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Akaike Information Criterion Pdf Free

 

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R.,,,References[edit].,,Claeskens,,G.;,Hjort,,N.,Akaike,,,,H.,,,AIC,,does,,not,,provide,,a,,test,,of,,a,,model,,in,,the,,sense,,of,,testing,,a,,null,,hypothesis;,,i.e.,,How,to,apply,AIC,in,practice[edit].,Software,unreliability[edit].,v,,t,,e,,Statistics,,Outline,,Index,,,,Descriptive,,statistics,,Continuous,,data,,Center,,Mean,,arithmetic,,geometric,,harmonic,,Median,,Mode,,Dispersion,,Variance,,Standard,,deviation,,Coefficient,,of,,variation,,Percentile,,Range,,Interquartile,,range,,Shape,,Moments,,Skewness,,Kurtosis,,L-moments,,Count,,data,,Index,,of,,dispersion,,Summary,,tables,,Grouped,,data,,Frequency,,distribution,,Contingency,,table,,Dependence,,Pearson,,product-moment,,correlation,,Rank,,correlation,,Spearman's,,rho,,Kendall's,,tau,,Partial,,correlation,,Scatter,,plot,,Graphics,,Bar,,chart,,Biplot,,Box,,plot,,Control,,chart,,Correlogram,,Fan,,chart,,Forest,,plot,,Histogram,,Pie,,chart,,QQ,,plot,,Run,,chart,,Scatter,,plot,,Stem-and-leaf,,display,,Radar,,chart,,,,Data,,collection,,Study,,design,,Population,,Statistic,,Effect,,size,,Statistical,,power,,Sample,,size,,determination,,Missing,,data,,Survey,,methodology,,Sampling,,Standard,,error,,stratified,,cluster,,Opinion,,poll,,Questionnaire,,Controlled,,experiments,,Design,,control,,optimal,,Controlled,,trial,,Randomized,,Random,,assignment,,Replication,,Blocking,,Interaction,,Factorial,,experiment,,Uncontrolled,,studies,,Observational,,study,,Natural,,experiment,,Quasi-experiment,,,,Statistical,,inference,,Statistical,,theory,,Population,,Statistic,,Probability,,distribution,,Sampling,,distribution,,Order,,statistic,,Empirical,,distribution,,Density,,estimation,,Statistical,,model,,Lp,,space,,Parameter,,location,,scale,,shape,,Parametric,,family,,Likelihood(monotone),,Location-scale,,family,,Exponential,,family,,Completeness,,Sufficiency,,Statistical,,functional,,Bootstrap,,U,,V,,Optimal,,decision,,loss,,function,,Efficiency,,Statistical,,distance,,divergence,,Asymptotics,,Robustness,,Frequentist,,inference,,Point,,estimation,,Estimating,,equations,,Maximum,,likelihood,,Method,,of,,moments,,M-estimator,,Minimum,,distance,,Unbiased,,estimators,,Mean-unbiased,,minimum-variance,,RaoBlackwellization,,LehmannScheff,,theorem,,Median,,unbiased,,Plug-in,,Interval,,estimation,,Confidence,,interval,,Pivot,,Likelihood,,interval,,Prediction,,interval,,Tolerance,,interval,,Resampling,,Bootstrap,,Jackknife,,Testing,,hypotheses,,1-,,&,,2-tails,,Power,,Uniformly,,most,,powerful,,test,,Permutation,,test,,Randomization,,test,,Multiple,,comparisons,,Parametric,,tests,,Likelihood-ratio,,Wald,,Score,,Specific,,tests,,Z,,(normal),,Student's,,t-test,,F,,Goodness,,of,,fit,,Chi-squared,,KolmogorovSmirnov,,AndersonDarling,,Normality,,(ShapiroWilk),,Likelihood-ratio,,test,,Model,,selection,,Cross,,validation,,AIC,,BIC,,Rank,,statistics,,Sign,,Sample,,median,,Signed,,rank,,(Wilcoxon),,HodgesLehmann,,estimator,,Rank,,sum,,(MannWhitney),,Nonparametric,,anova,,1-way,,(KruskalWallis),,2-way,,(Friedman),,Ordered,,alternative,,(JonckheereTerpstra),,Bayesian,,inference,,Bayesian,,probability,,prior,,posterior,,Credible,,interval,,Bayes,,factor,,Bayesian,,estimator,,Maximum,,posterior,,estimator,,,,Correlation,,Regression,,analysis,,Correlation,,Pearson,,productmoment,,Partial,,correlation,,Confounding,,variable,,Coefficient,,of,,determination,,Regression,,analysis,,Errors,,and,,residuals,,Regression,,model,,validation,,Mixed,,effects,,models,,Simultaneous,,equations,,models,,Multivariate,,adaptive,,regression,,splines,,(MARS),,Linear,,regression,,Simple,,linear,,regression,,Ordinary,,least,,squares,,General,,linear,,model,,Bayesian,,regression,,Non-standard,,predictors,,Nonlinear,,regression,,Nonparametric,,Semiparametric,,Isotonic,,Robust,,Heteroscedasticity,,Homoscedasticity,,Generalized,,linear,,model,,Exponential,,families,,Logistic,,(Bernoulli)/,,Binomial/,,Poisson,,regressions,,Partition,,of,,variance,,Analysis,,of,,variance,,(ANOVA,,,anova),,Analysis,,of,,covariance,,Multivariate,,ANOVA,,Degrees,,of,,freedom,,,,Categorical/,,Multivariate/,,Time-series/,,Survival,,analysis,,Categorical,,Cohen's,,kappa,,Contingency,,table,,Graphical,,model,,Log-linear,,model,,McNemar's,,test,,Multivariate,,Regression,,Anova,,Principal,,components,,Canonical,,correlation,,Discriminant,,analysis,,Cluster,,analysis,,Classification,,Structural,,equation,,model,,Factor,,analysis,,Multivariate,,distributions,,Elliptical,,distributions,,Normal,,Time-series,,General,,Decomposition,,Trend,,Stationarity,,Seasonal,,adjustment,,Exponential,,smoothing,,Cointegration,,Structural,,break,,Granger,,causality,,Specific,,tests,,DickeyFuller,,Johansen,,Q-statistic,,(LjungBox),,DurbinWatson,,BreuschGodfrey,,Time,,domain,,Autocorrelation,,(ACF),,partial,,(PACF),,Cross-correlation,,(XCF),,ARMA,,model,,ARIMA,,model,,(BoxJenkins),,Autoregressive,,conditional,,heteroskedasticity,,(ARCH),,Vector,,autoregression,,(VAR),,Frequency,,domain,,Spectral,,density,,estimation,,Fourier,,analysis,,Wavelet,,Survival,,Survival,,function,,KaplanMeier,,estimator,,(product,,limit),,Proportional,,hazards,,models,,Accelerated,,failure,,time,,(AFT),,model,,First,,hitting,,time,,Hazard,,function,,NelsonAalen,,estimator,,Test,,Log-rank,,test,,,,Applications,,Biostatistics,,Bioinformatics,,Clinical,,trials/,,studies,,Epidemiology,,Medical,,statistics,,Engineering,,statistics,,Chemometrics,,Methods,,engineering,,Probabilistic,,design,,Process/,,quality,,control,,Reliability,,System,,identification,,Social,,statistics,,Actuarial,,science,,Census,,Crime,,statistics,,Demography,,Econometrics,,National,,accounts,,Official,,statistics,,Population,,statistics,,Psychometrics,,Spatial,,statistics,,Cartography,,Environmental,,statistics,,Geographic,,information,,system,,Geostatistics,,Kriging,,Category,,Portal,,Commons,,WikiProject,,.,,Additionally,,,they,,present,,a,,few,,simulation,,studies,,that,,suggest,,AICc,,tends,,to,,have,,practical/performance,,advantages,,over,,BIC.,,(2008),,,,Information,,,Criteria,,,and,,,Statistical,,,Modeling,,,,Springer.,,,(1976),,,"",,[Distribution,,of,,informational,,statistics,,and,,a,,criterion,,of,,model,,fitting],,,Suri-Kagaku,,[Mathematical,,Sciences],,(in,,Japanese),,,153:,,1218.,,That,instigated,the,work,of,Hurvich,&,Tsai,(1989),,and,several,further,papers,by,the,same,authors,,which,extended,the,situations,in,which,AICc,could,be,applied.,

 

Akaike,,originally,,called,,his,,approach,,an,,"entropy,,maximization,,principle",,,because,,the,,approach,,is,,founded,,on,,the,,concept,,of,,entropy,,in,,information,,theory.,,In,,general,,,however,,,the,,constant,,term,,needs,,to,,be,,included,,in,,the,,log-likelihood,,function.[15],,Hence,,,before,,using,,software,,to,,calculate,,AIC,,,it,,is,,generally,,good,,practice,,to,,run,,some,,simple,,tests,,on,,the,,software,,,to,,ensure,,that,,the,,function,,values,,are,,correct.,,For,,,more,,,on,,,these,,,issues,,,,see,,,Akaike,,,(1985),,,and,,,Burnham,,,&,,,Anderson,,,(2002,,,,ch.2).,,,Using,,AIC,,,instead,,of,,AICc,,,when,,n,,is,,not,,many,,times,,larger,,than,,k2,,,increases,,the,,probability,,of,,selecting,,models,,that,,have,,too,,many,,parameters,,,i.e.,,R.,,Leave-one-out,,,cross-validation,,,is,,,asymptotically,,,equivalent,,,to,,,the,,,AIC,,,,for,,,ordinary,,,linear,,,regression,,,models.[17],,,Such,,,asymptotic,,,equivalence,,,also,,,holds,,,for,,,mixed-effects,,,models.[18].,,,(2014).,,If,all,the,candidate,models,fit,poorly,,AIC,will,not,give,any,warning,of,that.,Denote,,the,,AIC,,values,,of,,those,,models,,by,,AIC1,,,AIC2,,,AIC3,,,,,,AICR.,,(1998),,,,Selected,,,Papers,,,of,,,Hirotugu,,,Akaike,,,,Springer,,,,doi:10.1007/978-1-4612-1694-0.,,, 6704223018

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