations however this estimator does not incorporate the uncertainty in estimating the weights and tends to overestimate the variance leading to inefficient inference here we propose a new variance estimator that combines the estimation procedures for the hazard ratio and weights using stacked estimating equations with additional adjustments for the sum of terms that are not independently and identically distributed in a cox partial likelihood score equation we prove analytically that the robust sandwich variance estimator is conservative and establish the asymptotic equivalence between the proposed variance estimator and one obtained through linearization by hajage et al in 2018 in addition we extend our proposed variance estimator to accommodate clustered data we compare the finite sample performance of the proposed method with alternative methods through simulation studies we illustrate these different variance methods in both independent and clustered data settings using a bariatric surgery dataset and a multiple readmission dataset respectively to facilitate implementation of the proposed method we have developed an r package ipwcoxcsv

likelihood for statistically equivalent models in likelihood inference we usually assume that the model is fixed and then base inference on the corresponding likelihood function often however the choice of model is rather arbitrary and there may be other models which fit the data equally well we study robustness of likelihood inference over such statistically equivalent models and suggest a simple envelope likelihood to capture this aspect of model uncertainty robustness depends critically on how we specify the parameter of interest some asymptotic theory is presented illustrated by three examples

an efficient method of estimation for longitudinal surveys with monotone missing data panel attrition is frequently encountered in panel sample surveys when it is related to the observed study variable the classical approach of nonresponse adjustment using a covariate dependent dropout mechanism can be biased we consider an efficient method of estimation with monotone panel attrition when the response probability depends on the previous values of study variable as well as other covariates because of the monotone structure of the missing pattern the response mechanism is missing at random the proposed estimator is asymptotically optimal in the sense that it minimizes the asymptotic variance of a class of estimators that can be written as a linear combination of the unbiased estimators of the panel estimates for each wave and incorporates all available information using generalized least squares variance estimation is discussed and results from a simulation study are presented copyright 2012 oxford university press

cfd based application of the nyquist criterion to thermo acoustic instabilities a novel approach for the analysis of self excited instabilities in thermo acoustic systems is proposed combining computational fluid dynamics with low order acoustic modeling the open loop transfer function of the system under investigation is computed the system eigenmodes and the linear stability characteristics are then deduced from a nyquist plot the method is suitable for systems where due to geometrical complexities or non compact regions of heat release a low order formulation is not appropriate or not available explicit knowledge of the frequency response or the transfer matrix of the heat source is not required further advantages of the new approach are discussed in the paper to establish proof of concept the method is validated against a simple model of a rijke tube over the frequency range considered frequencies and growth rates of stable as well as unstable eigenmodes are predicted accurately the new method combining flow simulation low order acoustic modeling and control theory makes possible a comprehensive analysis of acoustic stability behavior of complex thermo acoustic systems at comparatively modest computational cost

the one dimensional acoustic field in a duct with arbitrary mean axial temperature gradient and mean flow abstract this paper presents an analytical solution for the one dimensional acoustic field in a duct with arbitrary mean temperature gradient and mean flow a wave equation for the pressure perturbation is derived which relies on very few assumptions an analytical solution for this is derived using an adapted wkb approximation the solution is a superposition of waves travelling in either direction and thus provides physical insight it is also very easy to calculate the proposed solution is applied to ducts with a mean temperature profile which varies axially with i a linear and ii a partial sine wave profile predictions are compared to those obtained by numerically solving the linearised euler equations lees the analytical solution reproduces the acoustic field very accurately across a wide range of flow conditions which span both low and moderate to high subsonic mach numbers it always performs well when the frequency exceeds a certain value when the mean temperature profile is linear it also performs well to very low frequencies this increased frequency range for linear mean temperature profiles leads to its application to more complicated profiles in a piecewise linear manner axially segmenting the temperature profile into regions that can be approximated as linear the acoustic field is predicted very accurately as long as enough segmentation points are used and the condition for the linear mean temperature profile is satisfied k 0 where k0 is the local wave number when there is no mean flow and is the normalised mean density gradient the proposed solution is extensively compared to previous analytical solutions and is found to be more accurate and reliable especially at higher mach numbers the entropy wave generated by communication between the acoustic waves and the distributed mean temperature zone is calculated using the lees it is found to remain very small across all operating conditions such that both the entropy wave and its impact on the acoustic field can be neglected

asymptotic equivalence and adaptive estimation for robust nonparametric regression asymptotic equivalence theory developed in the literature so far are only for bounded loss functions this limits the potential applications of the theory because many commonly used loss functions in statistical inference are unbounded in this paper we develop asymptotic equivalence results for robust nonparametric regression with unbounded loss functions the results imply that all the gaussian nonparametric regression procedures can be robustified in a unified way a key step in our equivalence argument is to bin the data and then take the median of each bin the asymptotic equivalence results have significant practical implications to illustrate the general principles of the equivalence argument we consider two important nonparametric inference problems robust estimation of the regression function and the estimation of a quadratic functional in both cases easily implementable procedures are constructed and are shown to enjoy simultaneously a high degree of robustness and adaptivity other problems such as construction of confidence sets and nonparametric hypothesis testing can be handled in a similar fashion

acoustic modes in combustors with complex impedances and multidimensional active flames two approaches for solving the corresponding nonlinear eigenvalue problem are proposed the first one is based on an asymptotic expansion of the solution the baseline being the acoustic modes and frequencies for a steady or passive flame and appropriate boundary conditions this method allows a quick assessment of any acoustic mode stabilitybutisvalidonlyforcaseswherethecouplingbetweenthe flameandtheacousticwavesissmallinamplitude the second approach is based on an iterative algorithm where a quadratic eigenvalue problem is solved at each subiteration it is more central processing unit demanding but remains valid even in cases where the response of the flametoacousticperturbationsislarge frequency dependentboundaryimpedancesareaccountedforinbothcases a parallel implementation of the arnoldi iterative method is used to solve the large eigenvalue problem that arises fromthespacediscretization ofthe helmholtzequation several academicandindustrial testcasesareconsideredto illustrate the potential of the method

stability analysis of thermo acoustic nonlinear eigenproblems in annular combustors part ii uncertainty quantification monte carlo and active subspace identification methods are combined with first and second order adjoint sensitivities to perform forward uncertainty quantification analysis of the thermo acoustic stability of two annular combustor configurations this method is applied to evaluate the risk factor i e the probability for the system to be unstable it is shown that the adjoint approach reduces the number of nonlinear eigenproblem calculations by as much as the monte carlo samples

adjoint based sensitivity analysis of low order thermoacoustic networks using a wave based approach strict pollutant emission regulations are pushing gas turbine manufacturers to develop devices that operate in lean conditions with the downside that combustion instabilities are more likely to occur methods to predict and control unstable modes inside combustion chambers have been developed in the last decades but in some cases they are computationally expensive sensitivity analysis aided by adjoint methods provides valuable sensitivity information at a low computational cost this paper introduces adjoint methods and their application in wave based low order network models which are used as industrial tools to predict and control thermoacoustic oscillations two thermoacoustic models of interest are analyzed first in the zero mach number limit a nonlinear eigenvalue problem is derived and continuous and discrete adjoint methods are used to obtain the sensitivities of the system to small modifications sensitivities to base state modification and feedback devices are presented second a more general case with non zero mach number a moving flame front and choked outlet is presented the influence of the entropy waves on the computed sensitivities is shown

estimation of regression coefficients when some regressors are not always observed abstract in applied problems it is common to specify a model for the conditional mean of a response given a set of regressors a subset of the regressors may be missing for some study subjects either by design or happenstance in this article we propose a new class of semiparametric estimators based on inverse probability weighted estimating equations that are consistent for parameter vector 0 of the conditional mean model when the data are missing at random in the sense of rubin and the missingness probabilities are either known or can be parametrically modeled we show that the asymptotic variance of the optimal estimator in our class attains the semiparametric variance bound for the model by first showing that our estimation problem is a special case of the general problem of parameter estimation in an arbitrary semiparametric model in which the data are missing at random and the probability of observing complete data is bounded away from 0 and then deriving a representation for the efficient score

a semiparametric approach to dimension reduction we provide a novel and completely different approach to dimension reduction problems from the existing literature we cast the dimension reduction problem in a semiparametric estimation framework and derive estimating equations viewing this problem from the new angle allows us to derive a rich class of estimators and obtain the classical dimension reduction techniques as special cases in this class the semiparametric approach also reveals that in the inverse regression context while keeping the estimation structure intact the common assumption of linearity and or constant variance on the covariates can be removed at the cost of performing additional nonparametric regression the semiparametric estimators without these common assumptions are illustrated through simulation studies and a real data example this article has online supplementary material

a note on a partial empirical likelihood a partial profile empirical likelihood for a semiparametric mixture model zou et al 2002 is shown to originate in a conditional likelihood involving additional nuisance parameters the partial likelihood is the conditional likelihood with the nuisance parameters replaced by their estimators from the full likelihood the conditional likelihood suggests alternative estimators we demonstrate that the partial likelihood estimator is more efficient than an estimator for which the nuisance parameters are known the practical implications of this counter intuitive result are discussed

on the estimation of quadratic functionals we discuss the difficulties of estimating quadratic functionals based on observations y t from the white noise model y t int t 0 f u du sigma w t quad t in lbrack 0 1 rbrack where w t is a standard wiener process on lbrack 0 1 rbrack the optimal rates of convergence as sigma rightarrow 0 for estimating quadratic functionals under certain geometric constraints are found specifically the optimal rates of estimating int 1 0 lbrack f k x rbrack 2 dx under hyperrectangular constraints sum f x j f leq cj alpha and weighted l p body constraints sum p f sum infty 1 j r x j f p leq c are computed explicitly where x j f is the j th fourier bessel coefficient of the unknown function f we develop lower bounds based on testing two highly composite hypercubes and address their advantages the attainable lower bounds are found by applying the hardest one dimensional approach as well as the hypercube method we demonstrate that for estimating regular quadratic functionals i e the functionals which can be estimated at rate o sigma 2 the difficulties of the estimation are captured by the hardest one dimensional subproblems and for estimating nonregular quadratic functionals i e no o sigma 2 consistent estimator exists the difficulties are captured at certain finite dimensional the dimension goes to infinity as sigma rightarrow 0 hypercube subproblems

empirical likelihood in missing data problems missing data is a ubiquitous problem in medical and social sciences it is well known that inferences based only on the complete data may not only lose efficiency but may also lead to biased results if the data is not missing completely at random mcar the inverse probability weighting method proposed by horvitz and thompson 1952 is a popular alternative when the data is not mcar the horvitz thompson method however is sensitive to the inverse weights and may suffer from loss of efficiency in this paper we propose a unified empirical likelihood approach to missing data problems and explore the use of empirical likelihood to effectively combine unbiased estimating equations when the number of estimating equations is greater than the number of unknown parameters one important feature of this approach is the separation of the complete data unbiased estimating equations from the incomplete data unbiased estimating equations the proposed method can achieve semiparametric efficiency if the probabilit