generalized principal component analysis projection of saturated model parameters principal component analysis pca is very useful for a wide variety of data analysis tasks but its implicit connection to the gaussian distribution can be undesirable for discrete data such as bi

selecting the number of principal components estimation of the true rank of a noisy matrix principal component analysis pca is a well known tool in multivariate statistics one significant challenge in using pca is the choice of the number of principal components in order to address this challenge we propose distribution based methods with exact type 1 error controls for hypothesis testing and construction of confidence intervals for signals in a noisy matrix with finite samples assuming gaussian noise we derive exact type 1 error controls based on the conditional distribution of the singular values of a gaussian matrix by utilizing a post selection inference framework and extending the approach of taylor loftus and tibshirani 2013 in a pca setting in simulation studies we find that our proposed methods compare well to existing approaches

a five element basis for the uncountable linear orders in this paper i will show that it is relatively consistent with the usual axioms of mathematics zfc together with a strong form of the axiom of infinity the existence of a supercompact cardinal that the class of uncountable linear orders has a five element basis in fact such a basis follows from the proper forcing axiom a strong form of the baire category theorem the elements are x o1 o 1 c c where x is any suborder of the reals of cardinality 1 and c is any countryman line this confirms a longstanding conjecture of shelah

asymptotically efficient parameter estimation using quantized output observations this paper studies identification of systems in which only quantized output observations are available an identification algorithm for system gains is introduced that employs empirical measures from multiple sensor thresholds and optimizes their convex combinations strong convergence of the algorithm is first derived the algorithm is then extended to a scenario of system identification with communication constraints in which the sensor output is transmitted through a noisy communication channel and observed after transmission the main results of this paper demonstrate that these algorithms achieve the cramer rao lower bounds asymptotically and hence are asymptotically efficient algorithms furthermore under some mild regularity conditions these optimal algorithms achieve error bounds that approach optimal error bounds of linear sensors when the number of thresholds becomes large these results are further extended to finite impulse response and rational transfer function models when the inputs are designed to be periodic and full rank

multiply robust causal inference with double negative control adjustment for categorical unmeasured confounding unmeasured confounding is a threat to causal inference in observational studies in recent years the use of negative controls to mitigate unmeasured confounding has gained increasing recognition and popularity negative controls have a long standing tradition in laboratory sciences and epidemiology to rule out non causal explanations although they have been used primarily for bias detection recently miao and colleagues have described sufficient conditions under which a pair of negative control exposure and outcome variables can be used to identify non parametrically the average treatment effect ate from observational data subject to uncontrolled confounding we establish non parametric identification of the ate under weaker conditions in the case of categorical unmeasured confounding and negative control variables we also provide a general semiparametric framework for obtaining inferences about the ate while leveraging information about a possibly large number of measured covariates in particular we derive the semiparametric efficiency bound in the non parametric model and we propose multiply robust and locally efficient estimators when non parametric estimation may not be feasible we assess the finite sample performance of our methods in extensive simulation studies finally we illustrate our methods with an application to the post licensure surveillance of vaccine safety among children

a stagewise rejective multiple test procedure based on a modified bonferroni test summary simes 1986 has proposed a modified bonferroni procedure for the test of an overall hypothesis which is the combination of n individual hypotheses in contrast to the classical bonferroni procedure it is not obvious how statements about individual hypotheses are to be made for this procedure in the present paper a multiple test procedure allowing statements on individual hypotheses is proposed it is based on the principle of closed test procedures marcus peritz gabriel 1976 and controls the multiple level a

almost sure convergence rates for system identification using binary quantized and regular sensors abstract this paper presents almost sure convergence rates for system identification under binary quantized and regular sensors to accommodate practical model complexity constraints the system under consideration is represented by a modeled part together with an unknown but bounded unmodeled dynamics under uncorrelated noise sequences identification errors with different sensor types are studied and tight error bounds are obtained without information or constraints on noise moment conditions the results are then extended to correlated noise sequences whose remote past and distant future are asymptotically independent in both cases almost sure error bounds of the laws of iterated logarithms type are derived

optimal algorithms theory for robust estimation and prediction this paper deals with the theory of optimal algorithms for problems which cannot be solved exactly the theory developed allows for the derivation of new and interesting results in parameter estimation and in time series prediction in situations where no reliable statistical hypothesis can be made on the functions and modeling errors involved but only a bound on them is known in particular the derivation of computationally simple optimal algorithms for these two problems is investigated the practical effectiveness of the algorithms obtained is illustrated by several numerical examples

asymptotically efficient identification of fir systems with quantized observations and general quantized inputs this paper introduces identification algorithms for finite impulse response systems under quantized output observations and general quantized inputs while asymptotically efficient algorithms for quantized identification under periodic inputs are available their counterpart under general inputs has encountered technical difficulties and evaded satisfactory resolutions under quantized inputs this paper resolves this issue with constructive solutions a two step algorithm is developed which demonstrates desired convergence properties including strong convergence mean square convergence convergence rates asymptotic normality and asymptotical efficiency in terms of the cramer rao lower bound some essential conditions on input excitation are derived that ensure identifiability and convergence it is shown that by a suitable selection of the algorithm s weighting matrix the estimates become asymptotically efficient the strong and mean square convergence rates are obtained optimal input design is given also the joint identification of noise distribution functions and system parameters is investigated numerical examples are included to illustrate the main results of this paper

recursive identification of fir systems with binary valued outputs and communication channels this paper investigates the recursive identification of the finite impulse response systems whose outputs are subject to both the binary valued quantization and the communication unreliability the discrete memoryless channel with packet losses and the additive white gaussian noise channel with time delay are considered a stochastic gradient type algorithm and a stochastic approximation type algorithm are respectively proposed to estimate the unknown system parameters under some mild conditions the algorithms can be proved to be convergent in the almost sure and mean square senses also the convergence rates are given numerical examples are included to illustrate the performance of the algorithms

optimal sparse singular value decomposition for high dimensional high order data in this article we consider the sparse tensor singular value decomposition which aims for dimension reduction on high dimensional high order data with certain sparsity structure a method named s

a solution to the l space problem received by the editors january 8 2005 2000 mathematics subject classification primary 54d20 54d65 03e02 03e75 secondary 54f15

persistent identification of time varying systems identification of time varying systems especially slowly time varying systems is of importance in the development of a comprehensive theory of adaptation the persistent identification measures employed in this paper capture a main characterization in such identification problems namely one input signal must be used for identification of all possible observation windows this paper establishes several essential features in persistent identification problems which highlight their potential utility in adaptation 1 they have computable upper and lower bounds for typical classes of prior uncertainty sets 2 any full rank n periodic signals are optimal and the simple least squares estimates are optimal identification algorithms 3 optimal probing inputs can be approximately generated in a closed loop configuration when the plant and the controller are slowly time varying and 4 n periodic signals are asymptotically optimal for slowly time varying systems the main results of this paper have been successfully combined with a certain slow h sup spl infin design to derive an adaptive stabilization scheme

quantized identification of arma systems with colored measurement noise this paper studies the identification of arma systems with colored measurement noises using finite level quantized observations compared with the case under colorless noises this problem is more challenging our approach is to jointly design an adaptive quantizer and a recursive estimator to identify system parameters specifically the quantizer uses the latest estimate to adjust its thresholds and the estimator is updated by using quantized observations to accommodate the temporal correlations of quantization errors and measurement noises we construct a second order statistics equivalent system from which the original arma system is identified the associated identifiability problem and convergence are analyzed as well finally numerical simulations are performed to demonstrate the effectiveness of the proposed algorithm

tracking and identification of regime switching systems using binary sensors this work is concerned with tracking and system identification for time varying parameters the parameters are markov chains and the observations are binary valued with noise corruption to overcome the difficulties due to the limited measurement information wonham type filters are developed first then based on the filters two popular estimators namely mean squares estimator msq and maximum posterior map estimator are constructed for the mean squares estimator we derive asymptotic normality in the sense of weak convergence and in the sense of strong approximation the asymptotic normality is then used to derive error bounds when the markov chain is infrequently switching we derive error bounds for map estimators when the markovian parameters are fast varying we show that the averaged behavior of the parameter process can be derived from the stationary measure of the markov chain and that can be estimated using empirical measures upper and lower error bounds on estimation errors are also established

invariance principles for mixing sequences of random variables in this note we prove weak invariance principles for some classes of mixing sequences of l 2 integrable random variables under the condition that the variance of the sum of n random variables is asymptotic to sigma 2n where sigma 2 0 one of the results is simultaneously an extension to nonstationary case of a theorem of ibragimov and an improvement of the varphi mixing rate used by mcleish in his invariance principle for nonstationary varphi mixing sequences

controlling the false discovery rate a practical and powerful approach to multiple testing summary the common approach to the multiplicity problem calls for controlling the familywise error rate fwer this approach though has faults and we point out a few a different approach to problems of multiple significance testing is presented it calls for controlling the expected proportion of falsely rejected hypotheses the false discovery rate this error rate is equivalent to the fwer when all hypotheses are true but is smaller otherwise therefore in problems where the control of the false discovery rate rather than that of the fwer is desired there is potential for a gain in power a simple sequential bonferronitype procedure is proved to control the false discovery rate for independent test statistics and a simulation study shows that the gain in power is substantial the use of the new procedure and the appropriateness of the criterion are illustrated with examples

a sequentially rejective test procedure based on a modified bonferroni inequality summary a sharper bonferroni procedure for multiple tests of significance is derived this procedure is an improvement of hochberg s 1988 procedure which contrasts the individual p values with corresponding critical points it is shown that hochberg s original procedure is conservative and can be made more powerful by enlarging the rejection region so that the type one error is exactly at the nominal level it is also shown that the modified procedure retains all the desired properties of the original procedure

recursive identification of systems with binary valued outputs and with arma noises abstract this paper considers the identification problem of the arma system followed by a binary sensor in which the internal variables are corrupted by additive arma noises recursive estimates for the parameters of the linear system and for the threshold of the binary sensor are given by the stochastic approximation algorithms with expanding truncations saawet under reasonable conditions all the estimates are proved to be convergent to the true values with probability one the almost surely convergence rates are also investigated a simulation example is included to justify the theoretical results

closed loop persistent identification of linear systems with unmodeled dynamics and stochastic disturbances the essential issues of time complexity and probing signal selection are studied for persistent identification of linear time invariant systems in a closed loop setting by establishing both upper and lower bounds on identification accuracy as functions of the length of observation size of unmodeled dynamics and stochastic disturbances we demonstrate the inherent impact of unmodeled dynamics on identification accuracy reduction of time complexity by stochastic averaging on disturbances and probing capability of full rank periodic signals for closed loop persistent identification these findings indicate that the mixed formulation in which deterministic uncertainty of system dynamics is blended with random disturbances is beneficial to reduction of identification complexity